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UNIVERSITA DEGLI STUDI DI CÁMERINO

FACOLTÁ DI SCIENZE E TECNOLOGIE

Corso di Laurea Specialistica in Fisica

Classe LM-17

Dipartimento di Fisica

Vortex dynamics in the HTSC iron pnictide SmFeAsO0.85F0.15

TESI DI LAUREA SPERIMENTALE IN

STRUTTURA DELLA MATERIA

Relatore:

Prof. Roberto Gunnella

Dr. Augusto.Marcelli, Dr. Daniele Di Gioacchino

Candidato:

Buerhan Shalamu

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contents

Abstract ................................................................................................................................... 4

Introduction ............................................................................................................................ 6

Chapter 1 ................................................................................................................................. 9

High temperature superconductors ......................................................................................... 9

1.1 Superconductivity and high-temperature superconductors ........................................................ 9

1.2 Superconductors in a magnetic field ....................................................................................... 10

1.2.1 Conventional type-II superconductors ............................................................................ 10

1.2.2 High-Tc superconductors ............................................................................................... 12

1.2.3 Vortex glass ................................................................................................................... 14

1.2.4 The irreversibility line .................................................................................................... 15

1.3 Magnetic susceptibility .......................................................................................................... 16

1.4 Application of HTCS ............................................................................................................. 20

Chapter 2 ............................................................................................................................... 22

Iron-pnictides superconductors (Fe-HTSC) .......................................................................... 22

2.1 SmFeAsO1-xFx ....................................................................................................................... 24

Chapter 3 ............................................................................................................................... 27

Experimental set-up and susceptibility measurements ........................................................... 27

3.1 AC gradiometer ..................................................................................................................... 27

3.1.1 INFN – LNF susceptometer ........................................................................................... 27

3.1.2 Lock-in amplifer ............................................................................................................ 29

Chapter 4 ............................................................................................................................... 31

AC-multi-harmonic magnetic susceptibility analysis ............................................................. 31

4.1 Summary ............................................................................................................................... 31

4.2 First harmonic susceptibility measurements ........................................................................... 32

4.3 Third harmonic susceptibility measurements .......................................................................... 36

4.4 Irreversibility line, liquid phase and vortex phase ................................................................... 41

4.5 Flux pinning dimensional analysis and the glass temperature ................................................. 44

4.6 Non-linear diffusivity ............................................................................................................ 48

Chapter 5 ............................................................................................................................... 51

Conclusion ............................................................................................................................ 51

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Acknowledgements ................................................................................................................ 54

Bibliography .......................................................................................................................... 55

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Abstract

In this work we present an investigation of the vortex flux dynamics of high temperature superconductor sample: SmFeAsO0.85F0.15, by measuring AC multi-harmonics χac as a function of temperature, magnetic field and frequency. Experiments have been performed in zero field cooling (ZFC) condition with an AC applied field (9.8 Gauss) at different frequencies from 107 Hz to 1070 Hz and with a DC magnetic field of 0T and 1T. Information on the magnetic susceptibility χac are fundamental to know the superconducting dynamic state response. In fact the real part of the first harmonic (χ’1) probes the diamagnetic behavior of the sample while the imaginary part (χ’’1) is a measure of the energy dissipation inside the sample in one cycle of the AC field. In addition, the real part (χ’3) and the imaginary (χ’’3) components of the third harmonic give unique information on the non-linear vortex response of the investigated sample.

This study shows that the SmFeAsO0.85F0.15 sample has a transition temperature of 50 K and 48~49 K at BDC=0 T and 1 T, respectively. Moreover, the sample exhibits with and without DC applied field a granular structure with both an intra-grain and an inter-grain response. Regarding the vortex flux dynamics, the analysis of the onsets of the imaginary part of the first harmonic (χ’’1) and the module of the third harmonic χ3 indicate that, due to the free flux motion the normal losses that limit the super-current, with the application of an external DC field of 1 T. increase the temperature regions of the free flux motion

The |χ3| onset defines the point where the system undergoes the transition from a vortex liquid state to an initial irreversible superconducting critical state, that evolve in a final vortex glass phase at a vortex glass temperature Tg. A slow down dynamics is expected near Tg with a power law divergence of the relaxation time τ ~ (|T-Tg|)

-vz, so that only below the irreversibility line (IL) of the process a high critical current can flow as a result of the flux pinning processes. The IL behavior of both the inter-grain and the intra-grain onsets of this sample shows a 3D bulk pinning both at 0 and 1 T. The experimental Cole-Cole polar plot, i.e., the graph of χ’3 vs. χ’’3,

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shows a flux dynamics almost independent by the frequency in the range 307~1070 Hz at 0 T moving from an ideal critical state towards a true vortex glass state at low frequency. In the time window defined by the experiments performed, the established final glass state is close to the initial critical state. The result points out that this sample has good pinning characteristics and may carry out a high critical current.

This research shows that the SmFeAsO0.85F0.15 sample has good superconductor characteristics. It exhibits also strong 3D pinning properties that may sustain a high current with an almost negligible dissipation.

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Introduction

The discovery of superconductivity in mercury in 1911 [Kamerlingh et al., 1911] opened a new fascinating research area. Although a huge number of advancements have been obtained during a century, the field is still growing, offering at present many opportunities and foreseen applications.

Superconducting (SC) materials have very interesting physical properties and useful applications at the temperature below their critical temperature (Tc). Superconductors can be used for zero-loss power transmission cable [Fossheim, 2004] or to produce large current capacity wires to generate large magnetic fields. Their diamagnetic behavior made possible the dream to see running in the real word magnetic levitation trains. However, the main drawback of real applications of superconductor materials is the need to cooled at the liquid helium temperature to sustain the superconducting state. The high cost of cryogenic systems is indeed the major obstacle to wider applications of superconducting materials in research and many industrial areas.

Actually, in 1986 after the discovery of the first layered high-temperature superconductor (HTSC) materials [Bednorz et al., 1986], with critical temperatures above the temperature of the liquid nitrogen, e.g., the YBaCu2O6+x, this scenario has been completely changed. At that time, it was thought that high temperature superconductors HTSC materials couldn’t be achieved at such high temperatures, and the big surprise was also that these superconductor materials were poor conductors at room temperature. When a magnetic field is applied to superconductor, the magnetic field cannot penetrate inside the material. They create a current that screen out the magnetic field, a mechanism well known as the Meissner effect. The expulsion of the magnetic field originates a supercurrent inside superconductor materials. Regarding this mechanism, superconductors can be divided in two classes: type I and type II superconductors. Type I superconductors will completely screen out external magnetic fields [Meissner et al., 1933] until the magnetic field becomes too large for the material to remain superconducting.

On the contrary, in type II superconductors the magnetic flux may penetrate inside the sample in its mixed normal-superconducting state. In these materials, above a critical field (Hc1) the magnetic field penetrates in quantized non-superconducting regions known as vortex cores. These are regions where super-electrons move in a vortex motion around the core

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screening the rest of the material from the magnetic field present in the core. In other words, the magnetic field penetrates in the superconductor as thin threads of material that return to a normal non-superconducting state. These threads, called fluxons, carry a quantized magnetic flux. The flux motion is the main problem of superconductivity and it is more amplified in layered HTSC. Its understanding is fundamental for applications. Under a magnetic field vortices move due to the Lorentz force through the whole sample. The magnetic vortices motions are of interest because they destroy with the electrical free flow resistance, the superconducting state. A moving vortex produces itself a variation in time of the magnetic field, which, by applying the right hand rule, will induce an electric field in opposition to the driving field, generating a resistance. Thus, when one attempts to use a superconductor in the presence of a magnetic field, a resistance in the material is induced and also a energy dissipation occurs inside the sample.

All real materials have always imperfections, structural faults, and vacancies. These inhomogeneities give local changes of the free energy superconducting state and represent potential wells for the fluxons, so that they cannot move inside the sample, but are trapped by specific wells called pinning centers. In this way a material may carry out a high current without dissipation. The analysis of pinning potential and force is the way to understand and eventually improve the properties of a superconducting material and increase its current flow.

