Enhanced Spin Conductance of a Thin-Film Insulating Antiferromagnet

We investigate spin transport by thermally excited spin waves in an antiferromagnetic insulator. Starting from a stochastic Landau-Lifshitz-Gilbert phenomenology, we obtain the out-of-equilibrium spin-wave properties. In linear response to spin biasing and a temperature gradient, we compute the spin transport through a normal-metal–antiferromagnet–normal-metal heterostructure. We show that the spin conductance diverges as one approaches the spin-flop transition; this enhancement of the conductance should be readily observable by sweeping the magnetic field across the spin-flop transition. The results from such experiments may, on the one hand, enhance our understanding of spin transport near a phase transition, and on the other be useful for applications that require a large degree of tunability of spin currents. In contrast, the spin Seebeck coefficient does not diverge at the spin-flop transition. Furthermore, the spin Seebeck coefficient is finite even at zero magnetic field, provided that the normal metal contacts break the symmetry between the antiferromagnetic sublattices.

Figure 1

(a) LNM-AF-RNM setup. A spin accumulation $\mathit{\mu }=\mu \mathbf{z}$ at the left interface inside the left normal metal and temperature gradient ${\partial }_{x}T$ across the heterostructure are applied; as a result a spin current $j$ flows across the right interface. (b) Metal-antiferromagnet interface, with unbroken (${\alpha }_a^{\prime }={\alpha }_b^{\prime }$, top) and broken (${\alpha }_a^{\prime }\ne {\alpha }_b^{\prime }$, bottom) sublattice symmetries. (c) Symmetry breaking in a synthetic antiferromagnet, composed of alternating metallic spacers and ferromagnetic layers with respective damping parameters ${\alpha }_1$, ${\alpha }_2\dots$. If, for example, the contact (blue) material differs from that of the interlayer spacer (gray), then ${\alpha }_1\ne {\alpha }_2$, analogously to (b).

Figure 2

Total conductance $G$ times $l^2\equiv A\chi$ for ${\chi }^{-1}=10H_c$, $d=l$, $\alpha ={\alpha }^{\prime }={\tilde{\alpha }}^{\prime }=0.1$, for varying temperatures $T/H_c$ from 1 to 5 in steps of 1. Inset: Symmetric magnon conductance ${\mathcal{G}}^{(\mathrm{S})}$ [defined below Eq. (9)] for a single magnon mode with energy $\hslash {\omega }^{(+)}=-H+\xi$ as a function of $\xi$ for fixed temperature $T$. As $\xi \to H$, corresponding to the closing of the magnon gap ($H\to H_c$) and thus approaching the spin-flop transition, the conductance diverges. Shown are different fields (corresponding to the vertical dashed lines) for 0 to $H_c$ in steps of $T/10$, with the corresponding curves for ${\mathcal{G}}^{(\mathrm{S})}$ shown in shades of purple to green. ${\mathcal{G}}^{(\mathrm{A})}$ is qualitatively similar and therefore not shown.

Figure 3

Total spin Seebeck coefficient $S$ for the symmetric case (${\tilde{\alpha }}^{\prime }=0$), Eq. (12) for ${\alpha }^{\prime }=0.1$, $d=l=\sqrt{A\chi }$, and ${\chi }^{-1}=10H_c$. ${\mathcal{S}}^{(\mathrm{S})}$ (upper inset) and ${\mathcal{S}}^{(\mathrm{A})}$ (lower inset) as functions of temperature for fixed $\xi$. While the symmetric contribution vanishes at high temperatures, the antisymmetric contribution saturates at ${\mathcal{S}}^{(\mathrm{A})}=8$. The solid purple or green curves correspond to $H$ ranging from 0 to $H_c$ in increments of $H_c/10$. At high temperatures, $S$ grows larger with temperature, in contrast with [7, 9]; see second section of Supplemental Material [17].