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Publication# Investigating field-induced magnetic order in Han purple by neutron scattering up to 25.9 T

Philippe Heller, Nicolas Laflorencie, Frédéric Mila, Bruce Normand

*AMER PHYSICAL SOC, *2022

Journal paper

Journal paper

Abstract

BaCuSi2O6 is a quasi-two-dimensional (2D) quantum antiferromagnet containing three different types of stacked, square-lattice bilayer hosting spin-1/2 dimers. Although this compound has been studied extensively over the last two decades, the critical applied magnetic field required to close the dimer spin gap and induce magnetic order, which exceeds 23 T, has to date precluded any kind of neutron scattering investigation. However, the HFM/EXED instrument at the Helmholtz-Zentrum Berlin made this possible at magnetic fields up to 25.9 T. Thus we have used HFM/EXED to investigate the field-induced ordered phase, in particular to look for quasi-2D physics arising from the layered structure and from the different bilayer types. From neutron diffraction data, we determined the global dependence of the magnetic order parameter on both magnetic field and temperature, finding a form consistent with 3D quantum critical scaling; from this we deduce that the quasi-2D interactions and nonuniform layering of BaCuSi2O6 are not anisotropic enough to induce hallmarks of 2D physics. From neutron spectroscopy data, we measured the dispersion of the strongly Zeeman-split magnetic excitations, finding good agreement with the zero-field interaction parameters of BaCuSi2O6. We conclude that HFM/EXED allowed a significant extension in the application of neutron scattering techniques to the field range above 20 T and in particular opened previously unavailable possibilities in the study of field-induced magnetic quantum phase transitions.

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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.

Henrik Moodysson Rønnow, Nikolay Tsyrulin

We present an experimental study of the two-dimensional S=1/2 square-lattice antiferromagnet Cu(pz)(2)(ClO4)(2) (pz denotes pyrazine-C4H4N2) using specific-heat measurements, neutron diffraction, and cold-neutron spectroscopy. The magnetic field dependence of the magnetic ordering temperature was determined from specific-heat measurements for fields perpendicular and parallel to the square-lattice planes, showing identical field-temperature phase diagrams. This suggest that spin anisotropies in Cu(pz)(2)(ClO4)(2) are small. The ordered antiferromagnetic structure is a collinear arrangement with the magnetic moments along either the crystallographic b or c axis. The estimated ordered magnetic moment at zero field is m(0)=0.47 (5)mu(B) and thus much smaller than the available single-ion magnetic moment. This is evidence for strong quantum fluctuations in the ordered magnetic phase of Cu(pz)(2)(ClO4)(2). Magnetic fields applied perpendicular to the square-lattice planes lead to an increase in the antiferromagnetically ordered moment to m(0)=0.93 (5)mu(B) at mu H-0= 13.5 T evidence that magnetic fields quench quantum fluctuations. Neutron spectroscopy reveals the presence of a gapped spin excitations at the antiferromagnetic zone center and it can be explained with a slightly anisotropic nearest-neighbor exchange coupling described by J(xy)(1)= 1.563 (13) meV and J(z)(1) = 0.9979(2)J(1)(xy).