Actually, there are no ideal superconductors, and in particular all known high-temperature superconductors are type II superconductors. The dynamics of vortex is not simple and, this motion strongly correlated to temperature, applied magnetic field, and field frequency or current is very complex. In the field-current-temperature phase space, a superconducting material can be found in three different phases: a Meissner phase, a glass vortex and a liquid vortex phase. The magnetic AC multi-harmonic susceptibility is a powerful technique that may exploit these phases returning several physical information about the magnetic materials, for instance, the superconducting critical temperature, the vortex phase region, the superconducting critical current, all under a non contact experimental conditions.

Iron-based superconductors are the family of the second highest critical temperature behind HTSC Cuprates. They contain layers of iron and pnictogen or chalcogens, and are poor metals at temperature higher than superconducting critical temperature Tc. These new high temperature superconductors are type II superconductors too.

In this work we investigated the SmFeAsO0.85F0.15, a member of iron-based high temperature superconductor family. As written above, because the driving force depends by the magnetic field strength, the latter strongly

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affects superconducting critical temperatures and vortex motions. Meanwhile, hysteretic motions of the vortex depend on driving field frequency. In order to investigate in the SmFeAsO0.85F0.15the motion of vortex in the different phase region we studied the fundamental and the higher harmonic susceptibility at different frequencies changing also the magnetic field.

The thesis is organized as follows, in chapter 1 a general introduction to superconductivity and conventional type I and type II superconductors, is given. In the next the magnetic behavior of type II superconductors is discussed. Because the vortex line motion with an external magnetic field has both a linear and non-linear response, the different phase spaces of HTSC materials vs. field and temperature will be discussed. In chapter 2 experimental achievements of the SmFeAsO1-xFx compound will be presented and discussed. In chapter 3 we describe the experimental setup available at the National Laboratories in Frascati (LNF) of the INFN: the AC multi-harmonic susceptometer, and the measurement procedure I used in this work. In chapter 4 is presented the analysis of the data of the SmFeAsO0.85F0.15: critical temperature, dynamical region, dimensionality of the pinning interaction and comparison of pinning strengths among different superconductors. Finally, in a summary of the obtained results is given.

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Chapter 1

High temperature superconductors

1.1 Superconductivity and high-temperature superconductors

In 1911, Kamerlingh Onnes and coworkers [Kamerlingh et al., 1911] found that mercury abruptly looses all of its electrical resistivity when cooled below a temperature of 4.2 K. This observation marks the discovery of the phenomenon of superconductivity, and opened up a completely new field of research in physics. During the following half century, a slow but continuous progress occurred. New phenomena, related to superconductivity, were discovered, theory was developed, and materials, having a higher superconducting transition temperature, were produced. Important landmarks are the discovery of the Meissner effect in 1933 [Meissner et al., 1933], and the completion of the microscopic theory by Bardeen, Cooper, and Schrieffer (BCS) in 1957 [Bardeen et al., 1957]. The BCS theory gives a limit for the transition temperature. In 1985, the record of transition temperatures stood at 23 K for the intermetallic Nb2Ge [Gavaler, 1993], which is near the maximum to be expected for metallic systems. In 1986, after a systematic search, Bednorz and Muller [Bednorz et al., 1986] discovered that the layered copper-oxide material La2-xBaxCu04-δ turns superconducting at temperatures above 30 K. The parent compounds of superconducting Cuprates are antiferromagnetic Mott insulators; when they are slightly doped by holes or electrons, they show a superconducting phase. The Cuprates are the only Mott insulators known to become superconducting. This breakthrough gave research in superconductivity a gigantic new momentum, and quickly led to devising a whole new generation of Cuprate superconductors. The most popular of these new superconductors has been the YBa2Cu307-δ (The crystal structure of this material showed in figure 1-1. From Ref. [Beyers et al., 1989]) because it has been the first copper-oxide material discovered to be superconducting above the boiling point of liquid nitrogen Tc = 92 K [Wu et al., 1987]. Moreover the transition temperatures as high as 133 K [Schilling et al., 1993], and under hydrostatic pressure 153 K [Chu et al. 1993], have been reported. Even higher Tc's seem within reach, which would make potential applications of superconductivity economical on account of the reduced

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costs for coolants. Equally important is that the intensive research of the new superconductors has led to a wave of new phenomena of fundamental interest to the physics of the solid state. As a result of their planar structure, the Cuprate superconductors are highly anisotropic.

The high-Tc superconductors placed in a magnetic field exhibit a very peculiar behavior. Conventional superconductors abruptly enter the superconducting phase irrespective of an external magnetic field, and this also holds true for HTSC superconductors in zero magnetic fields. In an applied magnetic field, however, the resistivity of high-Tc superconductors vanishes only gradually with decreasing temperature.

Figure 1-1 Crystal structure of YBa2Cu3O7-δ.

1.2 Superconductors in a magnetic field

1.2.1 Conventional type-II superconductors

Before turning to the puzzling behavior of the high-Tc materials in a magnetic field, we first consider the behavior of conventional type-II superconductors. Superconductivity in conventional superconductors originates from a collective pairing of the electric charge carriers into Cooper pairs, as is conclusively established on a microscopic basis by the BCS theory [Bardeen et al., 1957]. For most macroscopic problems,

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however, a treatment in terms of the BCS theory quickly becomes too complicated to handle. Instead, one resorts to an adequate macroscopic approximation, such as provided by the Ginzburg-Landau theory [Ginzburg et al., 1950]. This theory describes superconductivity in terms of a superconducting wave function, ψ, and studies the variations of the latter in time and space. The wave function can be written as ψ = |ψ|eiϕ, where ψ2 is the density of the superconducting Cooper pairs, and ϕ is a phase. Generally, both ψ and ϕ will vary in space and time. The standard magnetic field-temperature (H-T) phase diagram for a conventional type-II superconductor is shown in Fig. 1-2(a).

Figure 1-2 (a) Standard magnetic phase diagram of a conventional type-II superconductor, consisting of the normal, the vortex-lattice, and the Meissner phase. (b) Magnetic phase diagram of a typical high-Tc, superconductor, such as YBa2Cu3O7-δ. The vortex-lattice phase has disappeared, but instead, two new phases have emerged: the vortex-liquid

phase and the vortex-glass phase.

In this phase diagram three phases may be distinguished: (i) In the normal phase above the upper critical field Hc2(T), the superconductor behaves as a normal metal; (ii) Below the lower critical field Hcl (T), the superconductor is in the Meissner phase, i.e.. the magnetic field is totally expelled from the interior of the superconductor: (iii) In between Hcl(T) and Hc2(T), the magnetic field penetrates the superconductor non-uniformly, in the form of tubes of quantized magnetic flux. These flux lines, or vortices, each carry exactly one magnetic flux quantum Φ0 = hc/2e. The magnetic field in the vortex is screened from the rest of the superconductor by a local supercurrent, circulating around the vortex, and giving it its name screening

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current. Because of this current the phase ϕ of the superconducting wave function changes by 2π on completing a full circle around the vortex, no matter at what distance. Two length scales characterize the cross section of a vortex: (i) the coherence length ξ of the superconducting wave function. This length is a measure of the radius of the vortex core area, where superconductivity is significantly suppressed; (ii) the London penetration depth λ, which is the radius of the area around the vortex core in which the magnetic field penetrates. The defining property of a type-II superconductor is that the coherence length ξ is smaller than the London penetration depth λ. In particular, µ0Hc2=Φ0 /2πξ

2 (1.1) Because of the repulsive interaction between the vortices, the latter tend to order in a triangular lattice, the Abrikosov lattice [Abrikosov et al., 1950]. Such a lattice has two kinds of long-range order: (i) Long-range translational order, such as present in crystal lattices; (ii) Long-range order in the phase ϕ of the superconducting wave function ψ, reflecting the ordering of the vortices on their equilibrium positions. Resistivity in superconductors in a magnetic field is a consequence of motion of the vortices. An applied current exerts a Lorentz force on a vortex, pushing it across the current, and thereby causing resistance and dissipation.

It may be noted that an ideal type-II superconductor is not superconducting in the vortex-lattice mixed state, because an applied current density will induce a flow of the whole vortex lattice (flux flow motion). This, in turn, generates a voltage along the current, i.e., the superconductor has a finite resistivity, Real superconductors, however, always contain imperfections in the crystal lattice, which tend to pin the vortices. Because of this pinning, vortex motion is inhibited and superconductivity is restored.

