Anomalous Nernst effect related to magnetic domains in a microfabricated thermoelectric element made of noncollinear antiferromagnet Mn3Sn

Abstract

Recently, antiferromagnetic materials have attracted increasing attention because of their large magnetotransport and thermomagnetic effects, in which the electronic band structure associated with the noncollinear spin configuration is responsible for generating Berry curvature through spin-orbit coupling <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1–3</sup> . The anomalous Nernst effect (ANE) is a thermoelectric phenomenon typically observed in ferromagnets under the application of a temperature gradient, in which a transverse voltage is induced perpendicular to both the temperature gradients and the magnetization. Recent experimental studies have shown large ANE in a noncollinear antiferromagnetic metal Mn <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</inf> Sn with a vanishingly small magnetization of 0.002 μ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</inf> per Mn atom <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4, 5</sup> , whose band structure has the Weyl points near <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">6, 7</sup> . In previous studies, the fabrication of thermoelectric devices with the enhanced Seebeck effect has proven to be complicated, owing to the requirement for alternately aligned p- and n-type semiconductor pillars <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">8</sup> . On the other hand, the ANE allows the design of much simpler thermopiles composed of laterally series-connected wires. Toward realizing a thermopile made of the chiral anti-ferromagnet Mn <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</inf> Sn, focused ion beam (FIB) lithography was employed to microfabricate a thermoelectric element consisting of a Ta/Al <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> O <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</inf> /Mn <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</inf> Sn layered structure <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">9</sup> . Figures 1(a) and (b) show a schematic illustration of the microfabricated Mn <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</inf> Sn device structure for measuring ANE and the magnetic structure of the Mn <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</inf> Sn when the magnetic field is applied along the [01–10] axis, where the thermal gradient is applied along the [0001] axis. In this device, the Ta layer acts as a heater producing Joule heat diffusing across the Al <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> O <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</inf> insulating layer into the thin Mn <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</inf> Sn layer. All measurements were performed at room temperature in vacuum. Figure 2 shows the ANE results for the configuration shown in Fig. 1(a) obtained for a dc current of ±1.5 mA applied to the Ta heater. The measured AN signal exhibits a clear hysteresis in an applied temperature gradient and magnetic field. The $V_{ANE}$ is indeed independent of the direction of the applied electrical current in the Ta heater. This indicates that the hysteresis loop in Fig. 2(a) is arising from the ANE in Mn <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</inf> Sn. The observation of the spontaneous, zero field value is essential for construction of the thermopile element. Figure 2(b) shows the electrical current dependence of $V_{ANE}$. The voltage increases with the electrical current in the Ta heater. The sign and magnitude do not depend on the direction of the electrical current. The magnitude is also proportional to the square of the electrical current applied to the Ta heater. In addition, the angular dependence of ANE in the configuration shown in Figure 1(a) shows a small anomaly around 60° when the magnetic field is rotated from the [2-1-10] axis (0°) to the [01–10] axis (90°). On the other hand, in another ANE-measurement device of Mn <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</inf> Sn, the shape of the hysteresis of ANE has a step structure depending on the electrical current in the Ta heater just beside the microfabricated Mn <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</inf> Sn. According to the theoretical study, six magnetic domains that are different at each 60° are proposed in Mn <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</inf> Sn <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">10</sup> . However, an additional study is required to clarify the origin of this structure. In summary, we evaluated the ANE in a microfabricated device comprised of the chiral antiferromagnet Mn <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</inf> Sn as a first step to realize a thermopile device. The spontaneous, zero field voltage signal in the device is of the order of a few μV, which is almost the same order of magnitude as observed in the bulk single-crystal Mn <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</inf> Sn under a temperature gradient. The anomalous Nernst coefficient ${{S}_{\text{ANE}}}$ of the microfabricated element was determined using a temperature gradient simulated by finite-element modeling. The experiment and simulation revealed that the ANE coefficient is 0.27 μV/K which is in good agreement with the bulk value. This result indicates that the FIB microfabrication does not significantly alter the thermoelectric properties of bulk Mn <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</inf> Sn. As the chiral antiferromagnet produces almost no stray field, our study opens the avenue for the fabrication of an efficient thermopile by densely packing the microfabricated antiferromagnetic elements. In this work, the Mn <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</inf> Sn microdevice was fabricated from a bulk crystal, rather than through the deposition of thin films. This approach enables us to investigate thermoelectric phenomena on the nanoscale in wider range of materials than conventional materials used in thin film based devices.