Insights on the Thermal Hall Effect of Spin Excitations in a Kagome Magnet
The research paper under review presents a meticulous investigation into the thermal Hall effect induced by spin excitations in the Kagome magnet Cu(1-3, bdc). Contrary to classical expectations where charge-neutral spin waves are not anticipated to display a thermal Hall effect, this study elucidates the occurrence of a large thermal Hall conductivity $\kappa_{xy}$ in the Kagome lattice due to topological effects originating from Berry curvature. The study emphasizes quantitative observations and theoretical underpinnings, offering significant insight into quantum magnetic phenomena.
The Kagome magnet Cu(1,3-benzenedicarboxylate), referred to as Cu(1-3, bdc), presents unique spin configurations owing to its structure characterized by stacked Kagome planes. The interaction of spin-$\frac{1}{2}$ Cu${2+}$ moments is delineated by an in-plane ferromagnetic exchange $J$, a spin-orbit coupling induced Dzyaloshinskii-Moriya (DM) exchange $D$, and a weak antiferromagnetic exchange between planes $J_c$. The interaction of these components leads to an intricate spin texture with finite chirality, facilitating the emergence of a significant thermal Hall conductivity, which the authors meticulously measure and analyze in response to varying temperatures and magnetic fields.
Initial experiments reveal that the thermal conductivity $\kappa$ is dominated by phononic contributions at higher temperatures, presenting a broad peak around 45 K. However, at temperatures below the critical temperature $T_C$ of 1.8 K, the contribution from spin excitations, denoted as $\kappas$, becomes prominent. The thermal Hall conductivity manifests as a function that is non-monotonic with respect to the applied magnetic field $B$, displaying a positive peak at low fields followed by a reversal in sign at higher fields. Such observations are attributed to the alternation in Chern flux across magnon bands, underscoring the influence of the Berry curvature.
Theoretical interpretations build significantly upon the framework provided by Katsura, Nagaosa, and Lee (KNL) who posited that in systems with competition between DM exchange and Heisenberg exchange, as seen in Kagome lattices, finite chirality could stem in conjunction with substantial $\kappa_{xy}$. The relationship between thermal Hall conductivity and Berry curvature as amended by Matsumoto and Murakami emphasizes topological characteristics rather than dissipation-driven effects, analogous to the intrinsic anomalous Hall effect observed in metals.
Crucial insights emerge from the analysis of $\kappa_{xy}$ and $\kappa_{xx}$ with respect to applied magnetic fields, where $\kappa_{xy}$ undergoes sign reversals influenced by the occupancy of magnon bands. This behavior probes the Berry curvature and is insightful in understanding the thermal Hall effect in paramagnetic states and beyond. The large thermal Hall conductivity $\kappa_{xy}$, in conjunction with the observations of its temperature and field-dependent magnetic profiles, provides strong evidence of intrinsic magnon contributions to thermal transport.
The implications of this research pertain to both theoretical advancements and experimental pursuits. By establishing a strong correlation between Berry curvature and thermal transport, this study paves the way for deeper exploration into quantum magnetic materials, offering new dimensions to unravel topological phenomena in quantum systems. Future research could extend to exploring analogous effects in other frustrated lattice systems and developing theoretical models further to encapsulate the complexities observed in such quantum magnets.
The findings provided in this paper are instrumental in driving forward the understanding of topological effects in quantum magnets, shedding light on the thermal Hall effect beyond conventional paradigms associated with charge-carrying particles, and fostering advancements in material sciences dealing with quantum magnets and thermal management applications.