1.2.2 High-Tc superconductors

High-Tc superconductors display a very different behavior in a magnetic field. This is caused by the increased influence of fluctuations and disorder. The enhanced influence of fluctuations is caused by the fact that, on one hand, the energies to create and move vortices are lower, and, on the other hand, the temperatures are higher. The reduced energy finds its origin in the very small coherence length ξ (~ 10 Å) as compared to the London penetration depth λ (~ 103 Å). The energy for creation and movement of vortices is further reduced by the quasi-two-dimensional structure of these

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materials. As a result, the magnetic phase diagram is drastically different from the phase diagram of conventional type-II superconductors (See Fig.1-2(b)). The thermal fluctuations make the vortex lattice melt into a vortex liquid at "high" temperatures. In the liquid phase the vortices move around like the molecules in a liquid. There is no present any kind long-range order. The vortex-liquid phase is associated with a finite resistance like flux flow motion, and consequently it is not really superconducting. This also implies that the transition from the normal to the vortex-liquid phase at Hc2(T) is no longer a thermodynamic phase transition but a smooth crossover. Equally important for the altered magnetic phase diagram is the presence of disorder. Larkin [Larkin et al., 1970] showed that, even in the presence of weak pinning, the long-range translational order of the Abrikosov vortex lattice is destroyed beyond a certain length scale lL, which may be very long for clean superconductors.

Conventional theories of vortex structure in a disordered superconductor where the flux pinning is present are based on the critical state model Bean [Bean, 1964], where given a maximum available pinning force density αc, the condition for a zero dissipation is that the Lorenz force density never exceeds αc:

cc

BJ αα ≤×=

rrr (1.2)

the critical state can be then defined by

cc

BJ α=×

rr

(1.3)

The vortex motion has been proposed by Anderson and Kim [Anderson et al., 1964]. In this picture, thermally activated bundles of vortices of finite size jump independently over barriers of height U in a pinning potential landscape (creep model). Because of the finite size of these bundles, the height U of the barriers for these bundles is finite. Under an applied current - no matter how small - the vortex bundles will start moving, causing a finite resistivity: ρcreep ≈ exp(-U(B,T,J)/kBT) (1.4)

According to this picture, low temperature conventional superconductors would not be really superconducting in a magnetic field. However, U/kBT

usually is so large that the resistivity is immeasurably small for all practical

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purposes. In the high-Tc materials, on the other hand, U/kBT is not large, and therefore this simple picture of breaks down.

1.2.3 Vortex glass

In 1989, Fisher [Fisher, 1989] [Fisher et al., 1991] argued that, although the translational order of the vortex lattice is destroyed in the presence of random disorder, a new phase will arise at low temperatures. In this new phase, named the vortex glass, the vortices are fixed in random pattern, the details of which are determined by the sample-specific competition between vortex-vortex and vortex-lattice interactions. Although the pattern of the vortices has no long-range positional order, underlying this pattern is a long-range order in the phase of the superconducting wave function, which is associated with the fact that the vortices are immobile, i.e., the vortex-glass phase is a really superconducting ground state. To better comprehend the nature of the order parameter in the vortex glass phase, it is useful to consider the analogy between the various ordered phases of type-II superconductors and systems of magnetic spins (figure. 1-3). In this analogy, the gradient of the phase ϕ of the superconducting wave function plays the role of the spin orientation.

Figure 1-3 Comparison between various types of order in systems of magnetic spins and superconducting systems. For the magnetic systems, the arrows denote the directions of the local spins. For the superconducting system, the arrows denote the gradient of the

phase of the superconducting wave function. The vortices are denoted by the dots in the center of each circling arrow. On the extreme right. next to the vortex lattice and the vortex glass, are images of vortex-patterns obtained by decorating the surface of a

superconductor with magnetic particles that preferentially stick near vortices. [Huse et al., 1992]

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The analogue of the Meissner phase is the ferromagnet: both phases

are described by simple homogeneous wave functions. The magnetic equivalent of a vortex lattice is an antiferromagnet. In both these cases, the wave functions have a more complicated spatial structure, but possess long-range translational order, such as associated with the crystal lattice in a solid. Additionally, there is a more subtle long-range order in the phase ϕ of the superconducting wave function, which reflects the ordering in a lattice. The vortex-glass phase order is directly analogous to the order in the spin-glass phase: both phases have no apparent long-range order, however do possess an underlying order in the phase of their wave functions, which is associated with the fact that all spins or vortices are frozen onto their positions. Finally, the disordered vortex-fluid liquid phase at high temperatures has its magnetic analogue in the paramagnet. Both of these systems lack any long-range phase order. In the vortex-glass model the dissipation in the presence of an applied current is connected to a critical length, corresponding to a barrier height, U. It can be argued to scale with the current density J as U ≈ 1/Jµ

, which leads to an activated behavior of the resistivity according to ρcreep glass : exp(-U/kBT)≈exp[-(J0/J)

µ] (1.4) Where J0 is a temperature-dependent proportionality constant and µ is a constant. Thus, in the limit of zero current, the resistivity is indeed zero and the vortex glass is truly superconducting.

1.2.4 The irreversibility line

It is possible to define the ‘irreversibility’ line Tg (H) [Malozemoff et al., 1988] [Malozemoff et al., 1989], i.e. a line below which irreversibility in the magnetization sets in, as a result of flux pinning. This line marks the transition from the vortex glass phase where the flux lines are sufficiently strongly pinned that they are characterized by a non-linear response to the Lorenz force and no dissipation occurs, to the vortex liquid phase where the thermal activation allows unpinning of the flux lines within the time scale of the experiment (Fig. 1.2b) [Fisher, 1989] [Huse et al., 1992] [Nelson et al., 1989]. It can be described by a critical parameter in which the dimensionality D of the pinning-flux array interaction is present and depends by the amplitude of the magnetic field, the temperature and the critical current density [Huse et al., 1992]. The frequency dependence of the irreversible temperature Tg may be interpreted in the framework of the

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vortex glass phase transition model. For a second-order phase transition near the vortex glass phase-transition temperature Tg, a power-law divergence of the correlation length ξ ≈ |T-Tg|

-v characterized by a critical exponent v is observed. A critical slowing down of the dynamics near Tg, with a power-law divergence of the relaxation time τ ≈ |T-Tg|

-vz, where z is the dynamical critical exponent, is also expected. By inverting the latter relationship and inserting the system dimensionality D, we may deduce the frequency dependence of the irreversible temperature [Fisher et al., 1991] [Wolfus et al., 1994]: )2(/1)()(),( Dzv

gg fHAHTfHT −++= (1.5)

It is of practical importance to determine the irreversibility line, because high critical current densities can be supported only below this line.

1.3 Magnetic susceptibility

As is clear from previous chapters, in type-II superconductors a very important limitation to their use in technological applications is due to the dissipative normal losses phenomena associated with the vortex motion inside the sample. In order to improve both the fabrication process and the application perspectives of these materials, a crucial point is to investigate their flux pinning and vortex dynamics properties. Among the experimental techniques used in the past to investigate these issues, one of the most efficient is certainly the magnetic susceptibility [Ishida et al., 1990]. In general the magnetic susceptibility is a measure of a sample magnetization in reaction to a given applied magnetic field and it is defined as:

H

M=χ (1.6)

Where M is the magnetization and H is the applied magnetic field. The magnetic susceptibility can have positive and negative values, in particular paramagnetic, ferromagnetic or antiferromagnetic material shows positive response, while the diamagnetic substance have negative values.

In particular, DC magnetic measurements determine the equilibrium value of the magnetization in a sample. When a sample is magnetized by a constant magnetic field, its magnetic moment can be measured obtaining a DC magnetization curve M(H). The moment can be measured by a force, a torque or via induction techniques, the last being the most common in

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modern instruments. Moving the sample relatively to a set of pickup coils, either by mechanical vibration or by one-shot extraction, we perform an inductive measurement. In a conventional inductive magnetometer, one measures the voltage induced by the variation of the magnetic moment of the sample inside a set of copper pickup coils. A much more sensitive technique is based on a set of superconducting pickup coils and a SQUID that measure the current induced in the coils. This technique yields to a high sensitivity, independent from the sample speed during the extraction.

