Spin and thermal transport and critical phenomena in three-dimensional antiferromagnets

Abstract

We investigate spin and thermal transport near the Néel transition temperature $T_N$ in three dimensions, by numerically analyzing the classical antiferromagnetic $XXZ$ model on the cubic lattice, where in the model, the anisotropy of the exchange interaction $\Delta =J_z/J_x$ plays a role to control the universality class of the transition. It is found by means of the hybrid Monte-Carlo and spin-dynamics simulations that in the $XY$ and Heisenberg cases of $\Delta \le 1$, the longitudinal spin conductivity ${\sigma }_{\mu \mu }^s$ exhibits a divergent enhancement on cooling toward $T_N$, while not in the Ising case of $\Delta >1$. In all the three cases, the temperature dependence of the thermal conductivity ${\kappa }_{\mu \mu }$ is featureless at $T_N$, being consistent with experimental results. The divergent enhancement of ${\sigma }_{\mu \mu }^s$ toward $T_N$ is attributed to the spin-current relaxation time which gets longer toward $T_N$, showing a power-law divergence characteristic of critical phenomena. It is also found that in contrast to the $XY$ case where the divergence in ${\sigma }_{\mu \mu }^s$ is rapidly suppressed below $T_N$, ${\sigma }_{\mu \mu }^s$ likely remains divergent even below $T_N$ in the Heisenberg case, which might experimentally be observed in the ideally isotropic antiferromagnet RbMnF${}_3$.

17 pages, 9 figures. arXiv admin note: text overlap with arXiv:1908.06630

References in corpus (6)

• Superfluid spin transport through antiferromagnetic insulators
• Superdiffusion in spin chains
• Spin transport in Heisenberg antiferromagnets
• 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
• Observation of topological $Z_2$ vortex fluctuations in the frustrated Heisenberg magnet NaCrO${}_2$

Cited by in corpus (2)

• Spontaneous chirality selection and nonreciprocal spin wave in breathing-kagome antiferromagnets at zero field
• Longitudinal magnon transport properties in the easy-axis XXZ Heisenberg ferromagnet on the face-centered cubic lattice