Experimental evidence consistent with a magnon Nernst effect in the antiferromagnetic insulator ${\mathrm{MnPS}}_3$

A magnon Nernst effect, an antiferromagnetic analog of the magnon Hall effect in ferromagnetic insulators, has been studied experimentally for the layered antiferromagnetic insulator ${\mathrm{MnPS}}_3$ in contact with two Pt strips. Thermoelectric voltage in the Pt strips grown on ${\mathrm{MnPS}}_3$ single crystals exhibits nonmonotonic temperature dependence at low temperatures, which is unlikely to be explained by electronic origins in Pt but can be ascribed to the inverse spin Hall voltage induced by a magnon Nernst effect. Control of antiferromagnetic domains in the ${\mathrm{MnPS}}_3$ crystal by magnetoelectric cooling is found to modulate the low-temperature thermoelectric voltage in Pt, which is evidence consistent with the emergence of the magnon Nernst effect in Pt-${\mathrm{MnPS}}_3$ hybrid structures.

Figure 1

Schematics of (a) the magnon Hall effect in kagome ferromagnets and (b) the magnon Nernst effect in honeycomb antiferromagnets.

Figure 2

(a) Examples of ${\mathrm{MnPS}}_3$ single crystals. (b) X-ray diffraction pattern of a ${\mathrm{MnPS}}_3$ single crystal. (c) Temperature ($T$) dependence of the magnetization ($M$) for a ${\mathrm{MnPS}}_3$ single crystal. The measurement was performed under magnetic fields of 1 T applied along the $c$ axis. (d) Flow chart of sample setup in the magnon Nernst effect measurement. After the surface treatment by Ar-ion milling processes, 5-nm-thick Pt films were deposited on the ${\mathrm{MnPS}}_3$ surfaces. The Pt-${\mathrm{MnPS}}_3$ samples were fixed on two heat sinks for the measurement of thermoelectric voltages. (e) Surface images taken with a laser microscope for Pt1 and Pt2 of sample 1. (f) Distance distribution of surface heights for Pt1 and Pt2 of sample 1. This graph is obtained from the images shown in (e).

Figure 3

Temperature ($T$) dependence of (a) two-wire resistivity (${\rho }_{\mathrm{Pt}}^{2\mathrm{w}}$) for Pt1 and Pt2 of sample 1, (b) $V/\mathrm{\Delta }T$ for Pt1 and Pt2 of sample 1 ($S_{\mathrm{Pt}1}$ and $S_{\mathrm{Pt}2}$, respectively), and (c) the anomalous thermoelectric contribution defined as $\mathrm{\Delta }S\equiv 0.37\times S_{\mathrm{Pt}1}-S_{\mathrm{Pt}2}$ for sample 1. In (b), $0.37\times S_{\mathrm{Pt}1}$ at each $T$ is plotted for Pt1. Here, $P$ in (b) and (c) denotes the power level applied to the heater.

Figure 4

(a) A schematic illustration of the experimental configuration of magnetoelectric (ME) cooling. The electric field ($E$) is applied along the perpendicular-to-plane direction and the magnetic field ($H$) is applied along an in-plane direction. (b) Temperature ($T$) dependence of $V/\mathrm{\Delta }T$ for Pt2 ($S_{\mathrm{Pt}2}$) of sample 2 without ME cooling (circles) and after ME cooling of $E=1$ MV/m and $H=3$ kOe (squares). (c) Temperature ($T$) dependence of the change of $S_{\mathrm{Pt}2}$ values by ME cooling ($\mathrm{\Delta }S$) for Pt2 of sample 2 (circles). The data of $\mathrm{\Delta }S$ for Pt2 of sample 1 at $P=8$ mW is also shown for comparison. (d) Temperature ($T$) dependence of the magnon Nernst signal predicted theoretically for monolayer ${\mathrm{MnPS}}_3$ [10]. The calculation is only valid at low temperatures, and the magnon Nernst signal should vanish above $T_N$ of ${\mathrm{MnPS}}_3$ as indicated by dotted curves.

Figure 5

Temperature ($T$) dependence of (a) the applied temperature difference ($\mathrm{\Delta }T$), (b) $S_{\mathrm{Pt}1}$ of sample 1, and (c) $S_{\mathrm{Pt}2}$ of sample 1. The experimental data at different heater power ($P$) levels are distinguished by means of different symbols and colors.

Figure 6

Temperature ($T$) dependence of (a) two-wire resistivity (${\rho }_{\mathrm{Pt}}^{2\mathrm{w}}$) for Pt1 and Pt2 of sample 2, (b) the applied temperature difference ($\mathrm{\Delta }T$) in the measurement of the magnon Nernst effect for sample 2, (c) $S_{\mathrm{Pt}1}$ of sample 2, and (d) the change in $S_{\mathrm{Pt}1}$ by ME cooling ($\mathrm{\Delta }S$) for sample 2. In (c) and (d), the $T$ range where the finite $\mathrm{\Delta }S$ signal is observed in Pt1 and Pt2 of sample 2 [Fig. 4] is highlighted in yellow.

Figure 7

The sign-change temperature of the magnon Nernst coefficient, which is calculated as a function of the Dzyaloshinskii-Moriya (DM) parameter.

Figure 8

Two Néel states in ${\mathrm{MnPS}}_3$: (a) state 1 and (b) state 2.

Figure 9

Temperature ($T$) dependence of the two-wire resistivity (${\rho }_{\mathrm{Pt}}^{2\mathrm{w}}$) and the thermoelectric coefficient ($S_{\mathrm{Pt}}$) for (a) high-${\rho }_{\mathrm{Pt}}^{2\mathrm{w}}$ Pt-${\mathrm{MnPS}}_3$ samples (${\rho }_{\mathrm{Pt}}^{2\mathrm{w}}\gtrsim 5\times {10}^{-5} \mathrm{\Omega }\mathrm{cm}$), (b) low-${\rho }_{\mathrm{Pt}}^{2\mathrm{w}}$ Pt-${\mathrm{MnPS}}_3$ samples (${\rho }_{\mathrm{Pt}}^{2\mathrm{w}}\lesssim 5\times {10}^{-5} \mathrm{\Omega }\mathrm{cm}$), and (c) reference Pt samples, Pt1-${\mathrm{SrTiO}}_3$ and Pt2-${\mathrm{SiO}}_2$.

Figure 10

Temperature ($T$) dependence of $S_{\mathrm{Pt}}$ for (a) Pt1 of sample 2 and (b) Pt2 of sample 2, measured without the ME cooling (black dots, measurement results obtained before the ME cooling experiments; green triangles, measurement results obtained after the ME cooling experiments) and with the ME cooling (red squares).