The best way to study the dynamic magnetic response of a material is the AC magnetic measurement, where a time-varying exciting magnetic field Hac induces a voltage in a bridge pick-up coil, proportional to the AC moment of the sample. AC magnetic experiments are an important characterization tool in material science. Indeed, because the induced sample moment is time-dependent, an AC measurement yields information about magnetization dynamics that is not obtained by a DC measurement, an experimental approach in which the sample moment remains constant during the measurement time. In an AC measure, the magnetization is periodically changing in response to an applied alternating field

( ) ( ) ( )i t

ac acH t H Im e H sin tω ω= = (1.7)

Where Hac is amplitude of the external magnetic field. The response of a superconductor is both linear and nonlinear [Shatz, et al., 1993][Jeffries, et al., 1989]. As a result the pure sinusoidal field induces non-sinusoidal oscillations of the magnetization M and local magnetic induction B. These oscillations may be described as sum of sinusoidal components at harmonics of the driving frequency

( ) ( ) ( ) ( )( )i n t ' "

ac n ac n nM t H Im e H sin n t cos n tωχ χ ω χ ω= ∑ = ∑ − (1.8)

Where χ’n and χ”n are defined as in and out-of phase components of harmonic susceptibilities. For n = 1 the corresponding harmonics are known as fundamental harmonic susceptibility, and they have clear physical meaning: χ’1 is the shielding from external magnetic field; χ”1 is the dissipation of the magnetic energy inside the sample. In the complex notation χ’n and χ”n are combined to form the complex harmonic susceptibility χn =χ’n -i χ”n. Clearly, full characterization of materials with nonlinear magnetic response requires measurement of fundamental and higher harmonic susceptibility (n = 1, 2....).

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χ’n and χ”n can be calculated by integrating both sides of equation (1.8) respect to t, and, using the orthogonal properties of sine and cosine functions, we get corresponding real and imaginary parts of AC harmonic susceptibility

2

'

0( )sin( )

n

ac

M t n t dtH

πωχ ω

π= ∫ (1.9)

2

''

0( )cos( )n

ac

M t n t dtH

πωχ ω

π−

= ∫ (1.10)

The magnetization M(t) can be expressed in terms of magnetic induction B

0

BM H

µ= − (1.11)

From equations (1.9), (1.10), (1.11) we can easily get

2

'1 0

0

( )sin( ) 1ac

B t t dtH

πωχ ω

πµ−

= −∫ (1.12)

2''

1 00

( )cos( )ac

B t t dtH

πωχ ω

πµ−

= ∫ (1.13)

We can see that χ’1 gives us expression for the amount of magnetic flux penetration into the sample. For a complete Meissner expulsion the integral in equation (1.12) vanishes and real part of first harmonics equal to -1 and for full flux penetration the integral is 1 and χ’1 = 0. Similarly, for completely superconducting state χ’’1 = 0, while in the mixed superconducting state χ’’1 < 1, positive number reflecting ac losses. The energy that is converted in the heat per each magnetization cycle magnetization, corresponding to ac losses per cycle, is determined by

2 ' ''

0 001

[ ( sin( ) cos( ))] cos( ) ( )n n

n

Q H n t n t H t d tπ

χ ω χ ω ω ω∞

=

= −∑∫ (1.14)

Then the losses are given by 2 "

0 1Q H πχ= − (1.15)

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The magnetic field energy inside the sample averaged over one cycle of magnetization is

2

'10

0 0

1( ) ( )

2

TacH

w H t M T dtT

χµ µ

= =∫ (1.16)

2

'1

0

( 1)2

acnormal

Hw w w χ

µ∆ = − = − (1.17)

Where w and normalw are the magnetic energy of the superconducting and normal state materials respectively. It is evident from equations (1.15) and (1.17) that the first harmonic imaginary component represents energy dissipation inside the sample while the first harmonic real component is related to external field screening.

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1.4 Application of HTCS

Due to their very low transition temperatures, the commercial applications of first discovered superconductors were mainly limited by the high cost of the liquid helium, the cryogenic liquid necessary to keep them superconducting. Increasing their critical temperature, new devices could be realized on the market at lower cost. They offer several improvements. As an example, the superconducting magnetic energy storage (SMES) devices [Ginzburg, 2004] offer the important advantage that the time delay between charge and discharge is quite short. Power is available almost instantaneously and very high power output can be provided for a brief period of time [Hul, 2003]. Other energy storage methods, such as pumped hydro or compressed air have a substantial time delay associated with the energy conversion of the stored mechanical energy back into electrical power. In addition, the loss is lower than that of other storage methods because currents encounter almost no resistance, moreover SMES devices have no movable components offering a high reliability. Magnetic separation is another potential application. In this process magnetic materials are extracted from a mixture using a magnetic force. We can use HTSCs as magnetic separators, being them able to sustain a high critical currents and the magnetic field strength being proportional to the current. The goal of industrial separation processes is to make use of strong fields in the mainstream of the production. Conventional electromagnet devices have fields not strong enough to separate iron from aluminum or to work with copper wastes.

Fault current limiters (FCL) [Lehndorff, 2001] are other superconductor devices. They are used to protect an electric network and equipments from damage caused by fault currents occurring when a circuit is shortened. In this case the power current flowing through a local circuit can rise enormously damaging the electrical equipment or some of its components. HTSC materials offer improved solution to this problem. Indeed, in a HTSC-based FCL device, if the current exceeds the superconducting critical current the material shows a normal resistance and effectively quenches the fault current amplitude.

Without doubts, the most important applications of high temperature superconductors, at present and in the near future are power transmission cables. Several companies already exist for the development and the production of superconducting cables. These materials already support larger currents and an improved power capacity compared to conventional cables.

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The most sensitive magnetic field sensors are superconducting quantum interface devices (SQUID) which are superconducting loops with integrated Josephson contacts [Hook, 1995]. The resolution of high temperature superconducting SQUID, operating at the liquid nitrogen temperature range, are almost the same of low temperature SQUID operating in liquid helium temperature. However, a large commercial application is only expected for HTS SQUID systems that are able to detect magnetic signals even in the presence of high background fields. Mobile non-shielded high temperature superconducting SQUIDs were tested with success in many biomedical non-destructive evaluations and geophysical applications [Narlikar, 2004].

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Chapter 2

Iron-pnictides superconductors (Fe-HTSC)

Since the discovery of new class of high temperature superconductors, the FeAs compounds [Kamihara et al., 2006], a great effort has been devoted by scientists all over the world to understand the mechanisms and details of HTSC materials. Substantial progresses have been already achieved, although the researches were mainly concentrated on cuprate systems. Indeed, while the superconducting properties of the conventional systems are well described by BCS theory [Kamihara et al., 2006], and also other superconductors such as MgB2, RbCS2C60, KC60, etc. do not fulfill this theory. After the discovery of FeAs compounds, all the ideas and methods applied to cuprates have been considered to investigate iron–based superconductors. These materials contain layers of iron and pnictogen, such as arsenic and phosphorus, or chalcogen, e.g. selenium and tellurium [Lzyumov, 2010].

The discovery of superconductivity in LaOFeAs was first reported in 2006, with the critical temperature of Tc=3.2 K [Kamihara et al., 2006]. Moreover in 2008 researchers of Tokyo institute of technology published a paper in which LaFeAsO fluorine doped materials exhibited superconducting transition at 26 K [Cimberle, et al., 2009]. After that the attention towards iron-based high temperature superconductors (Fe-HTSC) increased at fast rate. Soon a Chinese team reported an increased of the critical temperature up to 41 K, replacing lanthanum with cerium and later, the Tc rose to 43 K using samarium [Lzyumov, 2004]. Other FeAs phases were discovered in addition to the LaOFeAs systems (1111); the SrFe2As2 (122), the LiFeAs (111) and the Fe1+xCSe (11). These formulas indicate typical representatives elements of each class, while numbers in parenthesis gives the relative compositions of constituent atoms. As outlined above, a large amount of research has been triggered by the recent discovery of high temperature superconductivity in iron-based oxypnictides (ReFeAs) systems. The characterization of the structural and pinning properties of these materials is fundamental to understand them, and design potential applications and the critical current Jc of certain superconducting alloys can

23

be improved by cooling or increasing defects that enhance the flux pinning [Thomas 1994]. Moreover as in the cuprate-HTSC also in the Fe-HTSC the crystal structure has a strong influence in the observed anisotropy of their electronic and mechanical properties Recent researches showed [Seren et al., 2009] that undoped parent compounds of iron pnictides exhibit a spin-density-wave antiferromagnetic order (figure 2-1) and undergo a structural phase transition from tetragonal-to-orthorhombic crystal symmetry upon cooling (figure 2-2). Increasing the doping concentration the antiferromagnetic order is suppressed and a superconducting phase appears. The structural transition does not affect the electronic transport properties of the sample. [Seren et al., 2009]

Figure 2-1 Spin density wave order observed by the neutron diffraction. The Fe magnetic moments along the (1,1) direction are aligned, while two nearest neighboring such chains

are antiferromagnetically aligned. (b) The familiar antiferromagnetic ordering of the cuprous oxides. The shaded square denotes the unit cell. The CuO2 unit cell differs from the Fe2As2 one by a magnetic atom missing from the centre [Manousakis et al., 2009].

