Efficient room-temperature magnetization direction detection by means of the enhanced anomalous Nernst effect in a Weyl ferromagnet

Spintronic phenomena exhibiting a longitudinal resistance change under magnetization reversal are a quite novel feature in nanoscience, which has been intensively studied in hopes of realizing all-electrical magnetization direction detection devices, where no reference ferromagnetic layer is required. However, cryogenic temperatures and/or high magnetic fields have been required to achieve noticeable effects. Here, the high heat-to-charge conversion efficiency of the Heusler alloy Weyl semimetal ${\mathrm{Co}}_2\mathrm{MnGa}$ is exploited in single layer nanoscaled wires at room temperature to produce at least two orders of magnitude enhancement of the resistance change ratio, when compared with conventional ferromagnets. Such resistance change under magnetization reversal is consistently explained through temperature distribution simulations and direct thermoelectric measurements of the large anomalous Nernst effect (ANE) in this topologically nontrivial material. Although many reports consider ANE signals as perturbations or undesired artifacts, we demonstrate that they are dominant in this system and can be seized for nonvolatile memory readout, as shown in a prototype device. These results open up new horizons of using enhanced thermoelectric voltages in novel materials for magnetization direction detection in any system where significant temperature gradients exist.

Figure 1

(a) Schematics of Hall bar devices. The definition of axis, angle scans, dimensions, and electrical connections are shown. (b) Longitudinal resistance for three perpendicular magnetic field scans. The odd component (top panel) is governed by ANE voltages for $xy$ and $zy$ scans, while the even component (bottom panel) is governed by AMR phenomena. (c) Transverse resistance for three perpendicular magnetic field scans. The odd component (top panel) is again dominated by ANE voltages, while the even component (bottom panel) is ruled by the AHE for $xy$ and $zy$ scans.

Figure 2

(a) Schematics of a piece of ${\mathrm{Co}}_2\mathrm{MnGa}$ wire on top of an MgO substrate, where a charge current ${\mathit{J}}_{\mathit{C}}^{+}$ or ${\mathit{J}}_{\mathit{C}}^{-}$ produces a thermal gradient due to Joule heating and the asymmetric boundary conditions. The ANE-generated electric field ${\mathit{E}}_{\mathrm{ANE}}$, which is independent of the direction of the electric current, produces an asymmetry in the total electric fields for each current direction ${\mathit{E}}_{\mathit{L}}^{+}$ and ${\mathit{E}}_{\mathit{L}}^{-}$, giving rise to the UMR effect. (b) Example of the longitudinal resistance measured for an $xy$ scan of magnetic field angle, for a current density of $2.75\times {10}^{11}$ A/${\mathrm{m}}^2$. The top panel shows the resistance measured for positive and negatives currents, while the bottom panel shows even and odd components. (c) Odd component of longitudinal resistance for an $xy$ scan for several current densities, in units of ${10}^{11}$ A/${\mathrm{m}}^2$. (d) Current density dependence of the UMR ratio. (e),(f) Magnetic field intensity dependence of the odd (e) and even (f) components of the longitudinal resistance for an $xy$ scan.

Figure 3

(a) Current density dependence of the UMR ratio measured for different widths of ${\mathrm{Co}}_2\mathrm{MnGa}$ Hall bars. (b) Current dependence of the UMR ratio measured for 200-nm-width and 30-nm-thick Hall bars made of different ferromagnetic materials, including low resistivity and high resistivity ${\mathrm{Co}}_2\mathrm{MnGa}$ samples.

Figure 4

(a) Simulated temperature spatial distribution, for a current density of $1.5\times {10}^{11}$ A/${\mathrm{m}}^2$ along $x$ direction. (b) Simulated temperature difference with respect to the bottom of the wire ($z=-30$ nm), normalized by current density, as a function of the distance along a vertical axis through the middle of the wire. Different plots correspond to different current densities, in units of ${10}^{11}$ A/${\mathrm{m}}^2$. (c) Current density dependence of the average temperature of the wire. Both simulation and estimation from resistivity measurements are shown, with the corresponding quadratic fittings in solid line. The inset shows the temperature dependence of the normalized resistivity. (d) Temperature gradient dependence of the ANE signal, which is obtained, as shown in the inset, by subtracting the saturation ANE voltages for positive and negative external magnetic fields.

Figure 5

(a) Microscope image of two-terminal devices showing electrical connections and magnetic field directions. The yellow areas are the connection pads made of gold and the thin gray strips are ${\mathrm{Co}}_2\mathrm{MnGa}$ electrodes. Since this is tested in a two-terminal configuration, the pads where the current is applied ($I^{+},I^{-}$) are the same pads used to measure the longitudinal voltage. There are also pads for a transversal voltage measurement, which are not used in this demonstration. (b) Odd component of the resistance, relative to total resistance, as a function of the external magnetic field, for $0^{\circ }$ and ${45}^{\circ }$ devices, for a current density of $1.5\times {10}^{11}$ $\mathrm{A}/{\mathrm{m}}^2$. (c) Current density dependence of the UMR ratio measured for a $0^{\circ }$ two-terminal device at room temperature.