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arXiv:1906.07579 · npj Quantum Materials

Dynamical and thermal magnetic properties of the Kitaev spin liquid candidate α-RuCl3

Pontus Laurell, Satoshi Okamoto

Published Jan 10, 2020• 92 citations
arXivHTMLPDF

Abstract

Abstract What is the correct low-energy spin Hamiltonian description of $$\alpha$$ α -RuCl $$_{3}$$ 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 $$\alpha$$ α -RuCl $$_{3}$$ 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.

DOI
10.1038/s41535-019-0203-y

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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.
Honeycomb-lattice magnet α-RuCl 3 is considered to be a potential candidate of realizing Kitaev spin liquid, although this material undergoes a phase transition to the zigzag magnetically ordered state at T N ∼ 7 K. Quite recently, inelastic neutron-scattering experiments using single crystal α-RuCl 3 have unveiled characteristic dynamical properties. We calculate dynamical spin structure factors of three ab-initio models for α-RuCl 3 with an exact numerical diagonalization method. We also calculate temperature dependences of the specific heat by employing thermal pure quantum states. We compare our numerical results with the experiments and discuss characteristics obtained by using three ab-initio models.
We use an exact numerical diagonalization method to calculate the dynamical spin structure factors of three ab initio models and one ab initio guided model for a honeycomb-lattice magnet $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$. We also use thermal pure quantum states to calculate the temperature dependence of the heat capacity, the nearest-neighbor spin-spin correlation function, and the static spin structure factor. From the results obtained from these four effective models, we find that, even when the magnetic order is stabilized at low temperature, the intensity at the $\mathrm{\ensuremath{\Gamma}}$ point in the dynamical spin structure factors increases with increasing nearest-neighbor spin correlation. In addition, we find that the four models fail to explain heat-capacity measurements whereas two of the four models succeed in explaining inelastic-neutron-scattering experiments. In the four models, when temperature decreases, the heat capacity shows a prominent peak at a high temperature where the nearest-neighbor spin-spin correlation function increases. However, the peak temperature in heat capacity is too low in comparison with that observed experimentally. To address these discrepancies, we propose an effective model that includes strong ferromagnetic Kitaev coupling, and we show that this model quantitatively reproduces both inelastic-neutron-scattering experiments and heat-capacity measurements. To further examine the adequacy of the proposed model, we calculate the field dependence of the polarized terahertz spectra, which reproduces the experimental results: the spin-gapped excitation survives up to an onset field where the magnetic order disappears and the response in the high-field region is almost linear. Based on these numerical results, we argue that the low-energy magnetic excitation in $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$ is mainly characterized by interactions such as off-diagonal interactions and weak Heisenberg interactions between nearest-neighbor pairs, rather than by the strong Kitaev interactions.
Possible effective model with strong Kitaev interaction for α\alphaα-RuCl3{\rm RuCl_3}RuCl3​
We calculate dynamical spin structure factors (DSFs) of three ab-initio models and one ab-initio-guided model for a honeycomb-lattice magnet α\alphaα-RuCl3_33​ with an exact numerical diagonalization method. We also calculate temperature dependences of the heat capacity, the nearest-neighbor (NN) spin-spin correlation function, and the static spin structure factor by employing thermal pure quantum states. From the obtained results for the four effective models, we find that, even when the magnetic order appears at a low temperature, the intensity at the Γ\GammaΓ point in the DSFs grows as the NN spin correlation grows. In addition, we find that the four models fail in explaining the features of both the inelastic-neutron-scattering experiments and the heat capacity measurements. In the four models, when temperature decreases, the heat capacity shows a prominent peak at a high temperature where the nearest-neighbor spin-spin correlation function grows. However, the peak temperatures in the heat capacity are too low in comparison with the observed values in the experiments. Thus, we propose an effective model with the strong ferromagnetic Kitaev coupling. We show that the proposed model quantitatively reproduces the above two experimental features. To discuss the further adequacy of the proposed model, we calculate the field dependence of the polarized terahertz spectra. We find that the proposed model successfully reproduces the experimental results: the spin-gapped excitation surviving up to an onset field where the magnetic order disappears and the almost linear response in the high field region. From the obtained numerical results, we argue that the feature of the low-energy magnetic excitation in α\alphaα-RuCl3_33​ is mainly characterized by the other interactions rather than the most dominant Kitaev interactions such as the off-diagonal interactions on the nearest-neighbor pairs.
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 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.
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.