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Publication# A quantum magnetic analogue to the critical point of water

Résumé

At the liquid-gas phase transition in water, the density has a discontinuity at atmospheric pressure; however, the line of these first-order transitions defined by increasing the applied pressure terminates at the critical point(1), a concept ubiquitous in statistical thermodynamics(2). In correlated quantum materials, it was predicted(3) and then confirmed experimentally(4,5) that a critical point terminates the line of Mott metal-insulator transitions, which are also first-order with a discontinuous charge carrier density. In quantum spin systems, continuous quantum phase transitions(6) have been controlled by pressure(7,8), applied magnetic field(9,10) and disorder(11), but discontinuous quantum phase transitions have received less attention. The geometrically frustrated quantum antiferromagnet SrCu2(BO3)(2) constitutes a near-exact realization of the paradigmatic Shastry-Sutherland model(12-14) and displays exotic phenomena including magnetization plateaus(15), low-lying bound-state excitations(16), anomalous thermodynamics(17) and discontinuous quantum phase transitions(18,19). Here we control both the pressure and the magnetic field applied to SrCu2(BO3)(2) to provide evidence of critical-point physics in a pure spin system. We use high-precision specific-heat measurements to demonstrate that, as in water, the pressure-temperature phase diagram has a first-order transition line that separates phases with different local magnetic energy densities, and that terminates at an Ising critical point. We provide a quantitative explanation of our data using recently developed finite-temperature tensor-network methods(17,20-22). These results further our understanding of first-order quantum phase transitions in quantum magnetism, with potential applications in materials where anisotropic spin interactions produce the topological properties(23,24) that are useful for spintronic applications.

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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.

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.

This work is devoted to the study of spin S = 1 systems, and more precisely to the emergence of exotic quantum phases in such systems, and to the establishment of tools to observe such phases. It is split in four main chapters. In the first chapter, we show how spin S = 1 systems can emerge from microscopic models, and which kinds of interaction might appear in the effective spin model. We start from a two-orbital Hubbard model, and by a strong coupling development to fourth order, we derive an effective model. We will see that three types of interaction appear beyond the Heisenberg interaction : a plaquette interaction, a biquadratic interaction and a three-spin interaction. In the second chapter, we study Raman scattering on systems with quadrupolar order to show that it can be used to probe such order. We first start by deriving an effective light scattering operator following Shastry and Shraiman calculation on spin S = 1/2 systems. Using this effective operator, we compute the Raman spectra with exact diagonalization and linear flavor-wave theory. We show that two different regimes appear depending on the incoming photon energy, and that combining this to different polarizations accessible with Raman scattering, the presence of quadrupolar order can be established with this probe. The third chapter is devoted to the study of the three-spin interaction that appeared in the first chapter on a chain. We start by establishing the classical and the mean field phase diagram of this system. We then turn to the quantum case. We show that, whatever the value of the spin is, the ground state is perfectly dimerized for a particular value of the three-spin interaction. The presence of such a point in the phase diagram implies the existence of a quantum phase transition when increasing the three-spin interaction. By an intensive numerical study, we show that this transition is continuous, and that its critical behavior is the one of a SU(2)k=2S Wess-Zumino-Witten model, at least for spins S = 1/2,1,3/2,2. In the last section of this chapter, we study the phase diagram of the chain for spin S = 1 under a magnetic field. We conclude this work with a study of the three-spin interaction on a square lattice. The classical and mean field phase diagram are established. It is shown that for a large three-spin interaction, the classical ground state is highly degenerate. This degeneracy is lifted in the quantum case by a process of order by disorder. We compute the quantum fluctuations with linear spin-wave theory, and show that some phases are selected over others. We confirm these results by an exact diagonalization study of the system.