Frustration and Randomness | EPFL Graph Search

Spin systems with strong magnetic interactions might remain disordered avoiding conventional magnetic long-range ordering due to zero-point quantum fluctuations, and supporting a Quantum Spin Liquid (QSL) state. Long-range quantum entanglement in QSLs promotes the emergence of non-local excitations and topological properties, unveiling unexplored quantum phenomena. The immense fundamental interest in this exotic phase of matter evinces the need for new crystalline designs and novel combinations of experimental methods in the study of QSLs. The present PhD thesis focuses on two organic low-dimensional charge-transfer salt families that might host Quantum Spin Liquid states due to geometrical frustration and designedly introduced randomness. Using the combination of multi-frequency high-field Electron Spin Resonance (ESR) and Muon Spin Rotation ( $\mu$ SR) techniques supplemented by $^1$ H Nuclear Magnetic Resonance and transport studies, I propose that organic frustrated magnetic systems are severely affected by the anion layers and by the weak antisymmetric exchange, the so-called Dzyaloshinskii-Moriya (DM) interaction. Amongst crystalline hybrid conductor-rotor structures comprising Brownian rotator anion layers, I survey experimentally four different materials illustrating a variety of magnetic ground states depending on their dimensionalities and interactions with the rotor components. In quasi-one-dimensional weakly coupled spin chain systems, the presence of the controlled disorder originating from the slowing-down of rotators creates a spin-gapped or long-range antiferromagnetically ordered ground state depending on the spatial relation of the anion and the spin-bearing cation layers. Remarkably, inhomogeneous distribution of the disorder of the rotor stopping positions induces a broad distribution of the N'{e}el temperatures at the microscopic length scales. In contrast, two quasi-one-dimensional distorted triangular lattice systems are identified as QSL candidates. In particular, low-temperature zero-field $\mu$ SR and high-field ESR measurements in (EDT-TTF-CONH $_2$ ) $_2^{+}$ [BABCO $^{-}$ ] (EDT-BCO) confirmed the absence of magnetic ordering down to 20 mK despite large, $J/k_{\text{B}}=365$ K nearest-neighbor antiferromagnetic exchange interactions and a moderate anisotropy of $t'/t=1.6$ of the interdimer transfer integrals. The linear field dependence of the ESR linewidth, i.e., the spectral density of the fluctuations, manifests fast spin excitations, reminiscent of motional narrowing. Despite a sizable DM interaction of 0.8 T suggested theoretically, the ESR lineshape remains unchanged down to 1.5 K, indicating the suppression of the effect of DM interaction. Longitudinal-field $\mu$ SR measurements reveal one-dimensional diffusive spin transport in EDT-BCO, and predominant fluctuations at the staggered component corresponding to the wave vector of $q=\pi/a$ . For comparison, I investigate the antisymmetric exchange in a nearly isotropic triangular lattice organic QSL candidate, $\kappa$ -(BEDT-TTF) $_2$ Ag $_2$ (CN) $_3$ ( $\kappa$ -Ag, $J/k_{\text{B}}=175$ K, $t'/t=0.97$ ). The recently discovered sister compound of the first two-dimensional QSL ( $\kappa$ -(BEDT-TTF) $_2$ Cu $_2$ (CN) $_3$ ) displays a spin liquid-superconductor phase transition above a critical pressure of $p_{\text{c}}>0.9$ GPa ( $T_{\text{c}}=5.2$ K). In $\kappa$ -Ag, multi-frequency and angle-dependent ambient-pressure ESR studies found large antiferromagnetic fluctuations, and a staggered moment of $\mu_{\text{s}}=6\cdot 10^{-3}$ $\mu_{\text{B}}$ at 2 K and at 15 T. Via globally fitting the field- and temperature-dependence of the ESR linewidth using the one-dimensional field theory of Oshikawa and Affleck, I assigned $\mu_{\text{s}}$ to a DM interaction of 1.2 T, weakly suppressed compared to its theoretical value of 5.5 T. Nevertheless, high-pressure multi-frequency ESR measurements reveal that the effect of the DM interaction is completely quenched with a moderate pressure of $p_{\text{DM}}=$ 0.3 GPa, as a result of moving away from the spiral-ordered phase. Above $p_{\text{DM}}$ Spin systems with strong magnetic interactions might remain disordered avoiding conventional magnetic