Berry phase investigation of spin-S ladders

We investigate the properties of antiferromagnetic spin-S ladders with the help of local Berry phases defined by imposing a twist on one or a few local bonds. In gapped systems with time-reversal symmetry, these Berry phases are quantized, hence able in principle to characterize different phases. In the case of a fully frustrated ladder where the total spin on a rung is a conserved quantity that changes abruptly upon increasing the rung coupling, we show that two Berry phases are relevant to detect such phase transitions: the rung Berry phase defined by imposing a twist on one rung coupling, and the twist Berry phase defined by twisting the boundary conditions along the legs. In the case of nonfrustrated ladders, we have followed the fate of both Berry phases when interpolating between standard ladders and dimerized spin chains, with the surprising conclusion that, at least far enough from dimerized chains, they define different domains in parameter space. A careful investigation of the spin gap and of edge states shows that a change of twist Berry phase is associated with a quantum phase transition at which the bulk gap closes, and at which, with appropriate boundary conditions, edge states appear or disappear, while a change of rung Berry phase is not necessarily associated with a quantum phase transition. The difference is particularly acute for regular ladders, in which the twist Berry phase does not change at all upon increasing the rung coupling from zero to infinity while the rung Berry phase changes 2S times. By analogy with the fully frustrated ladder, these changes are interpreted as crossovers between domains in which the rungs are in different states of total spin from 0 in the strong rung limit to 2S in the weak rung limit. This interpretation is further supported by the observation that these crossovers turn into real phase transitions as a function of rung coupling if one rung is strongly ferromagnetic, or equivalently if one rung is replaced by a spin 2S impurity.

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

Pulsed laser deposition of (SrBa)Nb2O6 thin films and their properties

Anna Infortuna

Strontium barium niobate (SrxBa1-xNb2O6, shortly SBN) is a solid solution system with tetragonal tungsten bronze crystal structure. It exhibits a ferroelectric phase with only one polar axis and a transition temperature depending on the Sr/Ba ratio. This thesis studies the growth of SBN thin films, in order to obtain a ferroelectric thin film model system for the study of 180° domain switching close to the ferroelectric phase transition. SBN has been chosen not only because uniaxial, but because it is possible to tune the temperature of phase transition varying the Sr/Ba ratio. It is thus possible to study electric properties of the phase transition close to room temperature, where conduction phenomena related to defects are normally lower. Thin films of SBN were grown by Pulsed Laser Deposition in a vacuum system constructed during this thesis work. For the formulation of a model it is desirable to have a system as close as possible to a single crystal. Therefore deposition parameters have been optimized to grow SBN thin films with the polar axis oriented perpendicular to the film plane. The films are integrated in parallel plate capacitor structures, in order to measure dielectric properties. The stability of the ferroelectric phase is found to be sensitive to impurities; contaminants with concentration below 1% induce a lowering of the transition temperature of about 100°C. Strain as well has influence on the phase transition; in the case of substrate with thermal expansion coefficients different from the SBN ones, the SBN film is under stress. A 0.6% tensile strain induces a lowering of the transition temperature of about 100°C, this is the case of silicon single crystal substrate. Grown on strontium titanate single crystals (STO), whose thermo-mechanical properties are close to the one of SBN, the films exhibit a phase transition temperature compatible with the one measured on single crystals. The obtained films suffer from leakage that is reduced by thermal treatment in oxygen rich atmosphere. The oxygen vacancies, created during the deposition process, are considered to be responsible of leakage. Vacancies recovery upon annealing does not eliminate the problem, and measurement of polarization at room temperature is difficult. However, piezoelectric measurements performed on individual grains, with atomic force microscope, prove that these have ferroelectric properties; by these experiment has been proved that it is possible to switch the polarization. Films with a disordered structure of grains are much less leaky than the ones with columnar grains spanning the whole cross section. These observations lead to the conclusion that conduction goes trough the grain boundaries. On STO single crystals, SBN grows epitaxial in Volmer-Weber mode. With a suitable preparation of the substrate surface, it is possible to induce the growth of films with different orientations of the polar axis: in the film plane, perpendicular to it or inclined of 45°. A model is proposed, explaining the epitaxial relation with the substrate on the basis of the perovskite kernel contained in the unit cell of the tetragonal tungsten bronze structure. The film grows from the nucleation of the perovskite structure that rules the orientation of the film; the high temperature at which the substrate is kept during the deposition, assure the necessary mobility for the arriving atoms to organize in the SBN structure around these nuclei. The study of literature data allows to state that such a model is valid not only for substrates with perovskite structure, but can be extended to substrates with a cubic crystal structure, like magnesium oxide.

EPFL2005

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