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Register a new userField-induced phase transitions of the Kitaev material $alpha$-RuCl$_3$ probed by thermal expansion and magnetostriction
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High-resolution thermal expansion and magnetostriction measurements were performed on single crystals of $alpha$-RuCl$_3$ in magnetic fields applied parallel to the Ru-Ru bonds. The length changes were measured in the direction perpendicular to the honeycomb planes. Our data show clear thermodynamic characteristics for the field-induced phase transition at the critical field $mu_0H_{c1} = 7.8(2)$ T where the antiferromagnetic zigzag order is suppressed. At higher fields, a kink in the magnetostriction coefficient signals an additional phase transition around $mu_0H_{c2} approx 11$ T. The extracted Gruneisen parameter shows typical hallmarks for quantum criticality near $H_{c1}$, but also displays anomalous behavior above $H_{c1}$. We compare our experimental data with linear spin-wave calculations employing a minimal Kitaev-Heisenberg model in the semiclassical limit. Most of the salient features are in agreement with each other, however, the peculiar features in the high-field region above $H_{c1}$ cannot be accounted for in our modelling and hence suggest a genuine quantum nature. We construct a phase diagram for $alpha$-RuCl$_3$ showing two low-temperature transitions induced by an in-plane field along the Ru-Ru bonds.
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Recently, $alpha$-$textrm{RuCl}_3$ has attracted much attention as a possible material realization of the honeycomb Kitaev model, which may stabilize a quantum-spin-liquid state. Compared to extensive studies on its magnetic properties, there is still a lack of understanding on its electronic structure, which is strongly related with its Kitaev physics. Here, the electronic structure of $alpha$-$textrm{RuCl}_3$ is investigated by photoemission (PE) and inverse photoemission (IPE) spectroscopies. The band gap, directly measured from PE/IPE spectra, is found to be 1.9 eV, much larger than previous estimations. The LDA calculations show that the on-site Coulomb interaction $textit{U}$ can open the band gap without spin-orbit coupling (SOC). However, the SOC should also be incorporated to reproduce the proper gap size, indicating that the interplay between $textit{U}$ and SOC plays an essential role in the physics of $alpha$-$textrm{RuCl}_3$. There exist some spectral features in PE/IPE spectra which cannot be explained by the LDA calculations. To explain such discrepancies, we perform the configuration-interaction calculations for a ${textrm{RuCl}}_6^{3-}$ cluster. The experimental data and calculations demonstrate that the 4$textit{d}$ compound $alpha$-$textrm{RuCl}_3$ is a $J_{textrm{eff}}$ = 1/2 Mott insulator rather than a quasimolecular-orbital insulator. Our study also provides important physical parameters, required in verifying the proposed Kitaev physics in $alpha$-$textrm{RuCl}_3$.
$alpha$-RuCl$_3$ has attracted enormous attention since it has been proposed as a prime candidate to study fractionalized magnetic excitations akin to Kitaevs honeycomb-lattice spin liquid. We have performed a detailed specific-heat investigation at temperatures down to $0.4$ K in applied magnetic fields up to $9$ T for fields parallel to the $ab$ plane. We find a suppression of the zero-field antiferromagnetic order, together with an increase of the low-temperature specific heat, with increasing field up to $mu_0H_capprox 6.9$ T. Above $H_c$, the magnetic contribution to the low-temperature specific heat is strongly suppressed, implying the opening of a spin-excitation gap. Our data point toward a field-induced quantum critical point (QCP) at $H_c$; this is supported by universal scaling behavior near $H_c$. Remarkably, the data also reveal the existence of a small characteristic energy scale well below $1$~meV above which the excitation spectrum changes qualitatively. We relate the data to theoretical calculations based on a $J_1$--$K_1$--$Gamma_1$--$J_3$ honeycomb model.
Heat transport mediated by Majorana edge modes in a magnetic insulator leads to a half-integer thermal quantum Hall conductance, which has recently been reported for the two-dimensional honeycomb material $alpha$-RuCl$_3$. While the conventional electronic Hall effect requires a perpendicular magnetic field, we find that this is not the case in $alpha$-RuCl$_3$. Strikingly, the thermal Hall plateau appears even for a magnetic field with no out-of-plane components. The field-angular variation of the quantized thermal Hall conductance has the same sign structure of the topological Chern number, which is either $pm$1, as the Majorana band structure of the pure Kitaev spin liquid. This observation of a half-integer anomalous thermal Hall effect firmly establishes that the Kitaev interaction is primarily responsible and that the non-Abelian topological order associated with fractionalization of the local magnetic moments persists even in the presence of non-Kitaev interactions in $alpha$-RuCl$_3$.
We study on transport and magnetic properties of hydrated and lithium-intercalated $alpha$-RuCl$_3$, Li$_x$RuCl$_3 cdot y$H$_2$O, for investigating the effect on mobile-carrier doping into candidate materials for a realization of a Kitaev model. From thermogravitometoric and one-dimensional electron map analyses, we find two crystal structures of this system, that is, mono-layer hydrated Li$_x$RuCl$_3 cdot y$H$_2$O~$(xapprox0.56, yapprox1.3)$ and bi-layer hydrated Li$_x$RuCl$_3 cdot y$H$_2$O~$(xapprox0.56, yapprox3.9)$. The temperature dependence of the electrical resistivity shows a temperature hysteresis at 200-270 K, which is considered to relate with a formation of a charge order. The antiferromagnetic order at 7-13 K in pristine $alpha$-RuCl$_3$~ is successfully suppressed down to 2 K in bi-layer hydrated Li$_x$RuCl$_3 cdot y$H$_2$O, which is sensitive to not only an electronic state of Ru but also an interlayer distance between Ru-Cl planes.
We use the constrained random phase approximation (cRPA) to derive from first principles the Ru-$t_{2g}$ Wannier function based model for the Kitaev spin-liquid candidate material $alpha$-RuCl$_3$. We find the non-local Coulomb repulsion to be sizable compared to the local one. In addition we obtain the contribution to the Hamiltonian from the spin-orbit coupling and find it to also contain non-negligible non-local terms. We invoke strong coupling perturbation theory to investigate the influence of these non-local elements of the Coulomb repulsion and the spin-orbit coupling on the magnetic interactions. We find that the non-local Coulomb repulsions cause a strong enhancement of the magnetic interactions, which deviate from experimental fits reported in the literature. Our results contribute to the understanding and design of quantum spin liquid materials via first principles calculations.
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