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Large field-induced gap of Kitaev-Heisenberg paramagnons in $alpha$-RuCl$_{3}$

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 Added by Richard Hentrich
 Publication date 2017
  fields Physics
and research's language is English




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The honeycomb Kitaev-Heisenberg model is a source of a quantum spin liquid with Majorana fermions and gauge flux excitations as fractional quasiparticles. In the quest of finding a pertinent material, $alpha$-RuCl$_{3}$ recently emerged as a prime candidate. Here we unveil highly unusual low-temperature heat conductivity $kappa$ of $alpha$-RuCl$_{3}$: beyond a magnetic field of $B_capprox$ 7.5 T, $kappa$ increases by about one order of magnitude, resulting in a large magnetic field dependent peak at about 7 K, both for in-plane as well as out-of-plane transport. This clarifies the unusual magnetic field dependence unambiguously to be the result of severe scattering of phonons off putative Kitaev-Heisenberg excitations in combination with a drastic field-induced change of the magnetic excitation spectrum. In particular, an unexpectedly large energy gap arises, which increases approximately linearly with the magnetic field and reaches a remarkably large $hbaromega_0/k_Bapprox $ 50 K at 18 T.



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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$_{3}$.
$alpha$-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.
$alpha$-RuCl$_{3}$ is a major candidate for the realization of the Kitaev quantum spin liquid, but its zigzag antiferromagnetic order at low temperatures indicates deviations from the Kitaev model. We have quantified the spin Hamiltonian of $alpha$-RuCl$_{3}$ by a resonant inelastic x-ray scattering study at the Ru $L_{3}$ absorption edge. In the paramagnetic state, the quasi-elastic intensity of magnetic excitations has a broad maximum around the zone center without any local maxima at the zigzag magnetic Bragg wavevectors. This finding implies that the zigzag order is fragile and readily destabilized by competing ferromagnetic correlations. The classical ground state of the experimentally determined Hamiltonian is actually ferromagnetic. The zigzag state is stabilized via a quantum order by disorder mechanism, leaving ferromagnetism -- along with the Kitaev spin liquid -- as energetically proximate metastable states. The three closely competing states and their collective excitations hold the key to the theoretical understanding of the unusual properties of $alpha$-RuCl$_{3}$ in magnetic fields.
$alpha$-RuCl$_3$ is drawing much attention as a promising candidate Kitaev quantum spin liquid. However, despite intensive research efforts, controversy remains about the form of the basic interactions governing the physics of this material. Even the sign of the Kitaev interaction (the bond-dependent anisotropic interaction responsible for Kitaev physics) is still under debate, with conflicting results from theoretical and experimental studies. The significance of the symmetric off-diagonal exchange interaction (referred to as the $Gamma$ term) is another contentious question. Here, we present resonant elastic x-ray scattering data that provides unambiguous experimental constraints to the two leading terms in the magnetic interaction Hamiltonian. We show that the Kitaev interaction ($K$) is ferromagnetic, and that the $Gamma$ term is antiferromagnetic and comparable in size to the Kitaev interaction. Our findings also provide a natural explanation for the large anisotropy of the magnetic susceptibility in $alpha$-RuCl$_3$ as arising from the large $Gamma$ term. We therefore provide a crucial foundation for understanding the interactions underpinning the exotic magnetic behaviours observed in $alpha$-RuCl$_3$.
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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