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Register a new userUnusual thermal Hall effect in a Kitaev spin liquid candidate $alpha$-RuCl$_3$
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The Kitaev quantum spin liquid displays the fractionalization of quantum spins into Majorana fermions. The emergent Majorana edge current is predicted to manifest itself in the form of a finite thermal Hall effect, a feature commonly discussed in topological superconductors. Here we report on thermal Hall conductivity $kappa_{xy}$ measurements in $alpha$-RuCl$_3$, a candidate Kitaev magnet with the two-dimensional honeycomb lattice. In a spin-liquid (Kitaev paramagnetic) state below the temperature characterized by the Kitaev interaction $J_K/k_B sim 80$ K, positive $kappa_{xy}$ develops gradually upon cooling, demonstrating the presence of highly unusual itinerant excitations. Although the zero-temperature property is masked by the magnetic ordering at $T_N=7$ K, the sign, magnitude, and $T$-dependence of $kappa_{xy}/T$ at intermediate temperatures follows the predicted trend of the itinerant Majorana excitations.
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We have investigated the sample dependence of the half-integer thermal Hall effect in $alpha$-RuCl$_3$ under a magnetic field tilted 45 degree from the $c$ axis to the $a$ axis. We find that the sample with the largest longitudinal thermal conductivity ($kappa_{xx}$) shows the half-integer quantized thermal Hall effect expected in the Kitaev model. On the other hand, the quantized thermal Hall effect was not observed in the samples with smaller $kappa_{xx}$. We suggest that suppressing the magnetic scattering effects on the phonon thermal conduction, which broaden the field-induced gap protecting the chiral edge current of the Majorana fermions, is important to observe the quantized thermal Hall effect.
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.
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 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.
The honeycomb Kitaev model in a magnetic field is a source of a topological quantum spin liquid with Majorana fermions and gauge flux excitations as fractional quasiparticles. We present experimental results for the thermal Hall effect of the material $alpha$-RuCl$_{3}$ which recently emerged as a prime candidate for realizing such physics. At temperatures above long-range magnetic ordering $Tgtrsim T_Napprox8$ K, we observe with an applied magnetic field $B$ perpendicular to the honeycomb layers a sizeable positive transversal heat conductivity $kappa_{xy}$ which increases linearly with $B$. Upon raising the temperature, $kappa_{xy}(T)$ increases strongly, exhibits a broad maximum at around 30 K, and eventually becomes negligible at $Tgtrsim 125$ K. Remarkably, the longitudinal heat conductivity $kappa_{xx}(T)$ exhibits a sizeable positive thermal magnetoresistance effect. Thus, our findings provide clear-cut evidence for longitudinal and transverse magnetic heat transport and underpin the unconventional nature of the quasiparticles in the paramagnetic phase of $alpha$-RuCl$_{3}$.
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