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${}_3$.

arXiv comment17 pages, 9 figures. arXiv admin note: text overlap with arXiv:1908.06630

References in corpus (27)

• Critical Phenomena and Renormalization-Group Theory
• Critical exponents and equation of state of the three-dimensional Heisenberg universality class
• Critical behavior of the three-dimensional XY universality class
• Kinetic theory of spin diffusion and superdiffusion in XXZ spin chains
• Superfluid spin transport through antiferromagnetic insulators
• Spin-current probe for phase transition in an insulator
• Super-diffusion in one-dimensional quantum lattice models
• Enhanced spin pumping efficiency in antiferromagnetic IrMn thin films around the magnetic phase transition
• Superdiffusion in spin chains
• Transformation of spin current by antiferromagnetic insulators
• Z_2-vortex ordering of the triangular-lattice Heisenberg antiferromagnet
• Fast spin dynamics algorithms for classical spin systems
• Spin transport in Heisenberg antiferromagnets
• Strong enhancement of the spin Hall effect by spin fluctuations near the Curie point of FexPt1-x alloys
• Spin dynamics simulation of the three-dimensional XY model: Structure factor and transport properties
• Spin injection and spin transport in paramagnetic insulators
• Thermal vector potential theory of magnon-driven magnetization dynamics
• Spin transport in the Neel and collinear antiferromagnetic phase of the two dimensional spatial and spin anisotropic Heisenberg model on a square lattice
• Critical dynamics of the simple-cubic Heisenberg antiferromagnet RbMnF${}_3$: Extrapolation to q=0
• Spin and thermal conductivity in classical disordered spin chain
• Z2-vortex order of frustrated Heisenberg antiferromagnets in two dimensions
• Relaxation mechanism driven by spin angular momentum absorption throughout antiferromagnetic phase transition in NiFe surface oxides
• Unraveling the influence of electronic and magnonic spin current injection near the magnetic ordering transition of IrMn metallic antiferromagnets
• Effects of magnetic anisotropy on spin and thermal transports in classical antiferromagnets on the square lattice
• Spin current as a probe of the ${\mathbb{Z}}_2$-vortex topological transition in the classical Heisenberg antiferromagnet on the triangular lattice
• Transport signature of the magnetic Berezinskii-Kosterlitz-Thouless transition
• 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