Figure 2-2 phase diagram of FeAs based HTCS

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Finally, another key experimental observation in REFeAsOF high temperature superconductors is the effect of pressure. Experimental data show that the pressure may enhance the critical temperature Tc of the FeAs based superconductors [Takahashi et al., 2008].

2.1 SmFeAsO1-xFx

As an example, the ReFeAsO based on Sm rare earth become superconducting, with a maximum transition temperature at Tc=55 K, when the active FeAs layers are doped through substitution of oxygen by fluorine [Takahashi, et al., 2008].

Figure 2-3 Crysal structure of SmFeAsO(F) composition

As it can be seen from figure 2-3 [Chen at al., 2008], the tetragonal unit cell of the SmFeAsO is strongly elongated, which explains the strong anisotropy of all its properties and a quasi-bidimensional nature of electronic states, with a higher electronic transport in the ab plane rather than c axis. The FeAs layer is thought to be responsible for superconducting characteristics and the SmO layers act as charge reservoirs. The crystal structure of SmFeAsOF shows that close to each Fe atoms are those of As, located underway of the Fe neighbors, so that the electron transfer processes over the Fe sub lattice are mediated by the Fe-As hybridization, and the exchange interaction between Fe atoms is of indirect character via the As atoms. Replacing oxygen atoms by fluorine, an extra electron goes into the FeAs layer; a condition is commonly referred to as electron doping. As showed in figure 2-4 [Drew et al. 2009], the phase diagram of the

25

SmFeAsO1-xFx is strongly dependent by the doping concentration x. It is shown a magnetic phase at low doping, a coexistence phase between magnetism and superconductivity at middle doping and a complete superconducting phase for higher doping values. Moreover, the SmFeAsO1-xFx compound presents an anomalous behavior around 150 K [Yang et al., 2009]. Although, it cannot show superconductivity without oxygen deficiency, its lattice parameter is the same of the parent compound SmFAsO [Yang et al., 2009].

Figure 2-4 Phase diagram of the magnetic and superconducting properties of SmFeAsO1-

xFx [Drew et al., (2009)] Experiments [Yang et al., 2009] have been performed on SmFeAsO1-

xF0.20 and SmFeAsO0.90Fx samples with different x, data show that increasing the oxygen vacancies and the fluorine substitutions an enhancement of the superconducting behavior of the parent compound occurs. Fluorine doping and oxygen deficiency produce similar effects in other initial stoichiometric compounds [Ren et al 2008]: they create electron carriers suppressing the anti-ferromagnetic (AFM) ordering in favor of the formation of the superconducting state. In the SmFeAsO family the doping concentration has a large effect on the transition temperature. The optimum doping concentration is x=0.2. [Margadonna et al., 2009]. Also oxygen vacancy in parent compounds produced by high pressure, which reduces the crystal lattice constant, induces an increment of the transition temperature Tc [Yang et al., 2009].

26

The relation of magnetization with temperature at different pressures [Takabayashi et al., 2008] is shown in figure 2.5; from this figure we can see that at constant doping concentration the superconducting response is different at different hydrostatic pressure. Figure 2.6 shows Tc vs. pressure relation at different doping concentration, the critical temperature increases with increasing pressure, fluorine doping up to the x=0.12. The pressure increase the electron transport property between the insulating RE(O,F) and FeAs slabs [Takahashi, et al., 2008].

Figure 2-5 temperature dependence of the magnetization, ZFC, at different pressure for

SmO0.90F0.10FeAs (square) and SmO0.80F0.20FeAs (circle)

Figure 2-6 Superconducting transition temperature, Tc vs applied pressure P, at different

doping.

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Chapter 3

Experimental set-up and susceptibility measurements

3.1 AC gradiometer

3.1.1 INFN – LNF susceptometer

At the INFN National Laboratories in Frascati (LNF) an AC multi-harmonic susceptometer working in a temperature variable cryostat (4 K-300 K) is available for experiments. The susceptometer works with a gradiometer based on a bridge made by two pickup coils connected in series, wounded in the opposite sense and surrounded by a drive excitation coil (figure 3-1) This set-up is called first derivative configuration of the gradiometer coil.

This design is used to reduce magnetic field fluctuations noise in the detection circuit caused by the applied magnetic field. Samples are located on a sapphire holder slab (figure 3-2) that fits at the center of one (sensing coil) of the two pick-up coils of the bridge while the second (balance coil) remains empty. The sapphire is used because it is a nonmagnetic material, a good thermal conductor and, to minimize current losses, it is also characterized by a low electric conductivity. The sample holder and the coils assembly are cooled by insertion in a double vessel, thermally controlled, He

Figure 3-1 the gradiometer insert with a section view of the insert inside the cryostat (left), sapphire sample holder in the coils system (right)

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gas flow cryostat (Figure. 3-3). Inside it, a superconducting magnet may operate in the range from 0 to 8 T in persistent or non-persistent modes.

Figure 3-2 SmFeAsO0.85 F0.15 sample, sapphire sample holder, CGR thermometer

The sample is set at the center of the superconducting magnet and the temperature can be changed via a cold He gas flow that is manually controlled via a throttle and a needle valve on the top of the cryostat. Before any measurement a purging of the sample compartment with clean helium gas is made.

Figure 3-3 (Left) photograph of the cryostat with the pumping unit, (Right) photograph of

the control units.

The AC driving magnetic field frequency f, can ranged from 17 Hz to 1070 Hz with variable amplitude from 0 to 20 G. During the experiment the AC field generated by the drive coil induces a variable magnetic moment on the sample and consequently a flux variation in the pick-up coils, whose voltage signal is measured by a multi-harmonic lock-in amplifier (SIGNAL RECOVERY model 7265 DSP) showed in figure 3-3. A platinum thermometer and a carbon resistor placed near the sample, in thermal contact with the sapphire holder, monitor the temperature. The susceptibility measurements can be performed both in a zero field cooled (ZFC) and in the field cooled (FC) modes. In the ZFC mode the sample is slowly cooled

29

below the transition temperature without the magnetic field, then the magnetic field is turned on. In the FC mode the magnetic field is turned on above the Tc then the sample is cooled down below the transition temperature and after the data are measured during the warming procedure. The device allows performing measurements of the AC magnetic multiharmonic susceptibility with a magnetic sensitivity of 1x10−6

emu and a temperature precision of 0.01 K. Higher components of the magnetic susceptibility can be acquired up to seven harmonics, at low and high DC magnetic field. Below are summarized the main technical specifications of the instrument: • 4.2-300 K temperature range • 17-1070 Hz frequency range • 3-20 G AC magnetic field range • 0-8 T DC magnetic field range Gradiometer (susceptometer) characteristics: • First derivative two pick-up coils bridge on a TORLON support within a sapphire glass • 1 x10−6 emu sensitivity at 0T • maximum probed volume: 5x5x2mm

3.1.2 Lock-in amplifer

The Lock-in amplifier is one of the most important tool of an Ac susceptibility experimental set-up. We used a SIGNAL RECOVERY model 7265 DSP multi-harmonic model, with a sensitivity up to nV. The instrument allow the readout of both in phase and out of phase components of the signal respect to the reference frequency defined by the exciting magnetic field of the experimental set-up. The Lock-in amplifier works with the phase-sensitive detection (PSD) technique, to single out the specific reference frequency and phase. In particular, signals of frequency other than the reference are rejected and do not affect measurements. The phase angle between the real and the imaginary parts of the first harmonic of the signal detected by the pick-up coil must be adjusted to properly separate the real and the imaginary parts of the AC susceptibility. This separation is done before collection of data, via the “auto-phase” tool of the Lock-in, providing that the sample is in a strongly superconducting state with low losses (low field, low temperature). Under these conditions, as mentioned before, the

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imaginary signal that represents the losses, is set to zero with a phase adjustment. In our case, the procedure with the SmFeAsO0.85F0.15 sample has been performed around 27 K, a temperature much lower than the critical temperature. Below are summarized the main characteristics of the Lock-in amplifier we used for the experiments: - frequency range of 1 mHz to 250 kHz, - full-scale voltage sensitivities down to 2 nV - current sensitivities to 2 fA.

