Magnon polarons in the spin Peltier effect

We report the observation of anomalous peak structures induced by hybridized magnon-phonon excitation (magnon polarons) in the magnetic field dependence of the spin Peltier effect (SPE) in a ${\mathrm{Lu}}_2{\mathrm{Bi}}_1{\mathrm{Fe}}_4{\mathrm{Ga}}_1{\mathrm{O}}_{12}$ (BiGa:LuIG) with Pt contact. The SPE peaks coincide with magnetic fields tuned to the threshold of magnon-polaron formation, consistent with the previous observation in the spin Seebeck effect. The enhancement of SPE is attributed to the lifetime increase in spin current caused by magnon-phonon hybridization in BiGa:LuIG.

Figure 1

(a) A schematic illustration of the SPE in the PM/FI junction (Pt/BiGa:LuIG/GGG sample) and measurement system with a thermocouple (TC). The heat current ${\mathbf{J}}_{\mathrm{q}}$ induced by the SPE leads to a temperature change between the Pt and BiGa:LuIG films in the vicinity of its interface, which is detected by the E-type TC attached on top of the Pt film with varnish [38]. (b) Input signal: A square-wave charge current $J_{\mathrm{c}}$ with amplitude $\mathrm{\Delta }{J}_{\mathrm{c}}$. (c) Output signal: A TC voltage $V_{\mathrm{TC}}$ that responds to the change in the $J_{\mathrm{c}}$ polarity, $\mathrm{\Delta }{V}_{\mathrm{TC}}(\equiv V_{\mathrm{high}}-V_{\mathrm{low}})$, which is originated from the SPE-induced temperature modulation of the Pt $\left(\propto \mathrm{\Delta }{J}_{\mathrm{c}}\right)$ [38]. Here the Joule-heating-induced temperature modulation $\left(\propto \mathrm{\Delta }{J}_{\mathrm{c}}^2\right)$ is constant in time and can thus be excluded.

Figure 2

(a) $\mathrm{\Delta }{V}_{\mathrm{TC}}\left(H\right)$ of the Pt/BiGa:LuIG/GGG sample for several $\mathrm{\Delta }{J}_{\mathrm{c}}$ values measured at $T=300\mathrm{K}$ and $\left|{\mu }_{0}H\right|<10\mathrm{mT}$. (b) $\mathrm{\Delta }{V}_{\mathrm{TC}}\left(\mathrm{\Delta }{J}_{\mathrm{c}}\right)$ measured at $T=300\mathrm{K}$ and ${\mu }_{0}H=8\mathrm{mT}$. The gray scale bar in (b) represents the temperature change $\mathrm{\Delta }T$ of $0.1\mathrm{mK}$, estimated by the relation $\mathrm{\Delta }T=\mathrm{\Delta }{V}_{\mathrm{TC}}/S_{\mathrm{TC}}$.

Figure 3

(a) Schematics of the magnon and TA-phonon dispersion relations for BiGa:LuIG when $H<H_{\mathrm{TA}},H=H_{\mathrm{TA}}$, and $H>H_{\mathrm{TA}}$. At $T=300\mathrm{K}$ the touching frequency and wave number at $H=H_{\mathrm{TA}}$ are $\omega /2\pi \sim 0.02\mathrm{THz}$ and $k\sim 5\times {10}^7{\mathrm{m}}^{-1}$, respectively [29]. (b) $\mathrm{\Delta }{V}_{\mathrm{TC}}\left(H\right)$ for several $\mathrm{\Delta }{J}_{\mathrm{c}}$ values measured at $T=300\mathrm{K}$ and $\left|{\mu }_{0}H\right|<0.8\mathrm{T}$. The $\mathrm{\Delta }{V}_{\mathrm{TC}}$ peaks at $H_{\mathrm{TA}}$ are marked by blue triangles. (c) Magnified views of $\mathrm{\Delta }{V}_{\mathrm{TC}}\left(H\right)$ around $H_{\mathrm{TA}}$ for $\mathrm{\Delta }{J}_{\mathrm{c}}=10.0$ and $0.0\mathrm{mA}$, where $\mathbf{H}\left|\right|\widehat{\mathbf{z}}$ (i.e., ${\mathit{\mu }}_{\mathrm{s}}\left|\right|\mathbf{M})$. (d) Magnified view of $\mathrm{\Delta }{V}_{\mathrm{TC}}\left(H\right)$ around $H_{\mathrm{TA}}$ for $\mathrm{\Delta }{J}_{\mathrm{c}}=10.0\mathrm{mA}$, where $\mathbf{H}\left|\right|\widehat{\mathbf{x}}$ (i.e., ${\mathit{\mu }}_{\mathrm{s}}\perp \mathbf{M})$. (e) Peak amplitude $\mathrm{\Delta }{V}_{\mathrm{TC}}^{\mathrm{peak}}$ at $H_{\mathrm{TA}}$ as a function of $\mathrm{\Delta }{J}_{\mathrm{c}}$ at $T=300\mathrm{K}$. The gray scale bar in (e) represents $\mathrm{\Delta }T=0.01\mathrm{mK}$.

