The Neutron Scattering Structure Factor

In the experience of neutron scattering, the structure factor is a value that can be almost directly measured (through the differential inelastic neutron scattering cross section). Thus it can be interesting to have a calculation which could give a theoretical point of view, even if the system used in the calculation cannot be as complex as in the real case. Although this calculation (of a simplified system) could be a bad representation of the real system, it is already a point of comparison which yields finally to a better understanding. The present work has the aim to provide a useful matlab code for the computation of the structure factor of small magnetic cluster in “spin-only” scattering. A concrete exemple and the result for a special configuration will be also given.

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

Stabilization of the chiral phase of theSU(6m)Heisenberg model on the honeycomb lattice withmparticles per site formlarger than 1

Jérôme Dufour, Frédéric Mila

Low-dimensional quantum magnets at finite temperatures present a complex interplay of quantum and thermal fluctuation effects in a restricted phase space. While some information about dynamical response functions is available from theoretical studies of the one-triplet dispersion in unfrustrated chains and ladders, little is known about the finite-temperature dynamics of frustrated systems. Experimentally, inelastic neutron scattering studies of the highly frustrated two-dimensional material SrCu2(BO3)2 show an almost complete destruction of the one-triplet excitation band at a temperature only 1/3 of its gap energy, accompanied by strong scattering intensities for apparent multi-triplet excitations. We investigate these questions in the frustrated spin ladder and present numerical results from exact diagonalization for the dynamical structure factor as a function of temperature. We find anomalously rapid transfer of spectral weight out of the one-triplet band and into both broad and sharp spectral features at a wide range of energies, including below the zero-temperature gap of this excitation. These features are multi-triplet bound states, which develop particularly strongly near the quantum phase transition, fall to particularly low energies there, and persist all the way to infinite temperature. Our results offer valuable insight into the physics of finite-temperature spectral functions in SrCu2(BO3)2 and many other highly frustrated spin systems.

2016

Order and dynamics in Kagome like compound Cu2OSO4 and other quantum magnets

Virgile Yves Favre

This thesis presents results of studies of novel compounds modeling complex fundamental physics phenomena. Cu2OSO4 is a copper based magnetic Mott Insulator system, where spin half magnetic moments form a new type of lattice. These intrinsically quantum pins are exhibiting atypical magnetic order and spin dynamics. The recent success in the growth of large single crystals of Cu2OSO4 enabled to perform measurements probing its static and fluctuating properties. The peculiarity of this sample is that its atoms are forming layers, with a geometry close to the intensively studied Kagomé lattice, but with a third of its spins replaced by dimers. This quantum magnetism system has been probed in its bulk, by the means of heat capacity and DC-susceptibility measurements, revealing a transition to a magnetically long range ordered state upon cooling, the details of which are revealed by neutron scattering. Single crystal inelastic neutron scattering shed light on the spin-dynamics in the system, with clear spin waves appearing as fluctuations around the peculiar ground state of the system: a 120 degrees spin configuration where the magnetic moment of the spin-dimer causes the sample to be globally ferrimagnetic. The presented results indicate that Cu2OSO4 represents a new type of model lattice with frustrated interactions where interplay between magnetic order, thermal and quantum fluctuations can be explored. The magnetic excitations of the compound can be modeled by a yet-to-be-understood internal effective mean-field that no simple magnetic coupling seems to reproduce. K2Ni2(SO4)3 is another compound that allows for the existence of non-trivial topological phases. This thesis presents results of the study of the unusual magnetic behavior of K2Ni2(SO4)3. No clear sign of well-established magnetic long range order has been observed down to dilution temperatures. Neutron scattering reveals the details of the competition between frustration and fluctuations that prevent order from settling in. Low temperature spin excitations take the form of a continuum at 500 mK, but also of broad, energy independent continua at higher temperatures. Bulk and neutron scattering measurements are put in perspective and linked together with a view to building up a better understanding of how quantum spin liquids can be stabilized in general, and in particular in this model compound. Finally, the last contribution of this thesis to the field of condensed matter physics regards the establishment of a state-of-the-art technique to fit heat capacity and unit cell volume of samples to try and make the extraction of magnetic information from specific heat measurements more robust. This newly-developed technique consists in modeling lattice contributions with better accuracy by using data from multiple experimentally accessible quantities to consolidate the fitting scheme. This method has been cautiously applied to several compounds at the forefront of research in experimental physics.