The instrument may operate in different modes, signal recovery or vector voltmeter. To optimize the measurement accuracy in different conditions the use of DSP techniques ensures exceptional performance for the acquisition

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Chapter 4

AC-multi-harmonic magnetic susceptibility analysis

4.1 Summary

The AC multi-harmonic magnetic susceptibility it is an effective method to characterize the properties of HTSC materials [Dongol, 2000], such as phase transition from normal to superconducting state, the vortex liquid phase where vortices are highly mobile, the vortex lattice glass phase where vortices are pinned by defects (pinning center) randomly distributed in the sample, and arranged in a glassy configuration (see figure 1-2(b)).

In this chapter we present the measurements of the fundamental and third harmonic susceptibility, to investigate the vortex dynamics in the superconducting SmFeAsO0.85F0.15 sample. Experiments have been performed in the frequency range 107 Hz < f < 1070 Hz, at fixed Hac= 9.8 Gauss with and without the DC field at the amplitude of 1 T. A zero field cooling (ZFC) (see pag. 23-24) experimental set-up has been used. In this procedure the sample is cooled down far below its superconducting critical temperature and after the excitation magnetic field is switched on. To observe the variation of the superconductor magnetic response under the magnetic field excitation the temperature is smoothly increased while collecting data.

This study may allow the investigation of the granular structure of the sample [Gomory, 1997], and varying frequency, magnetic field and temperature we may describe the flux dynamic evolution of the system in the B-T-J phenomenological space [Blatter et al., 1994]. Moreover the liquid and vortex lattice phase transition can be measured by comparison between the different onsets of the χ’’1 and the |χ3|. Furthermore the dimensionality of the flux motion with the glass transition temperature can be determined via frequency dependent irreversibility line (IL), measurement of the |χ3| onsets [Fisher at al., 1991] [Wolfus et al., 1994]. Finally, the characteristics of intra and inter granular pinning properties can be investigated by means of χ3 Cole-Cole polar plots.

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4.2 First harmonic susceptibility measurements

The real and imaginary components of the first harmonic of the susceptibility of SmFeAsO0.85F0.15 show typical trends expected for a superconductor. The onset of the Tc temperature is around 50 K when BDC = 0 T, and between 47 K and 48 K when a field BDC=1 T is applied (see table (1)). The onset is taken at the point just starting to deviate from the horizontal axis. The real part of the first harmonic, χ’1 exhibits the characteristic superconducting diamagnetic behavior, while the imaginary part of first harmonic, χ”1 measures the energy dissipation inside the sample (paragraph 1.3) showing the typical ‘bell’ behavior. The energy losses include both linear and the non-linear contributions. Non-linear losses arise from the hysteretic motion of the flux lines inside the sample described by the flux-pinning processes. Linear losses are associated to the motion of free uncoupled electrons and the free flux flow motion. These losses limit the superconducting state while the hysteretic losses prevent and delay the motion of flux quanta sustaining the superconducting state [Di Gioacchino et al., 2010].

The first harmonic susceptibility vs. temperature for different frequencies are shown in figure from 4-1 to 4-4 at 0 T and, 1 T DC fields amplitudes.

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Figure 4-1 The real part first harmonics vs. temperature for different frequency at Hac=9.8 G and BDC=0 T

Figure 4-2 The real part of the first harmonics vs. temperature for different frequency at

Hac=9.8 G and BDC=1 T Figures 4-1 and 4-2 show diamagnetic behavior of the superconductor after the transition at Tc and the curve has similar shape in frequency. The behavior points out a good flux pinning state. In fact, greater is the block of

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the hysteretic jump motion of the thermally activated fluxes over pinning potential barriers, and weaker is the dependence of the superconducting system by the frequency (paragraphs 1.2.1, 1.2.2). Moreover, the figure 4-2 shows that when a DC magnetic field is applied, the superconducting state decreases and appears at lower temperatures. In figure 4-3 and 4-4 are shown the variation of χ”1 and are evident two peaks as a function of the temperature, this underlines that the sample shows typical granular response to external applied magnetic field [Gomory, 1997].

Figure 4-3 The imaginary part of the first harmonics vs. temperature for different

frequency at Hac=9.8 G and BDC=0T

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Figure 4-4 The imaginary part the first harmonics vs. temperature for different frequency

at Hac=9.8G and BDC=1T

The peak at higher temperature, describes the single grain behavior due to the shielding current flowing in separated grains. The second peak is connected to the magnetic response of the total sample, for this temperature the superconducting grains are connected and the current flow through whole sample [Gomory, 1997].

To compare these behaviors, we show in figure 4-5 the χ”1 temperature onsets vs. frequency for HDC = 0 T and 1 T. It is evident here that the χ”1 onsets have different behaviors: for HDC = 0 T the onset is frequency independent while for HDC = 1 T decreasing the frequency the χ”1 onsets rise. To understand this behavior we need to remember that linear losses have two contributions and occur mainly at temperatures near the χ”1 onsets. The figure 4-5 shows that at small amplitudes of the AC magnetic field, the frequency does not affect the normal losses near the onset of the susceptibility, while at 1 T of the DC field, the trend vs. frequency points out that losses are due to free flux flow of the quanta because, compared to the normal electron motion the ‘flux core’ viscous motion is more efficient at low frequency. In fact, normal skin losses show an enhancement increasing the frequency, opposite to the behavior observed in Figure 4-5.

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Figure 4-5. The frequency dependence onset temperature of χ”1 at Hac=9.8 G for BDC=0

and BDC=1 T.

4.3 Third harmonic susceptibility measurements

To characterize the flux pinning processes that sustain the vortex hysteretic dinamics described by a non-linear flux diffusion motion, higher harmonics must be considered (paragraph 1.3) In the superconducting state this motion is affected by temperature, applied field frequency and amplitudes of Hac and HDC fields [Di Gioacchino et al., 2010]. The frequency dependence of the third harmonic susceptibility components versus temperature are illustrated in figures from 4-6 to 4-11 for HDC = 0 T and 1 T. It describes the change of the effective flux diffusivity connected with the flux pinning interaction. The variation is due to the different potential V induced inside the sample by the different frequency of the applied AC field and the different BDC fields [Di Gioacchino et al. 2004].

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Figure 4-6 The real part of the third harmonics vs. temperature for different frequency for

Hac=9.8 G with BDC=0 T.

Figure 4-7 The real part of the third harmonics vs. temperature for different frequency for

Hac=9.8 G with BDC=1 T.

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Figure 4-8 The imaginary part of third harmonics vs. temperature for different frequency

for Hac=9.8 G with BDC=0 T.

Figure 4-9 The imaginary part of the third harmonics vs. temperature for different

frequency for Bac=9.8 G with BDC=1 T.

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Figure 4-10 The variation of |χ3| vs. frequency for Bac =9.8 G and BDC=0 T.

Figure 4-11 The variation of |χ3| vs. frequency for Bac =9.8 G and BDC=1 T.

With these experimental conditions and with the ZFC set-up measuring third harmonic we probe the evolution in time (or the evolution of the current) of the superconducting state, determined from the flux pinning dynamic. In particular, different AC frequencies set different “window time” on this process. Moreover, when the magnetic field is applied to the

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superconducting sample, at first it goes into an initial flux pinning critical state [Di Gioacchino et al., 2010]. Later, this state decays via thermally activated flux creep process in to a final stable flux pinning glass state phase [Blatter et al., 1994]. This behavior is schematically shown in figure 4-12.

