Simulated annealing study of the disordered quantum magnet LiHoxEryY1-x-yF4

Thermal and quantum phase transitions of some rare earth compounds (LiErF4, LiYbF4, LiGdF4 and LiTmF4) are established using the mean field theory. These preliminary calculations allowed evidencing the existence of a novel high-field antiferromagnetic phase in LiErF4, and a still unexplained symmetry breaking in LiGdF4. But the discrepancies with experimental results impel a more sophisticated method. We then present analytical and numerical evidence for the validity of an effective approach to the description of the dipolar coupled antiferromagnet LiErF4. We show that the approach, when implemented in mean field calculations, is able to capture both the qualitative and quantitative aspects of the physics of LiErF4 at small external field and low temperature, yielding results that agree with those obtained in the full Hilbert space using mean field theory. This model nevertheless still fails to describe the LiHoF4 system and needs to be improved. We finally use this toy model as a basis for classical Monte Carlo simulations of LiErF4, which allows the calculation of thermodynamical quantities of the system, as well as the evolution of the order parameters as a function of field H and temperature T. These calculations yield results that are much closer to the experiments than those based on the mean field approximation. Although the theoretical critical temperature is still overestimated by 34%, the critical exponents computed from this effective model correspond to those found experimentally.

Etude par microscopie électronique à transmission à haute résolution de l'élargissement thermique des parois de domaines ferroélectriques dans un système de premier ordre

The macroscopic properties of ferroelectric materials depend directly on the domain configuration and the structure of the domain boundaries. For this reason, their study is of great scientific and technological interest. Several models have been developed to describe the properties of domain walls (structure, thickness, stress at the interface, mobility, …). However, few quantitative experimental observations of ferroelectric domain walls at an atomic scale have been reported, and even less results exist at higher temperatures. The ferroelectric domain-wall thickness is an important parameter whose behavior as a function of temperature is directly related to the order of the phase transition. In a second-order system, the temperature dependence of the domain-wall thickness follows a power law L ~ (Tc - T)-ω where ω is the critical exponent characterizing the divergence of L near the critical temperature Tc The predictions concerning the numerical value of are different depending on the theoretical model considered. Nevertheless, the majority of ferroelectric materials are known to undergo a first-order transition. In these systems the domain-wall thickness increases when the transition temperature is approached, but without diverging as for a second-order phase transition. The major objective of this work was to measure this broadening predicted by the theory for the first time at the approach of the phase transition temperature. We have shown that high resolution transmission electron microscopy is powerful technique for the study of ferroelectric domain walls not only at room temperature but also at higher temperatures. This method allows a direct and local observation of interfaces at an atomic scale which is a considerable advantage over diffraction techniques (X-ray, neutron, electron) and most of the other electron microscopy methods. However, the requirements of this method concerning the performance of the optical system of the microscope, the quality of the specimen and its stability in the column are very high, and today high resolution microscopy at high temperature remains a major challenge. The domain-wall thickness is obtained from the measurement of the crystal lattice distortion near the interface using two different numerical techniques of image analysis. The first method is based on the accurate determination of the center of bright peaks which appear on high resolution images for a judicious choice of the experimental parameters (delocalization and crystal thickness) and which represent the crystal lattice nodes. The second technique consists in selecting a circular region of the power spectrum around a reflection peak, centering the Fourier space on this reflection and performing the inverse Fourier transform. The information about the local displacement of atomic planes corresponding to the selected reflection is extracted form the phase component of the obtained complex image. Both techniques have been successfully applied to the measurement of the thickness of the 90° ferroelectric domain walls in PbTiO3 single crystals. This perovskite presents a first order phase transition at Tc = 492.2°C. which corresponds to the transformation of the crystal from the high-temperature paraelectric cubic phase to the low-temperature ferroelectric tetragonal phase. For the first time, the thermal broadening of domain walls has been measured quantitatively using HRTEM. The results are compared with the predictions made by phenomenological theories. We find that the domain wall thickness increases continuously from 0.7 nm at room temperature up to 5.5 nm near the transition temperature. Our results are consistent with those obtained by other authors at room temperature and those of a very recent study performed at higher temperatures using weak-beam microscopy. The measured domain-wall broadening is greater than the one predicted by a three-dimensional Ginzburg-Landau model where the polarization which is the primary order parameter is coupled to the elastic strain which plays the role of secondary order parameter. Our results are better described by a one-dimensional Ginzburg-Landau model without secondary order parameter. In this case the gradient coupling coefficient κ of the Ginzburg-Landau free energy is found to be 1.3 · 10-10 m3F-1. The methods developed for the measurement of the domain-wall thickness can by applied not only to other first-order ferroelectric crystals but also to ferroelectric systems presenting a second-order phase transition thus allowing the determination of the critical exponent ω. Characteristics only present in 2-D systems could also be detected by studying very thin specimens. Moreover, the same techniques can be adapted to the study of domain walls in purely ferroelastic materials.