long-range ordering due to zero-point quantum fluctuations, and supporting a Quantum Spin Liquid (QSL) state. Long-range quantum entanglement in QSLs promotes the emergence of non-local excitations and topological properties, unveiling unexplored quantum phenomena. The immense fundamental interest in this exotic phase of matter evinces the need for new crystalline designs and novel combinations of experimental methods in the study of QSLs. The present PhD thesis focuses on two organic low-dimensional charge-transfer salt families that might host Quantum Spin Liquid states due to geometrical frustration and designedly introduced randomness. Using the combination of multi-frequency high-field Electron Spin Resonance (ESR) and Muon Spin Rotation ( $\mu$ SR) techniques supplemented by $^1$ H Nuclear Magnetic Resonance and transport studies, I propose that organic frustrated magnetic systems are severely affected by the anion layers and by the weak antisymmetric exchange, the so-called Dzyaloshinskii-Moriya (DM) interaction. Amongst crystalline hybrid conductor-rotor structures comprising Brownian rotator anion layers, I survey experimentally four different materials illustrating a variety of magnetic ground states depending on their dimensionalities and interactions with the rotor components. In quasi-one-dimensional weakly coupled spin chain systems, the presence of the controlled disorder originating from the slowing-down of rotators creates a spin-gapped or long-range antiferromagnetically ordered ground state depending on the spatial relation of the anion and the spin-bearing cation layers. Remarkably, inhomogeneous distribution of the disorder of the rotor stopping positions induces a broad distribution of the Néel temperatures at the microscopic length scales. In contrast, two quasi-one-dimensional distorted triangular lattice systems are identified as QSL candidates. In particular, low-temperature zero-field $\mu$ SR and high-field ESR measurements in (EDT-TTF-CONH $_2$ ) $_2^{+}$ [BABCO $^{-}$ ] (EDT-BCO) confirmed the absence of magnetic ordering down to 20 mK despite large, $J/k_{\text{B}}=365$ K nearest-neighbor antiferromagnetic exchange interactions and a moderate anisotropy of $t'/t=1.6$ of the interdimer transfer integrals. The linear field dependence of the ESR linewidth, i.e., the spectral density of the fluctuations, manifests fast spin excitations, reminiscent of motional narrowing. Despite a sizable DM interaction of 0.8 T suggested theoretically, the ESR lineshape remains unchanged down to 1.5 K, indicating the suppression of the effect of DM interaction. Longitudinal-field $\mu$ SR measurements reveal one-dimensional diffusive spin transport in EDT-BCO, and predominant fluctuations at the staggered component corresponding to the wave vector of $q=\pi/a$ . For comparison, I investigate the antisymmetric exchange in a nearly isotropic triangular lattice organic QSL candidate, $\kappa$ -(BEDT-TTF) $_2$ Ag $_2$ (CN) $_3$ ( $\kappa$ -Ag, $J/k_{\text{B}}=175$ K, $t'/t=0.97$ ). The recently discovered sister compound of the first two-dimensional QSL ( $\kappa$ -(BEDT-TTF) $_2$ Cu $_2$ (CN) $_3$ ) displays a spin liquid-superconductor phase transition above a critical pressure of $p_{\text{c}}>0.9$ GPa ( $T_{\text{c}}=5.2$ K). In $\kappa$ -Ag, multi-frequency and angle-dependent ambient-pressure ESR studies found large antiferromagnetic fluctuations, and a staggered moment of $\mu_{\text{s}}=6\cdot 10^{-3}$ $\mu_{\text{B}}$ at 2 K and at 15 T. Via globally fitting the field- and temperature-dependence of the ESR linewidth using the one-dimensional field theory of Oshikawa and Affleck, I assigned $\mu_{\text{s}}$ to a DM interaction of 1.2 T, weakly suppressed compared to its theoretical value of 5.5 T. Nevertheless, high-pressure multi-frequency ESR measurements reveal that the effect of the DM interaction is completely quenched with a moderate pressure of $p_{\text{DM}}=$ 0.3 GPa, as a result of moving away from the spiral-ordered phase. Above $p_{\text{DM}}$ , a linear field dependence and fast spin fluctuations are found, similarly to the ambient-pressure EDT-BCO. Furthermore, detailed analysis of the high-pressure ESR linewidth gives evidence of the effect of high pressure upon inherent charge fluctuations.

