Low-temperature suppression of the spin Nernst angle in Pt

Letter

Low-temperature suppression of the spin Nernst angle in Pt

T. Wimmer, J. Gückelhorn, S. Wimmer, S. Mankovsky, H. Ebert, M. Opel, S. Geprägs, R. Gross, H. Huebl, and M. Althammer

Phys. Rev. B 104, L140404 – Published 11 October 2021

Abstract

The coupling between electrical, thermal, and spin transport results in a plethora of novel transport phenomena. However, disentangling different effects is experimentally very challenging. We demonstrate that bilayers consisting of the antiferromagnetic insulator hematite ( $α − {Fe}_{2} O_{3}$ ) and Pt allow one to precisely measure the transverse spin Nernst magnetothermopower (TSNM) and observe the low-temperature suppression of the platinum (Pt) spin Nernst angle. We show that the observed signal stems from the interplay between the interfacial spin accumulation in Pt originating from the spin Nernst effect and the orientation of the Néel vector of $α − {Fe}_{2} O_{3}$ , rather than its net magnetization. Since the latter is negligible in an antiferromagnet, our device is superior to ferromagnetic structures, allowing one to unambiguously distinguish the TSNM from thermally excited magnon transport, which usually dominates in ferri/ferromagnets due to their nonzero magnetization. Evaluating the temperature dependence of the effect, we observe a vanishing TSNM below $\sim 100 K$ . We compare these results with theoretical calculations of the temperature-dependent spin Nernst conductivity and find excellent agreement. This provides evidence for a vanishing spin Nernst angle of Pt at low temperatures and the dominance of extrinsic contributions to the spin Nernst effect.

Received 23 March 2021
Revised 28 September 2021
Accepted 28 September 2021

DOI:https://doi.org/10.1103/PhysRevB.104.L140404

Physics Subject Headings (PhySH)

Magnetism Magnetotransport Nernst effect Spin Hall magnetoresistance Spin accumulation Spin current Spin diffusion Spintronics Thermal Hall effect Thermomagnetic effects Thermopower

Antiferromagnets Magnetic insulators

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

T. Wimmer^1,2,*, J. Gückelhorn ^1,2, S. Wimmer ³, S. Mankovsky³, H. Ebert³, M. Opel ¹, S. Geprägs ¹, R. Gross ^1,2,4, H. Huebl ^1,2,4, and M. Althammer ^1,2,†

¹Walther-Meißner-Institut, Bayerische Akademie der Wissenschaften, D-85748 Garching, Germany
²Physik-Department, Technische Universität München, D-85748 Garching, Germany
³Department Chemie, Physikalische Chemie, Universität München, Butenandtstraße 5-13, D-81377 München, Germany
⁴Munich Center for Quantum Science and Technology (MCQST), Schellingstraße 4, D-80799 München, Germany

^*tobias.wimmer@wmi.badw.de
^†matthias.althammer@wmi.badw.de

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Vol. 104, Iss. 14 — 1 October 2021

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Images

Figure 1
(a) Sketch of an AFI/HM bilayer. In open circuit conditions, a temperature gradient generates a spin accumulation $s$ at the AFI/Pt interface with $s ⊥ - \nabla T$ . Depending on the relative orientation of $s$ and $N$ , the spin accumulation at the interface is either unaffected by the AFI (for $s ∥ N$ , left panel) or partially dissipated via a spin current $J_{s}^{dis}$ in the AFI (for $s ⊥ N$ , right panel). (b) Schematic depiction of the device, the electrical connection scheme and the coordinate system. A charge current $I_{q}$ is fed through the left Pt electrode acting as a heat source (heater). To determine the transverse magnetothermopower, a voltage signal $V_{\det}$ in a second Pt stripe (detector) is measured as a function of the magnetic field orientation $φ$ . (c) Joule heating induces a thermal injection of the two antiferromagnetic magnon modes (blue and red wiggly arrows). The effective magnetic moment is given by their superposition and is dominantly proportional to the canted net magnetization $M_{net}$ . The diffusing magnons are measured at the Pt detector via the inverse SHE. Simultaneously, a lateral temperature gradient across the width of the Pt detector leads to the emergence of the TSNM. The canting of the two sublattice magnetizations $M_{1, 2}$ in $α − {Fe}_{2} O_{3}$ leading to a net magnetization $M_{net}$ is schematically depicted on the left.
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Figure 2
(a) Detector signal $V_{\det}^{th}$ as a function of magnetic field orientation $φ$ for different external magnetic field strengths, where a superposition of both the TMT and TSNM signal is observed. The data are shown for a device with a heater-detector distance $d = 750 nm$ at $T = 200 K$ . Solid lines are fits to Eq. (1). (b) Detector signal $V_{\det}^{th}$ measured on a similar device fabricated on the ferrimagnetic insulator $Y_{3} {Fe}_{5} O_{12}$ (YIG) for $d = 2.1 μ m$ at $T = 220 K$ and $μ_{0} H = 1 T$ . The white solid line is a fit to a $sin (φ)$ -type function. (c) Residual signals $V_{\det}^{th, res}$ extracted from (a) using the different angular symmetries of the TMT (light gray points) and TSNM (dark gray points) for $μ_{0} H = 7 T$ . (d) Residual signal $V_{\det}^{th, res}$ of the fit to the data shown in (b), exhibiting the TSNM in YIG/Pt. A $90^{\circ}$ phase shift is observed compared to the TSNM in hematite.
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Figure 3
Signal amplitudes of the (a) TMT and (b) TSNM extracted from the fits of the experimental data shown in Fig. 2 at $T = 200 K$ . (a) TMT signal amplitude $ν_{\det}^{TMT}$ plotted as a function of the external magnetic field strength for different heater-detector distances $d$ . Each of the devices shows a linearly increasing TMT signal for increasing field strength. (b) TSNM signal $Γ_{\det}^{TSNM}$ as a function magnetic field, showing an increase of the signal at low field strength and a saturation above $\sim 2 T$ .
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Figure 4
Normalized TSNM signal amplitude $Γ_{\det}^{TSNM}$ extracted from the fits to Eq. (1) plotted as a function of temperature for a device with $d = 950 nm$ at $μ_{0} H = 7 T$ (black data points). Blue data points correspond to the theoretical calculation of the spin Nernst conductivity $α_{SN}$ . The green line depicts the scaling law $Γ_{\det}^{TSNM} \propto T^{1.6}$ extracted from the experimental data. (b) Theoretical calculation of the temperature dependence of the conventional (longitudinal) Seebeck coefficient $S_{xx}$ of Pt (black points) and experimentally determined conductivity $σ_{xx}$ of the Pt heater (purple points).
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