EPFL2000

Thermopower as a Unique Tool to Probe Quantum Phase Transitions

Stevan Arsenijevic

In my thesis, transport measurements such as resistivity and, more importantly, thermopower S, were used to explore the phase diagram of bad metals. Bad metals are electronically correlated systems whose ground state lies close to a quantum phase transition. By tuning the control parameters, such as temperature (T ), magnetic field (B), hydrostatic pressure (p) or chemical substitution (x), we can induce phase transitions between the various electronic, magnetic and structural phases. Here, the thermopower is presented as a unique tool for probing quantum phase transition because it is a measure of the entropy of conducting electrons. The main part of the thesis is dedicated to the study of Fe-based superconductors (FeSC) discovered in 2008. Their parent compound has an antiferromagnetic (AF) ground state, where the itinerant electrons form a spin-density wave (SDW), a periodic modulation of spin density. This coincides or is preceded by a structural, tetragonal-to-orthorhombic transition. The nesting between the electron and hole Fermi surface is believed to be the driving mechanism for the SDW state. By changing the structural or chemical properties the AF ground state of FeSC is suppressed, giving way to superconductivity (SC). The remaining antiferromagnetic fluctuations above the transition can provide a glue for SC pairing. Here, the analysis of the thermopower S/T of BaFe1−xCoxAs2 (BFCA) in the x-T phase diagram shows the signatures of the spin fluctuation which have a dome-like dependence and follow the trend of superconducting Tc . The logarithmic increase of S/T upon decreasing T is ascribed to the proximity of the spin-density-wave quantum critical point. It can be understood as an increase of entropy due to the incommensurate AF spin fluctuations. We can ascribe the high values of thermopower in BFCA at intermediate- and room-temperatures to the influence of low-T quantum criticality. To probe the response of the electronic system in FeSC to structural changes, we performed measurements under pressure of the parent compound BaFe2As2 (BFA), the SC electron-doped BFCA, and hole-doped Ba1−xKxFe2As2 (BKFA). In the parent compound pressure suppresses the structural/SDW transition, similar to the effect of doping. For doped systems, in order to describe the behavior of thermopower in the high-T range (above 100K) we used a semi-metallic two-band model which was fitted to the data in order to extract the pressure dependence of the band parameters. In both doping cases the effect of pressure was similar, an increase of the band overlap and of the effective number of charge carriers. With this model we can explain the high-T , x and p dependence of thermopower in both electron- and hole-doped BFA. In a structurally simpler Fe-chalcogenide Fe1+yTe1−xSex compound, the excess of Fe has a Kondo-like influence on the charge carriers which dramatically changes the physics of the normal state. To probe the normal state, pressure, doping, magnetic Fe-excess concentration (y) and temperature were used as control parameters. At low-T a characteristic upturn of resistivity (ρmag ) is observed, followed by an increase of thermopower (Smag ), which we identify as the magnetic contribution caused by the spin-flip scattering events. Increasing the y resulted in an increase of ρmag , and a decrease of Smag , which is in agreement with the behavior of canonical Kondo-systems. Pressure suppresses the magnetic contribution to transport, thus increasing the itinerancy of the system. MnSi is another system in which the sensitivity of thermopower to entropy brings new information related to the complex magnetic structure. Pressure was used to drive the system from a helically ordered, canonical Fermi-liquid (FL) phase with T 2-resistivity to the intrinsically disordered, non-Fermi-liquid (NFL) phase above pc with T3/2-dependence. Our contour plot of S/T demonstrated how powerful the thermopower technique is, by reproducing the whole previously established T -p phase diagram. At the phase transition from the magnetically-ordered FL phase to the disordered NFL, the thermopower is dramatically enhanced. We bring useful information about the mysterious partial order (PO) phase inside the NFL phase, previously detected only by neutron scattering. The fluctuating helices scenario can describe the observed increase of entropy/thermopower in the PO phase. At ambient pressure, close to the helical transition of MnSi, a moderate magnetic field can stabilize the skyrmion lattice - the lattice of topological magnetic whirls, vortices. We observe a signature of the skyrmion lattice as a minute drop in thermopower. It is located exactly in the same region of the T − B phase diagram where an increase in magnetoresistance and Hall effect was reported previously. This feature originates from the additional scattering of conducting electrons on magnetic vortices, while the change in S is dominated by the decrease of entropy as the stable skyrmion lattice is formed. Overall, resistivity was used to confirm the established phase diagram, while thermopower, as an interesting and not sufficiently understood technique, was used to probe the sensitive changes of the charge carriers at the Fermi surface. We explored various phases showing how useful thermopower is to probe the entropy of electronic system on the verge of quantum phase transition.