Emergence and Detection of Exotic Phases in Spin-1 Systems

Frédéric Alexis Michaud

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.

EPFL2013

Possible spin-orbit driven spin-liquid ground state in the double perovskite phase of Ba

Arash Alahgholipour Omrani, Henrik Moodysson Rønnow

We report the structural transformation of hexagonal Ba3YIr 2O9 to a cubic double perovskite form (stable in ambient conditions) under an applied pressure of 8 GPa at 1273 K. While the ambient pressure synthesized sample undergoes long-range magnetic ordering at ∼4 K, the high-pressure (HP) synthesized sample does not order down to 2 K as evidenced from our susceptibility, heat capacity, and nuclear magnetic resonance (NMR) measurements. Further, for the HP sample, our heat capacity data have the form γT+βT3 in the temperature (T) range of 2-10 K with the Sommerfeld coefficient γ=10 mJ/mol-Ir K2. The 89Y NMR shift has no T dependence in the range of 4-120 K and its spin-lattice relaxation rate varies linearly with T in the range of 8-45 K (above which it is T independent). Resistance measurements of both the samples confirm that they are semiconducting. Our data provide evidence for the formation of a 5d-based, gapless, quantum spin-liquid in the cubic (HP) phase of Ba3YIr 2O9. In this picture, the γT term in the heat capacity and the linear variation of 89Y 1/T1 arises from excitations out of a spinon Fermi surface. Our findings lend credence to the theoretical suggestion that strong spin-orbit coupling can enhance quantum fluctuations and lead to a QSL state in the double perovskite lattice. © 2013 American Physical Society.

2013

SrCu2(BO3)(2) under pressure: A first-principles study

Frédéric Mila

Using density-functional theory (DFT) band-structure calculations, we study the crystal structure, lattice dynamics, and magnetic interactions in the Shastry-Sutherland magnet SrCu2(BO3)(2) under pressure, concentrating on experimentally relevant pressures up to 4 GPa. We first check that a ferromagnetic spin alignment shortens the nearest-neighbor Cu-Cu distance and reduces the Cu-O-Cu angle compared to the state with the antiferromagnetic spin alignment in the dimers, in qualitative agreement with the structural changes observed at ambient pressure as a function of temperature and applied field. Next, we determine the optimal crystal structures corresponding to the magnetic structures consistent with, respectively, the dimer phase realized at ambient pressure, the Neel ordered phase realized at high pressure, and two candidates for the intermediate phase with two types of dimers and different stackings. For each phase, we performed a systematic study as a function of pressure, and we determined the exchange interactions and the frequencies of several experimentally relevant phonon modes. In the dimer phase, the ratio of the inter- to intradimer couplings is found to increase with pressure, in qualitative agreement with various experiments. This increase is mostly due to the decrease of the intradimer coupling due to the reduction of the Cu-O-Cu angle under pressure. The phonon frequency of the pantograph mode is also found to increase with pressure, in qualitative agreement with recent Raman experiments. In the Neel phase, the frequency of the pantograph mode is larger than the extrapolated value from the dimer phase, again in agreement with the experimental results, and accordingly the intradimer coupling is smaller than the extrapolated value from the dimer phase. Finally, all tendencies inside the candidate intermediate phases are thoroughly worked out, including specific predictions for some Raman active phonon modes that could be used to pin down the nature of the intermediate phase.