Figure 4

(a) $\mathrm{\Delta }{V}_{\mathrm{TC}}\left(H\right)$ measured at various temperatures from $T=325$ to $100\mathrm{K}$ for $\mathrm{\Delta }{J}_{\mathrm{c}}=10\mathrm{mA}$ and ${\mu }_{0}H<0.8\mathrm{T}$. The $\mathrm{\Delta }{V}_{\mathrm{TC}}$ peaks at $H_{\mathrm{TA}}$ are marked by blue triangles. The dashed straight lines are eye guides. (b) $T$ dependencies of $\mathrm{\Delta }{V}_{\mathrm{TC}}$ (blue plots, left vertical axis) and $\mathrm{\Delta }T$ (gray plots, right vertical axis) at ${\mu }_{0}H=0.085\mathrm{T}\left(<{\mu }_0{H}_{\mathrm{peak}}\right)$. (c) $T$ dependencies of the peak amplitude $\mathrm{\Delta }{V}_{\mathrm{TC}}^{\mathrm{peak}}$ (blue plots, left vertical axis) and $\mathrm{\Delta }{T}_{\mathrm{peak}}$ (gray plots, right vertical axis) at the peak field $H_{\mathrm{peak}}$. (d) $T$ dependence of $H_{\mathrm{peak}}$. The $\mathrm{\Delta }T$ values are estimated by the relation $\mathrm{\Delta }T=\mathrm{\Delta }{V}_{\mathrm{TC}}/S_{\mathrm{TC}}$, where $S_{\mathrm{TC}}$ is the $T$-dependent Seebeck coefficient of TC. The data for $250\mathrm{K}\le T\le 325\mathrm{K}\left(100\mathrm{K}\le T\le 225\mathrm{K}\right)$ were obtained by averaging $6\times \left(12\times \right)$ repetition measurements (that took $\sim 1$ day $(\sim 2$ days) for the data acquisition; see also Ref. [46] and Sec. B of the Supplemental Material [47]).

Figure 5

(a) Schematics of the magnon, TA-phonon, and LA-phonon dispersion relations for BiGa:LuIG when $H=H_{\mathrm{TA}}$ and $H_{\mathrm{LA}}$. (b) $\mathrm{\Delta }{V}_{\mathrm{TC}}\left(H\right)$ measured at $T=100\mathrm{K}$ and $\mathrm{\Delta }{J}_{\mathrm{c}}=10\mathrm{mA}$ for ${\mu }_{0}H<1.8\mathrm{T}$ [higher than that for Fig. 4 to observe the hybridized $\text{magnon}-\text{LA}$-phonon feature]. The gray scale bar in (b) represents $\mathrm{\Delta }T=0.01\mathrm{mK}$. The $\mathrm{\Delta }{V}_{\mathrm{TC}}$ peaks at $H_{\mathrm{TA}}$ and $H_{\mathrm{LA}}$ are marked by blue and red triangles, respectively. The magnon-polaron signal at $H_{\mathrm{TA}}$ is clearer than that shown in Fig. 4 (for 100 K). This stems from the improved signal-to-noise ratio for Fig. 5 by the increased data accumulation time; the data were obtained by averaging $30\times$ repetition measurements (that are the highest accumulation number in the present work and took $\sim 7$ days for the data acquisition [note that the $H$ range is also increased compared to that for Fig. 4], see also Ref. [46]).