Figure 4-12 Phenomenological phase diagram of a HTSC, showed in a space whose axes are time (or current), magnetic field and temperature. After ZFC procedure, it has been switch on the magnetic field and the sample goes in a well-defined meta-stable critical

state at point A, when time goes on, it evolves in a final stable glass state. Points B, C, D, E and F are represent others meta-stable critical states probed at specific time windows

defined by frequency values. As shown in figures from 4-6 to 4-11 the applied DC field has clear effects changing the pinning potential Up barriers. The χ3 at BDC = 1 T, show a significant decay of the amplitude of third harmonic signal vs. temperature corresponding to a lowering of the barrier of the superconductive state. In fact, with an applied magnetic field BDC = 1 T, the transition temperature shifts to lower temperature, and also the onset temperatures of inter-grain and intra-grain contributions shift to lower temperature. In particular, the inter-grain temperature onset for BDC=1 T does not appear in figures 4-7, 4-9 and 4-11 because is at a temperature too low respect to the experimental temperature range.

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4.4 Irreversibility line, liquid phase and vortex phase

To further study the interaction of the pinning effects in the flux motion in SmFeAsO0.85F0.15, we analyzed the transition between the vortex liquid and the vortex lattice phase. In particular, we compared the behavior of the χ”1 temperature onset, that defines the transition between the normal to the superconducting state, with the |χ3| onset temperature, that defines in the superconducting state only the hysteretic flux lattice response. It represents the boundary between the vortex lattice phase and the liquid vortex phase previously called the irreversibility line (IL). The temperature difference marks the liquid vortex range present in the superconductor. As an example, the comparison procedure is showed in the figures 4-13 and 4-14 where we plotted both χ”1 and |χ3| vs. temperature at a characteristic frequency, with and without the BDC field.

Figure 4-13 The onset temperature of χ”1 and |χ3|, Bac =9.8 G BDC= 0 T.

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Figure 4-14 The onset temperature of χ”1 and |χ3|, 9.8 G BDC=1 T.

The values of the onsets for all measurements are reported in table 1.

Frequency (Hz) 107 507 707 1070 Tonset(χ”1) (K) BDC=0T 50.40 50.33 50.24 50.44 Tonset(|χ3|)(K) BDC=0T 49.20 49.70 49.44 50.04

Frequency (Hz) 507 707 1070

Tonset(χ”1) (K) BDC=1T 48.67 48.24 47.52 Tonset(|χ3|)(K) BDC=1T 45.65 46.60 46.84

Table 1. The onset temperature of χ”1, and |χ3| at different frequency, fixed amplitude

Hac=9.8 G, when BDC=0and BDC=1 T.

In order to better visualize the liquid phase region, in figure 4-15 and 4-16 we plot Tonset(χ”1), Tonset(|χ3|) vs frequency. A discussion on the frequency behavior of the onset temperature of χ”1 for BDC = 0 T and 1 T is given in the previous section. As discussed above, Tonset(χ’’1) indicates the beginning of the formation of the vortex liquid phase inside the sample, while the Tonset(|χ3|) indicates the lattice vortex to liquid phase transition temperature. It is evident from this analysis that the linear dissipative phenomena occurs in the temperature range ∆Tonset(χ”1-|χ3|) [Ishida et al., 1990]. Looking at the figure 4-15 and 4-16 in the SmFeAsO0.85F0.15 sample

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the temperature flux liquid state is present for BDC = 0 T in the temperature and frequency range: 1.2 K > ∆Tonset > 0.45 K for 107 Hz < f < 1070Hz and for BDC = 1 T in the range: 2.9 K > ∆Tonset > 0.9 K for 107 Hz < f < 1070 Hz. It can be seen from a comparison of the ∆Tonset(χ”1-|χ3|) range that, when a DC magnetic field is applied respect to the same experiment with no DC field at the same frequency, the ∆Tonset(χ”1-|χ3|) is increased.

Figure 4-15 The frequency dependent onset temperature of χ”1, and |χ3| at Hac=9.8 G,

BDC= 0 T.

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Figure 4-16 The frequency dependent onset temperature of χ”1, and |χ3| at Hac=9.8 G,

BDC=1 T.

The application of a strong magnetic field weakens the pinning potential barriers and as consequence, it amplifies the free motion of magnetic flux quanta (flux flow motion) and the liquid free flux temperature range widens. Moreover, in both cases BDC = 0 T and 1 T, the ∆Tonset(χ”1-|χ3|) decreases while increasing frequency. The result confirms that high frequency measurements describe a ‘window time’ of the flux dynamic processes where the superconducting response is defined by a stronger meta-stable state because it is adjacent to the “initial critical state“ (figure 4-12).

4.5 Flux pinning dimensional analysis and the glass

temperature

To have more insight of the grain pinning characteristics of the material, in particular the flux pinning dimensionality, we have also studied the Irreversibility Line (IL) behavior vs. frequency. In this framework it will be possible to define also the final stationary temperature of the glass state [Di Gioacchino1et al., 2003]. For the SmFeAsO0.85F0.15, we plot the intra-grain |χ3| onset temperature vs. frequency for Bdc= 0 T and 1 T. Using the equation (4-1) [Fisher, et al., 1991] [Wolfus et al., 1994] defined in the

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vortex glass weak pinning approach, we may estimate the dimensionality D of the single grain flux-pinning interaction from the intra-grain onsets, as shown in figure 4-17 and 4-19. The same equation can be used considering the inter-grain |χ3| onsets to know also the dimensionality by the flux-pinning response of the whole sample (figure 4-18 and 4-20). (1/(( ( 2 ))))( ) ( ) * v z D

girrT T H A H f + −= + (4.1) Where v > 0 and z > 0 are the static and dynamic exponents and D is the dimensionality.

Figure 4-17 The Irreversibility Line defined by the |χ3| onset temperature as a function of frequency (intra-grain contribution when BDC=0)

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Figure 4-18 The |χ3| onset temperature vs. frequency (the inter-grain contribution at

BDC=0 T)

Figure 4-19 The Irreversibility Line defined by the |χ3| onset temperature vs. frequency

(the intra-grain contribution at BDC=1T)

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Figure 4-20 The |χ3| onset temperature vs. frequency (the inter-grain contribution at

BDC=1 T).

The analysis of both intra-granular and inter-granular superconducting phases shows a three-dimensional (3D) bulk pinning for both values of the DC magnetic field. The result points out that: 1) the flux lines in the grain interact with the superconductor planes and all the defects in the volume of grain participate together to pinning of flux quanta, 2) the grain boundaries connecting grains contribute to the flux pinning collectively in the entire volume of the sample.

This behavior is in agreement with a strong flux pinning scenario. In fact the application of the magnetic field does not change the flux dynamic going from 3D to 2D, a transition generally observed in HTSC weak pinning superconductors [Blatter et al., 1994]. In table 2 are summarized the Glass temperature of the grain and of the bulk sample.

BDC=0 T BDC=1 T Intra-grain Glass Temperature (Tg) 47.71K 40.22K

Inter-grain Glass Temperature 42.73K 38.34K Table 2

The DC magnetic effect on Tg intra-grain and inter-grain underline that:

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∆Tg(intra-grain)=7.49 K ∆Tg(inter-grain)=4.39 K and the grain boundaries pinning effect is larger than pinning in the individual grains.

4.6 Non-linear diffusivity

To learn more about the pinning properties of the sample, we analyzed also the behavior of third harmonic polar plot (χ” 3 versus χ’3) vs. frequency [Gilchrist et al., 1994] [Van der Beek, et al., 1996] [Di Gioacchino et al., 2005]. In figure 4.21 is showed the χ3 polar plots at HDC = 0 T. We can see two kinds of patterns: one of greater area that develops mainly in the third quadrant, while other of smaller area is located mostly in the fourth quadrant. The former define the low temperature superconductive inter-grain pinning behavior, while the latter describes the pinning intra-grain characteristic at high temperature.

