Longitudinal magnon transport properties in the easy-axis XXZ Heisenberg ferromagnet on the face-centered cubic lattice

TL;DR

This paper analyzes longitudinal magnon-mediated spin and thermal transport in a $S=1/2$ ferromagnetic XXZ model with easy-axis anisotropy on a four-sublattice FCC lattice. Using linear spin-wave theory and the Kubo formalism, it shows that a finite magnon gap yields activated transport at low temperature and establishes a universal magnon Wiedemann-Franz-like relation with $L=\frac{5}{2}(k_B/(g\mu_B))^2$, independent of the anisotropy parameter and magnetic field. The transport is dominated by the lower gapped magnon branch, and a nonzero field tunes the gap, reducing transport while preserving the WF ratio. The results provide a theoretical framework applicable to other FCC lattices and arbitrary spin, with implications for magnonics in insulating magnets and low-damping materials.

Abstract

We present a detailed investigation of longitudinal magneto-thermal transport in the $S=1/2$ ferromagnetic XXZ model with easy-axis exchange anisotropy ($Δ>1$) on a face-centered cubic lattice consisting of four sublattices. We employ linear spin-wave theory and the Kubo formalism to evaluate the longitudinal spin and thermal conductivities, both of which exhibit activated temperature dependence in the low-temperature regime, and to determine their magnetic-field dependence. Our analysis indicates that a magnon gap is crucial for ensuring the convergence of these conductivities. Furthermore, by examining the ratio of thermal conductivity to spin conductivity, we identify an analog of the Wiedemann-Franz law for magnon transport at low temperatures. Finally, we demonstrate that these results can be generalized to systems with arbitrary spin.

Figures (4)

• Figure 1: Schematic representation of our FCC lattice with four sublattices per unit cell. Nearest-neighbor (NN) bonds are shown by thin and dashed lines, while the next-nearest-neighbor (NNN) bonds are indicated by solid lines.
• Figure 2: (a) Magnon dispersion relations along the high-symmetry path $\Gamma-M-A-R-\Gamma$ in the first Brillouin zone. The symmetry points are $\Gamma=(0,0,0)$, $M=(\pi,\pi,0)$, $A=(\pi,\pi,\pi)$, and $R=(0,\pi,\pi)$. Here, $\Delta=1.1$, $|J_1|=1$, $|J_2|=0.8$, and $H=0$. The upper and lower branches are $\omega_{\bm q+}$ and $\omega_{\bm q-}$, respectively. (b) Schematic representation of the high-symmetry path in the first octant of the Brillouin zone ($q_x, q_y, q_z>0$).
• Figure 3: The temperature dependence of (a) spin conductivity $\sigma$ and (b) thermal conductivity $\kappa$ are shown for several values of the anisotropy parameter $\Delta$. The temperature is measured in dimensionless units $T \equiv k_B T/|J|$. The parameters used are $\alpha=0.01$, $|J_1|=|J|$, $|J_2|=0.8|J|$, and $g=2$ ( $S=1/2$).
• Figure 4: The magnetic field dependence of (a) spin conductivity $\sigma$ and (b) thermal conductivity $\kappa$ are shown for several values of the anisotropy parameter $\Delta$. The magnetic field is measured in dimensionless units $H \equiv g\mu_B H/|J|$. The parameters used are $\alpha=0.01$, $|J_1|=|J|$, $|J_2|=0.8|J|$, and $g=2$ ( $S=1/2$).