Effects of magnetic anisotropy on spin and thermal transports in classical antiferromagnets on the square lattice

Abstract

Transport properties of the classical antiferromagnetic XXZ model on the square lattice have been theoretically investigated, putting emphasis on how the occurrence of a phase transition is reflected in spin and thermal transports. As is well known, the anisotropy of the exchange interaction $\Delta \equiv J_z/J_x$ plays a role to control the universality class of the transition of the model, i.e., either a second-order transition at $T_N$ into a magnetically ordered state or the Kosterlitz-Thouless (KT) transition at $T_{KT}$, which respectively occur for the Ising-type ($\Delta >1$) and $XY$-type ($\Delta <1$) anisotropies, while for the isotropic Heisenberg case of $\Delta =1$, a phase transition does not occur at any finite temperature. It is found by means of the hybrid Monte-Carlo and spin-dynamics simulations that the spin current probes the difference in the ordering properties, while the thermal current does not. For the $XY$-type anisotropy, the longitudinal spin-current conductivity ${\sigma }_{xx}^s$ ($={\sigma }_{yy}^s$) exhibits a divergence at $T_{KT}$ of the exponential form, ${\sigma }_{xx}^s\propto \exp [B/\sqrt{T/T_{KT}-1}]$ with $B=\mathcal{O}(1)$, while for the Ising-type anisotropy, the temperature dependence of ${\sigma }_{xx}^s$ is almost monotonic without showing a clear anomaly at $T_N$ and such a monotonic behavior is also the case in the Heisenberg-type spin system. The significant enhancement of ${\sigma }_{xx}^s$ at $T_{KT}$ is found to be due to the exponential rapid growth of the spin-current-relaxation time toward $T_{KT}$, which can be understood as a manifestation of the topological nature of a vortex whose lifetime is expected to get longer toward $T_{KT}$. Possible experimental platforms for the spin-transport phenomena associated with the KT topological transition are discussed.

20 pages, 15 figures

References in corpus (9)

• Theory of magnon-driven spin Seebeck effect
• Spin Seebeck effect in antiferromagnets and compensated ferrimagnets
• Spin transport in Heisenberg antiferromagnets
• Signature of a Z_2 vortex in the dynamical correlations of the triangular-lattice Heisenberg antiferromagnet
• Antiferromagnetic anisotropy determination by spin Hall magnetoresistance
• Spin transport in the Neel and collinear antiferromagnetic phase of the two dimensional spatial and spin anisotropic Heisenberg model on a square lattice
• Relaxation mechanism driven by spin angular momentum absorption throughout antiferromagnetic phase transition in NiFe surface oxides
• Investigation of the spin-1 honeycomb antiferromagnet BaNi${}_2$V${}_2$O${}_8$ with easy plane anisotropy
• Spin Seebeck effect in paramagnets and antiferromagnets at elevated temperatures

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• Transport signature of the magnetic Berezinskii-Kosterlitz-Thouless transition
• Berezinskii-Kosterlitz-Thouless transition transport in spin-triplet superconductor
• Spin and thermal transport and critical phenomena in three-dimensional antiferromagnets
• Spontaneous chirality selection and nonreciprocal spin wave in breathing-kagome antiferromagnets at zero field
• Spin Hall effect of vorticity
• Incoherent transport in a classical spin liquid
• Machine-Learning Detection of the Berezinskii-Kosterlitz-Thouless Transitions
• Longitudinal magnon transport properties in the easy-axis XXZ Heisenberg ferromagnet on the face-centered cubic lattice