The experimental curves for inter-grain pinning behavior resemble a characteristic lens shape, which confirm the previous chapter analysis, i.e. that in the SmFeAsO0.85F0.15 system is present a bulk inter-grain pinning behavior [Gilchrist, et al., 1994]. Increasing the frequency the plots move toward to the ideal bulk pinning critical state curve [Shatz, et al 1993]. This rotation with the frequency is connected to the changing of the temporal shift between surface applied filed (Hac) and induced magnetic response inside the sample (Hin). This variation describes the temporal evolution of the flux distribution in the sample. The behavior is related to the type of pinning and of the vortex activation during the flux evolution from initial meta-stabile pinning critical state to final pinning glass state with a bulk slab pinning configuration [Quin et al., 2000] [Gilchrist et al., 1994]. In particular, the polar plots have a small frequency dependence for BDC = 0 T, in the frequency range 307~1070 Hz. This indicates that, in this region we have good pinning and the sample is able to sustain high enough critical current.

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Figure 4-21 Experimental and theoretical Bulk pinning critical model χ3 cole-cole plot vs

frequency at Hac=9.8 G, when BDC=0 T. The bigger dome shaped curve inter-grain contributions while the smaller are intra-grain contributions.

The polar plots intra-grain pinning behaviors are shown in figure 4-22

and 4-23 at Bdc = 0 T and 1 T, respectively. Different shapes can be recognized compared to the inter-grain pinning showed in figure 4-21. The intra-grain plots are closed ovoids in the complex plane. These plot refer to the pinning surface barrier present in a slab [Gilchrist, at al. 1993]. The comparison among different areas for BDC = 0 T and BDC = 1 T points out as expected, that the magnetic field weakens the superconducting grains response.

Actually, the 3D flux pinning dynamic of intra-grain and inter-grain responses analyzed in the chapter 4.5 is consistent with the above Cole-Cole plot analysis. We may claim that the intra-grain flux dynamics has a barrier-like pinning within a 3D slab geometry while the inter-grain 3D flux dynamic is compatible with a distribution of pinning centers determined by a grain boundary through the entire sample.

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Figure 4-22 Zoom in the intra-grain contributions to χ3 Cole-Cole plot BDC=0 T, Hac=9.8

G, of figure 4.21.

Figure 4-23 The intra-grain contributions to χ3 Cole-Cole plot BDC=1 T, Hac=9.8 G

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Chapter 5

Conclusion

Increasing the critical temperature of superconducting materials to improve and develop applications a very important issue also for our daily life. However, understand their physical properties to exploit their potential use is also fundamental. The ac multi-harmonic susceptibility measurement is one of the most efficient methods to understand and describe the physical properties of superconductors.

The aim of this thesis is that to investigate the superconducting behavior of a high temperature superconductor in a magnetic field, to gain more insight in the field and frequency dependent dynamics of vortices motion near the vortex-glass phase transition temperature of the SmFeAsO0.85F0.15, a superconductor belonging to the family of the new type high Tc, iron-based superconductor called iron-pnictides. All the described experiments were carried out on a bulk sample with dimension 4×4mm2. The experimental data shows that this is a granular superconducting material characterized by intra-grain and inter-grain effects and a strong pinning at high frequency. Moreover, it highly disordered at the microscopic scale.

In chapter 1 we discussed the superconductivity giving emphasis to layered high critical temperature superconductors, to the behavior of superconducting materials under an applied magnetic field and to the theory of the collective weak pinning, in the vortex glass framework. Chapter 2 gives a description of the new iron–based high temperature superconductors family, with a description of the SmFeAsO0.85F0.15.

We measured the magnetic AC multi-harmonic susceptibility with the experimental setup described in chapters 3 and 4. AC multi-harmonic χ measurements on the SmFeAsO0.85F0.15 probe the superconducting critical temperature Tc, that has been determined around 50 K when BDC=0 and ~47-48 K when BDC=1 T. The behavior of the first harmonic AC susceptibility, also pointed out the granular structure of this sample. The intra-grain signals, located at higher temperature, are the response of separate grains while the inter-grain signals, occurring at lower temperature, are the response of all connected grains so

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that the current flow through the whole sample. The magnetic analysis of the onset of the linear losses χ”1 showed that the onset temperature of χ”1 is nearly independent by the frequency without a DC field, while for HDC=1 T when the frequency decreases the χ”1 onsets gradually increase. This behavior is well described by a free flux flow motion inside a superconducting sample. The third harmonic AC susceptibility probes only the flux pinning processes and the frequency, magnetic field, temperature dependent flux dynamic evolution of the system in the B-T-J phenomenological space. The experimental data we collected showed that: a) the application of a DC field changes the pinning potential Up, lowering the superconducting state shifting the transition temperature to lower values. b) the onset temperature of |χ3| defines the irreversibility line (IL) and the comparison between temperature onsets of χ”1 and |χ3| identifies the liquid and vortex glass phases. In particular the temperature difference represents the liquid vortex phase presents in a superconductor: when BDC=0 T, 1.2 K>∆Tonset>0.45 K in the for frequency range 107 Hz<f< 1070 Hz while when BDC=1 T it is 2.9 K>∆Tonset>0.9 K in the frequency range 307 Hz<f< 1070 Hz. The difference between the two onsets, ∆Tonset(χ”1-|χ3|) increased when we applied a DC field. The application of a strong magnetic field depresses the pinning potential barriers and amplifies the free motion of the magnetic flux flow motion while the liquid free flux temperature range widens. Moreover, in both cases, the ∆Tonset(χ”1-|χ3|) decreases increasing the frequency. Under an AC driving frequency the superconducting response is defined by meta-stable states. At higher frequency it remains near the “initial critical state” so it showing a strong pinning. This result confirms that at high frequency, a susceptibility measurement describes the “window” of the flux dynamic process. c) the analysis of the frequency dependent onset temperature of |χ3| (IL), both for intra-granular and inter-granular phases, shows a 3D bulk pinning for the values of the DC magnetic field 0 and 1 T. This means that the flux lines interact among the superconductor planes and at the inter-grain level, the grain boundaries contribute to the entire volume of the sample. This

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behavior is compatible with a strong flux pinning. If we define a Glass temperature as that the final vortex glass phase of the grain and the bulk sample is reached: Tg(intra-grain)= 47.71 K when HDC=0 T and 40.22 K when HDC=1 T while the Tg(inter-grain)= 42.73 K when HDC=0 T and 38.34 K when HDC=1 T. The variation of Tg respect to the magnetic field BDC, ∆Tg(intra-grain)=7.49 K and ∆Tg(inter-grain)=4.39 K, shows that the flux pinning in the grain boundaries is greater than the pinning in the grains. d) The third harmonic Cole-Cole polar plots (χ”3 versus χ’3) confirm that there are two kinds of patterns in the SmFeAsO0.85F0.15 system: i) the inter-grain pinning behavior with a lens shape that verifies a 3D bulk pinning behavior. In this case, at high frequency near the initial flux pinning, the configuration reproduces the ideal bulk pinning critical state curve while the flux evolution shows a final pinning glass state with a bulk slab pinning pattern. With no field data showed a small frequency dependence, in the frequency range 307 Hz<f<1070 Hz, and indicating that the SmFeAsO0.85F0.15 system in the inter-granular scenario has a good pinning compatible with a high enough critical current; ii) the intra-grain pinning behavior with a closed ovoidal shape connected with a pinning surface barrier present in a 3D slab configuration. The magnetic field analysis shows a reduction of the superconducting grains response with a intra-grain pinning less efficient than inter-grain pinning.

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Acknowledgements

A special acknowledgment is due to my supervisor Professor Roberto Gunnella, who continuously encouraged me and supported my decision to accept the thesis offered by the Laboratori Nazionali di Frascati of the INFN (National Institute for Nuclear Physics) performing the set of experiments described in this work.

This thesis would not have been possible without the continuous support

of Prof.s Augusto Marcelli, Daniele Di Gioacchino, Doctor Alessandro Puri and the technician Fabio Tabacchioni.

It is a pleasure to thank Professor Augusto Marcelli who gave me the

opportunity to experience the life and the research of a large laboratory such as the Laboraori Nazionali di Frascati of the INFN that I sincerely thank for the hospitality and support.

I would like to thank Prof. Daniele Di Gioacchino and Dr. Alessandro

Puri who help me running the experiments and analyzing data, in particular in these last weeks.

I owe my deepest gratitude to my family, roommate and all

colleagues. A special acknowledgment goes to my girlfriend, Munewer that with her encouragement and patient love really enable me to complete the thesis successfully. Thank you!

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