2010Electronic and magnetic properties of quasi-one dimensional ormore widely low-dimensional systems aswell as their related correlated electron phenomena have been at the very frontier of condensed matter physics for quite some time. The reduced dimensionality in these systems offers a unique possibility of direct comparison with model calculations. Furthermore the competing ordered ground states in strongly correlated low-dimensional systems lead to rich phase diagrams comprising many electronic phases, such as superconductivity, charge/spin densitywaves, different electric charge distributions, or a novel formof metalicity. These phases are generically sensitive to a variety of parameters, such as temperature, magnetic field, pressure, a certain degree of irregularity, etc. In this thesis, we employ Electron Spin Resonance (ESR) spectroscopy using strong magnetic fields, high microwave frequencies and high hydrostatic pressure to study a recently discovered family of quasi-one-dimensional organic charge transfer salts, the δ-(EDT-TTF-CONMe2)2X; family to gain insight into the complex physics of strongly correlated low-dimensional compounds. ESR is a highly efficient technique to study organic conductors. This can be easily understood if one realizes that ESR is observable inmost organic conductorswhile only very few "ordinary" metals show detectable ESR signals, even at low temperatures. Indeed, this feature results principally from the electronic low-dimensionality of these systems which controls the spin relaxation process. This tendency is even more reinforced by the fact that most organic molecules only contain light chemical elements for which the effect of the spin-orbit coupling on the ESR linewidth remains small. For this reason, ESR spectroscopy is certainly amajor tool to investigate the paramagnetic state of organic conductors. Moreover, in samples where a magnetic order is present, the large frequency bandwidth of the spectrometers used in the experimental setup (4 GHz–420 GHz) makes the resonance signal accessible at low temperatures in the ordered state, where the resonance frequencywould be too high for conventional ESRspectrometers. Our device hence represents an efficient tool to probe different magnetic ground states and, in particular, the antiferromagnetic state, which is most commonly found in organic salts. Organic conductors exhibit a high degree of sensitivity with respect to magnetic fields and applied pressure. To combine the high sensitivity of the ESR method with the sensitivity and thus fine tuneability of these organic systems by magnetic field and pressure, we build a unique high-field, high-frequency and high-pressure ESR spectrometerwhich is well suited to the study of organic materials. Compared to other devices of its kind, the ESR spectrometer built in our laboratory as a part of this thesis enables a wide parameter space to be explored: magnetic fields from 0 – 16 T, microwave frequencies in the 105 – 420 GHz range and by making use of a custom-made pressure cell, the sample applied pressure can be elevated up to 1.6GPa. To the best of our knowledge, the addition of such a pressure regulating unit to an ESR is unique. Through varying the applied pressure, it can be used to investigate the competition of different ground states: bymodifying the lattice parameters, it can tune the interactions without introducing disorder. The first Part of the thesis is dedicated to a general overview about the physical properties of quasi-one-dimensional organic systems. It also contains a more specific introduction to the crystallographic and electronic properties of the δ-(EDT-TTF-CONMe2)2X family of charge transfer salts. In Part II, we focus on the theoretical description of electronic correlations with a special emphasis on lowdimensional electron systems and on the effect of dimensionality. The objective of this part is to assemble the necessary theoretical notions to understand the phenomena observed in the system under investigation. We show that Coulomb-repulsion in general leads to antiferromagnetism, and give a brief phenomenological description of the antiferromagnetically ordered state. Then, a standard description of the physicalprinciples of Electron Spin Resonance follows. We also give a briefdescription of antiferromagnetic resonance (AFMR) and Conduction Electron Spin Resonance (CESR) with a special focus on quasi-one-dimensional situations. Part III presents the technical details of the ESR spectrometer developed as a part of this thesis. The final Part describes the experimental observations collected during the thesis. In Chapter 9, the phase transitions at atmospheric pressure of a sample of δ-(EDT-TTF-CONMe2)2AsF6 as a function of temperature are presented and discussed. We found a spin-chain behavior at high temperatures and a complicated antiferromagnetic structure below TN=8 K. In the intermediate temperature range we found a suppression of the susceptibility what we explained by the opening of a spin-pseudogap. In Chapter 10, the same procedure is performed for a δ-(EDT-TTF-CONMe2)2Br sample and the findings are really similar to the case of the AsF6 salt. Finally, in Chapter 11, we describe and evaluate measurements performed under high hydrostatic pressure on the δ-(EDT-TTF-CONMe2)2Br sample. We followed the deconfinement transition of the salt and then identified a dimensional crossover from a quasi-one dimensional metal to a more conventional higher dimensional conducting state. At the end of the thesis we drown a general pressure temperature phase diagram of this family of charge transfer salts.