EPFL2012

Normal state transport properties of novel superconductors

Balazs Sipos

The discovery of high temperature superconductivity in the cuprates in 1986 has boosted the research in strongly correlated materials. One strong motivation was and stays the understanding the high-Tc phenomenon with the hope that one can ultimately engineer new materials with even higher Tc. Besides the in-depth investigation of cuprates, there is a strong tendency in the solid state community to find new superconductors, which by themselves are interesting for applications, or by their properties they can contribute to the understanding of the high-Tc phenomenon. The program of my doctoral thesis was three-fold: i) to address one important issue in the cuprate superconductors, that of the role of homogeneity in the underdoped part of the phase diagram; ii) what is the effect of disorder in MgB2 superconductor, which has high potentials for applications; iii) to discover new superconductors in the family of transition metal dichalcogenides. All these materials are in some sense unconventional superconductors. The cuprates by their high Tc and the symmetry of the order parameter, MgB2 by its two-band superconductivity and Tc of 39 K, and the dichalcogenides by the appearance of superconductivity on the background of competing interactions. Measurements of transport properties, such as resistivity and thermoelectric power, were used to get insight in the behavior of these materials. Besides temperature as variable, I applied high pressure, extreme magnetic fields and controlled disorder introduced by fast electron irradiation. In the first part I present the pressure dependent study of two members of the transition metal dichalcogenides having 1T structure, 1T-TiSe2 and 1T-TaS2, where superconductivity was never observed in a pristine sample. 1T-TiSe2 has a CDW phase below 220 K which origin, weather it is driven by an excitonic mechanism or by a Jahn-Teller distortion, is an ongoing question. By applying pressure I showed that the pristine sample is superconducting in the pressure range of 2.0–4.0 GPa. This range remarkably coincides with the short range fluctuating CDW before its disappearance at the upper pressure value. If CDW is due to excitonic interactions than our observations suggest that it can be at the origin of superconductivity, as well. The second dichalcogenide is the 1T-TaS2, where a Mott-insulator phase appears on the top of a commensurate CDW. By applying pressure I was able to melt that Mott-phase, and reveal that the material is superconducting above 2.5 GPa with Tc of 5.9 K. Unexpectedly, superconductivity is born from a nonmetallic phase, and stays remarkably stable up to the highest applied pressure of 24 GPa. In the second part I tried to give my contribution to the field of high-Tc superconductors. I carefully selected few high quality underdoped Bi2Sr2PrxCa1-xCu2O8-δ sample, to address the nature of the low temperature ground state by applying high magnetic field. Although former measurements by other groups showed that at high underdoping, the ground state is an insulator, I found that a sample with as low Tc as 15 K exhibits metallic behavior up to 60 T. Furthermore, I showed that a inhomogeneous distribution of the doping atoms can completely mask the intrinsic normal state of a high-Tc superconductor. In the last part of my thesis I focused on the two-band superconductor MgB2 by studying the scattering between the bands by the means of the Matthiessen's rule. I made a systematic study of the influence of defects created by fast electron irradiation, and found that the the Matthiessen's rule is satisfied for the defect concentration range I induced. I further compare the influence of defects on the critical temperature and the residual resistivity in MgB2 with superconductors with various order parameters, and found that the decrease-rate of Tc in our system is within the range of a response of a superconductor with an s-wave order parameter.

EPFL2008