Spin Seebeck effect in two-sublattice ferrimagnets in the vicinity of $T_{\rm C}$

TL;DR

The paper addresses the puzzle of convex downward spin Seebeck response near the Curie temperature in ferrimagnetic systems such as YIG/Pt. It develops a Ginzburg-Landau framework for two-sublattice ferrimagnets, introducing both magnetic and Néel interfacial couplings to the heavy-metal spin accumulation and deriving TDGL/Bloch dynamics to compute the interfacial spin current. A key finding is that only the Néel coupling can explain the downward curvature of the SSE near $T_{\rm C}$, with the SSE decomposed into magnetic, Néel, and mixed contributions linked to acoustic and optical magnon modes; quantitative analysis suggests a ratio $J_n/J_m \approx -5$ best matches experiments, aided by a microscopic argument based on Fe-site environment. This work clarifies the essential role of Néel coupling in ferrimagnetic spintronics and provides a guidance for engineering interfacial interactions in ferrimagnet/heavy-metal devices, especially near criticality.

Abstract

Spin Seebeck effect refers to the magnonic thermal spin injection from a magnet into the adjacent heavy metal. A ferrimagnetic insulator yttrium iron garnet (YIG) is the material most studied for the spin Seebeck effect. Here, to account for a convex downward temperature dependence of the spin Seebeck effect observed in YIG/Pt system near the Curie temperature $T_{\rm C}$, we develop Ginzburg-Landau theory of the spin Seebeck effect in two-sublattice ferrimagnets. We find that only when we take into account the "Néel coupling", i.e., interfacial exchange coupling between the Néel order parameter of YIG and spin accumulation of Pt, the convex downward temperature dependence is explained. The present result sheds light on the importance of the Néel coupling in ferrimagnetic spintronics.

Figures (6)

• Figure 1: Schematic drawing of the system considered in this paper. Here, FiI and M refer to a ferrimagnetic insulator and a heavy metal with local temperatures $T_{\rm F}$ and $T_{\rm M}$, respectively. The FiI layer consists of $A$ sublattice and $B$ sublattice. For sublattice spins ${\bm S}^A$ and ${\bm S}^B$, see the definition below Eq. (\ref{['eq:ndef01']}).
• Figure 2: Temperature dependence of $m_{\rm eq}$ and $n_{\rm eq}$ for $H_0/\mathfrak{h}_0 = 0.01$, where $r_0 = 1.0$, $L_{AB}= 0.2$, and $u_4= 0.1$ are used.
• Figure 3: Temperature dependence of the gap $\Delta \widetilde{\omega}= |\widetilde{\omega}_-| - |\widetilde{\omega}_+|$ between the acoustic mode $\omega_+$ and optical mode $\omega_-$, where the frequencies are normalized as $\widetilde{\omega}_\pm= \omega_\pm/(\gamma \mathfrak{h}_0)$. Here, parameters are chosen the same as in Fig. \ref{['fig:mneq01']}, i.e., $H_0/\mathfrak{h}_0 = 0.01$, $r_0 = 1.0$, $L_{AB}= 0.2$, $u_4= 0.1$. Besides, we use $K_0 = 0.001$, $\Gamma_m/(\gamma \mathfrak{h}_0)= 0.01$, and $\Gamma_n/(\gamma \mathfrak{h}_0)= 0.01$. Inset: Temperature dependence of $\widetilde{\omega}_\pm$.
• Figure 4: Temperature dependence of (a) $\widetilde{\cal L}_m = {\cal L}_m \gamma \mathfrak{h}_0$ and $\widetilde{\cal L}_m^{(\pm)} = {\cal L}_m^{(\pm)} \gamma \mathfrak{h}_0$, (b) $\widetilde{\cal L}_n = {\cal L}_n \gamma \mathfrak{h}_0$ and $\widetilde{\cal L}_n^{(\pm)} = {\cal L}_n^{(\pm)} \gamma \mathfrak{h}_0$, and (c) $\widetilde{\cal L}_{mn} = {\cal L}_{mn} \gamma \mathfrak{h}_0$ and $\widetilde{\cal L}_{mn}^{(\pm)} = {\cal L}_{mn}^{(\pm)} \gamma \mathfrak{h}_0$. Here, the same parameters as Fig. \ref{['fig:Domega01']} are used, and we set $\gamma \mathfrak{h}_0 \tau_{\rm M} = 1.0$.
• Figure 5: Temperature dependence of $\widetilde{\cal L}_m= {\cal L}_m \gamma \mathfrak{h}_0$, $\widetilde{\cal L}_n = {\cal L}_n \gamma \mathfrak{h}_0$, and $\widetilde{\cal L}_{mn} = {\cal L}_{mn} \gamma \mathfrak{h}_0$ in Fig. \ref{['fig:L_mnmn01']} are shown on the same scale.