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arXiv:2006.02428 · Physical Review Letters

Thermodynamic Perspective on Field-Induced Behavior of α−RuCl3

Sebastian Bachus, David A. S. Kaib, Y. Tokiwa, Anton Jesche, V. Tsurkan, Alois Loidl, Stephen M. Winter, Alexander A. Tsirlin, Roser Valentí, P. Gegenwart

Published Aug 25, 2020• 56 citations
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Abstract

Measurements of the magnetic Gr\"uneisen parameter (${\mathrm{\ensuremath{\Gamma}}}_{B}$) and specific heat on the Kitaev material candidate $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$ are used to access in-plane field and temperature dependence of the entropy up to 12 T and down to 1 K. No signatures corresponding to phase transitions are detected beyond the boundary of the magnetically ordered region, but only a shoulderlike anomaly in ${\mathrm{\ensuremath{\Gamma}}}_{B}$, involving an entropy increment as small as ${10}^{\ensuremath{-}5}R\mathrm{log}2$. These observations put into question the presence of a phase transition between the purported quantum spin liquid and the field-polarized state of $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$. We show theoretically that at low temperatures ${\mathrm{\ensuremath{\Gamma}}}_{B}$ is sensitive to crossings in the lowest excitations within gapped phases, and identify the measured shoulderlike anomaly as being of such origin. Exact diagonalization calculations demonstrate that the shoulderlike anomaly can be reproduced in extended Kitaev models that gain proximity to an additional phase at finite field without entering it. We discuss manifestations of this proximity in other measurements.

DOI
10.1103/physrevlett.125.097203

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Measurements of the magnetic Gr"uneisen parameter (\ensuremathΓB{\mathrm{\ensuremath{\Gamma}}}_{B}\ensuremathΓB​) and specific heat on the Kitaev material candidate \ensuremathα\ensuremath-RuCl3\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}\ensuremathα\ensuremath-RuCl3​ are used to access in-plane field and temperature dependence of the entropy up to 12 T and down to 1 K. No signatures corresponding to phase transitions are detected beyond the boundary of the magnetically ordered region, but only a shoulderlike anomaly in \ensuremathΓB{\mathrm{\ensuremath{\Gamma}}}_{B}\ensuremathΓB​, involving an entropy increment as small as 10\ensuremath−5Rlog2{10}^{\ensuremath{-}5}R\mathrm{log}210\ensuremath−5Rlog2. These observations put into question the presence of a phase transition between the purported quantum spin liquid and the field-polarized state of \ensuremathα\ensuremath-RuCl3\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}\ensuremathα\ensuremath-RuCl3​. We show theoretically that at low temperatures \ensuremathΓB{\mathrm{\ensuremath{\Gamma}}}_{B}\ensuremathΓB​ is sensitive to crossings in the lowest excitations within gapped phases, and identify the measured shoulderlike anomaly as being of such origin. Exact diagonalization calculations demonstrate that the shoulderlike anomaly can be reproduced in extended Kitaev models that gain proximity to an additional phase at finite field without entering it. We discuss manifestations of this proximity in other measurements.
The pursuit of quantum spin liquid (QSL) in the Kitaev honeycomb magnets has drawn intensive attention recently. In particular, $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$ has been widely recognized as a promising candidate for the Kitaev QSL. Although the compound exhibits an antiferromagnetic order under zero field, it is believed to be endowed with fractionalized excitations and can be driven to the QSL phase by magnetic fields. Here, based on a realistic $K\text{\ensuremath{-}}J\text{\ensuremath{-}}\mathrm{\ensuremath{\Gamma}}\text{\ensuremath{-}}{\mathrm{\ensuremath{\Gamma}}}^{\ensuremath{'}}$ model for $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$, we exploit the exponential tensor renormalization group approach to explore the phase diagram of the compound under magnetic fields. We calculate the thermodynamic quantities, including the specific heat, Gr\"uneisen parameter, magnetic torque, magnetotropic susceptibility, and so on, under a magnetic field with a tilting angle $\ensuremath{\theta}$ to the c∗{c}^{*}c∗-axis perpendicular to the honeycomb plane. We find an extended QSL in the angle-field phase diagram determined with thermodynamic responses. The gapless nature of such field-induced QSL is identified from the specific heat and entropy data computed down to very low temperatures. The present study provides guidance for future high-field experiments for the QSL in $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$ and other candidate Kitaev magnets.
Abstract The frustrated magnetα-RuCl3constitutes a fascinating quantum material platform that harbors the intriguing Kitaev physics. However, a consensus on its intricate spin interactions and field-induced quantum phases has not been reached yet. Here we exploit multiple state-of-the-art many-body methods and determine the microscopic spin model that quantitatively explains major observations inα-RuCl3, including the zigzag order, double-peak specific heat, magnetic anisotropy, and the characteristic M-star dynamical spin structure, etc. According to our model simulations, the in-plane field drives the system into the polarized phase at about 7 T and a thermal fractionalization occurs at finite temperature, reconciling observations in different experiments. Under out-of-plane fields, the zigzag order is suppressed at 35 T, above which, and below a polarization field of 100 T level, there emerges a field-induced quantum spin liquid. The fractional entropy and algebraic low-temperature specific heat unveil the nature of a gapless spin liquid, which can be explored in high-field measurements onα-RuCl3.
Abstract The frustrated magnet α-RuCl3 constitutes a fascinating quantum material platform that harbors the intriguing Kitaev physics. However, a consensus on its intricate spin interactions and field-induced quantum phases has not been reached yet. Here we exploit multiple state-of-the-art many-body methods and determine the microscopic spin model that quantitatively explains major observations in α-RuCl3, including the zigzag order, double-peak specific heat, magnetic anisotropy, and the characteristic M-star dynamical spin structure, etc. According to our model simulations, the in-plane field drives the system into the polarized phase at about 7 T and a thermal fractionalization occurs at finite temperature, reconciling observations in different experiments. Under out-of-plane fields, the zigzag order is suppressed at 35 T, above which, and below a polarization field of 100 T level, there emerges a field-induced quantum spin liquid. The fractional entropy and algebraic low-temperature specific heat unveil the nature of a gapless spin liquid, which can be explored in high-field measurements on α-RuCl3.
Abstract What is the correct low-energy spin Hamiltonian description of α\alphaα α -RuCl 3_{3}3​ 3 ? The material is a promising Kitaev spin liquid candidate, but is also known to order magnetically, the description of which necessitates additional interaction terms. The nature of these interactions, their magnitudes and even signs, remain an open question. In this work we systematically investigate dynamical and thermodynamic magnetic properties of proposed effective Hamiltonians. We calculate zero-temperature inelastic neutron scattering (INS) intensities using exact diagonalization, and magnetic specific heat using a thermal pure quantum states method. We find that no single current model satisfactorily explains all observed phenomena of α\alphaα α -RuCl 3_{3}3​ 3 . In particular, we find that Hamiltonians derived from first principles can capture the experimentally observed high-temperature peak in the magnetic specific heat, while overestimating the magnon energy at the zone center. In contrast, other models reproduce important features of the INS data, but do not adequately describe the magnetic specific heat. To address this discrepancy we propose a modified ab initio model that is consistent with both magnetic specific heat and low-energy features of INS data.
High-field fate of the Kitaev quantum spin liquid in ααα-RuCl3_33​
Kitaev quantum spin liquids (KQSLs) host fractionalized excitations described by itinerant Majorana quasiparticles and gapped Z2Z_2Z2​ fluxes (visons), providing a platform for emergent topological matter. Whether such a state survives under strong magnetic fields, however, remains an open question. The layered honeycomb magnet ααα-RuCl3_33​ is a leading candidate material: an in-plane field of ∼\sim∼ 7 T suppresses antiferromagnetic order and induces a quantum-disordered phase exhibiting signatures consistent with Majorana excitations, including an anomalous thermal Hall effect and field-angle-dependent specific heat. At higher fields, the magnetization approaches saturation, suggesting a transition to a spin-polarized state, yet the microscopic evolution between these limits remains unresolved. Here we report high-field specific heat measurements up to 24 T that reveal a distinct crossover at $μ_0H^*\approx$15 T, beyond which the perturbative Kitaev description breaks down. Above H∗H^*H∗, the characteristic six-fold angular modulation of the specific heat collapses and the excitation gap deviates from the predicted H3H^3H3 scaling. Meanwhile, the gap decreases with increasing field and the in-plane magnetization anisotropy persists up to ∼\sim∼ 24 T, both in sharp contrast to a trivial spin-polarized state, indicating that KQSL signatures are preserved even at ∼\sim∼ 90 % of magnetization saturation. These results reveal that the KQSL in ααα-RuCl3_33​ extends well beyond the perturbative window, persisting as a nonperturbative regime in which the Majorana and vison energy scales merge, before eventually giving way to spin polarization. This thermodynamic roadmap provides a basis for understanding how fractionalized phases evolve under strong magnetic fields.
It is known that α-RuCl3 has been studied extensively because of its proximity to the Kitaev quantum-spin-liquid (QSL) phase and the possibility of approaching it by tuning the competing interactions. Here we present the first polarized inelastic neutron scattering study on α-RuCl3 single crystals to explore the scattering continuum around the Γ point at the Brillouin zone center, which was hypothesized to be resulting from the Kitaev QSL state but without concrete evidence. With polarization analyses, we find that, while the spin-wave excitations around the M point vanish above the transition temperature T N, the pure magnetic continuous excitations around the Γ point are robust against temperature. Furthermore, by calculating the dynamical spin-spin correlation function using the cluster perturbation theory, we derive magnetic dispersion spectra based on the K–Γ model, which involves with a ferromagnetic Kitaev interaction of –7.2 meV and an off-diagonal interaction of 5.6 meV. We find this model can reproduce not only the spin-wave excitation spectra around the M point, but also the non-spin-wave continuous magnetic excitations around the Γ point. These results provide evidence for the existence of fractional excitations around the Γ point originating from the Kitaev QSL state, and further support the validity of the K–Γ model as the effective minimal spin model to describe α-RuCl3.