Anomalous Nernst effect dependence on composition in Fe_100−XRh_X alloys

Recently, spin-caloritronics based on spintronics and thermoelectronics have received considerable attention. ^1–3) The anomalous Nernst effect (ANE) is a type of thermoelectric power generation where heat is converted into an electric current in the direction perpendicular to the temperature gradient. Unlike the conventional Seebeck effect, a complicated three-dimensional structure is not required, which is advantageous because a large area of power can be easily generated along the heat source. However, ANE produces a small amount of power, and practical application is difficult. To improve the ANE, various ferromagnetic and noncolinear antiferromagnetic materials have been investigated. ^4–17) In general, the anomalous Nernst coefficient can be decomposed into two terms as shown below: ^17–19)

$$\begin{eqnarray}&&{S}_{yx}\,=\,{\rho }_{xx}{\alpha }_{yx}-\displaystyle \frac{{\rho }_{yx}}{{\rho }_{xx}}{S}_{xx}\,=\,{\rho }_{xx}{\alpha }_{yx}-\,\tan \left({\theta }_{{\rm{AHE}}}\right){S}_{xx},\end{eqnarray} \tag{ 1 }$$

where ${\rho }_{xx}$ is the longitudinal resistivity, ${\alpha }_{yx}$ is the transverse thermoelectric conductivity, ${\rho }_{yx}$ is the Hall resistivity, ${S}_{xx}$ is the Seebeck coefficient, and $\tan \left({\theta }_{{\rm{AHE}}}\right)$ is the anomalous Hall angle defined as $\tfrac{{\rho }_{yx}}{{\rho }_{xx}}.$ Here, the first term represents the intrinsic ANE term that converts heat flow into a transverse voltage, and the second term is due to the Seebeck and anomalous Hall effects. In Eq. (1), ${\alpha }_{yx}$ is considered one of the essential determinants of ${S}_{yx},$ and ${\alpha }_{yx}$ is attributed to the band structure because it increases with the Berry curvature at the Fermi energy. ^20,21)

In this study, we focused on FeRh alloy, which has a magnetic phase transition that depends on the temperature and composition. ^22–36) It has been reported that FeRh alloys undergo a magnetic phase transition from antiferromagnetic (AFM) to ferromagnetic (FM) with a change in the band structure when the FeRh alloy has a CsCl-type ordered structure. ^37,38) Therefore, FeRh is a suitable material for investigating the relationship between ${\alpha }_{yx}$ and the band structure by continuously changing the composition of FeRh. It has already been reported that Fe₅₀Rh₅₀ has a large ANE, ³⁹⁾ but systematic composition dependences have not been reported. Compared to this, we observed the strong composition dependence of ANE in Fe_100−X Rh_X by applying the temperature gradient in perpendicular to plane. ⁴⁰⁾ Therefore, for the detail discussion, we measured the ANE under the temperature gradient in plane. The purpose of this study was to investigate the ANE of Fe_100−X Rh_X by changing its composition (X = 45, 48, 50, 52, 54, 60) for a transition from the AFM state to the FM state with changing a band structure and discuss the relationship with between the band structure and ${\alpha }_{yx}.$

Fe_100−X Rh_X (50 nm)/SiN (5 nm) was deposited on a thermally oxidized Si substrate by co-sputtering Fe and Rh, where the composition X was changed to X = 45, 48, 50, 52, 54, and 60, and SiN is an oxidation barrier. To obtain the ordered FeRh alloy, they were annealed in a vacuum at 750 °C for 1 h. The crystalline structure of FeRh was identified using θ–2θ X-ray diffraction (XRD), and the magnetic properties were measured using a vibrating sample magnetometer (VSM) and superconducting quantum interference device (SQUID). As shown in Fig. 1(a), the anomalous Nernst electromotive force was measured by applying a temperature gradient ΔT = 3.3–8.0 K in the longitudinal plane and sweeping a magnetic field from −1.65 to 1.65 T in the perpendicular plain, and ${S}_{yx}$ was calculated using ${S}_{yx}\,=\,\tfrac{V}{{\rm{\Delta }}T}\cdot \tfrac{l}{w},$ where l is the distance between the Peltier devices and w is the distance between two probes. To avoid electrical shunting with the Si substrate, a Fe_100−X Rh_X /SiN film was patterned on the substrate. The Seebeck coefficient ${S}_{xx}$ was derived from the average of the voltages measured by exchanging the high-and low-temperature sides in Fig. 1(b) to eliminate the voltage generated in the probes. The longitudinal and Hall resistivities, ${\rho }_{xx},$ ${\rho }_{yx},$ were measured as shown in Figs. 1(c) and 1(d), and ${\alpha }_{yx}$ was determined using the measured parameters from Eq. (1). Here, ${S}_{yx},$ ${S}_{xx},$ ${\rho }_{xx},$ and ${\rho }_{yx}$ for Fe are taken from a prior paper ¹⁷⁾ because the magnetization of our Fe film did not saturate within 1.65 T perpendicular to the plane.

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3.1. Crystal structure analysis

Figure 2 shows the XRD profiles of Fe_100−X Rh_X with X = 45–60. The diffraction peaks of the CsCl-type ordered phase FeRh (100) (110), which is necessary for phase transition, were obtained for all compositions. However, in the Rh composition, X ranged from 50 to 60, the diffraction peaks of the disordered fcc phase were detected, and the peak intensity of the fcc phase increased as the Rh content increased. Generally, the disordered fcc phase does not exhibit magnetization, and the ANE should only be observed when there is magnetization. Therefore, the ANE voltage depends on the volume of the FM phase in the sample. If the sample has a mixed state of the CsCl FM phase and fcc phase without magnetization, the volume of the fcc phase must be subtracted, but in this composition range, the CsCl phase showed the AFM phase at room temperature, as shown later.

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3.2. Magnetic properties

Figure 3(a) shows the magnetization curves of all the samples at room temperature. While a large magnetization was observed only for X = 45 and 48, the magnitude of magnetization drastically decreased above X = 50, indicating that a phase transition composition exists between X = 48 and 50 at room temperature. Figure 3(b) shows the temperature dependence of magnetization for X = 48, 50, and 52 at elevated temperatures. The phase transition temperatures were approximately 310 K, 415 K, and 445 K for the compositions of X = 48, 50, and 52, respectively. It should be noted that the sample with X = 48 has a phase transition temperature near room temperature and a mixed phase of AFM and FM states, even below the phase transition temperature.

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3.3. Anomalous Nernst effect

Figure 4(a) shows the composition dependence of ${S}_{yx}$ obtained from the measured ANE electromotive force, as shown in Fig. 1(a). All the samples had a negative ${S}_{yx},$ which is opposite to the that of Fe, and the sample with X = 48 had the largest $| {S}_{yx}| .$ To determine the transverse thermoelectric conductivity ${\alpha }_{yx},$ the Seebeck coefficient ${S}_{xx},$ longitudinal resistivity ${\rho }_{xx},$ and Hall resistivity ${\rho }_{yx}$ were estimated as shown in Figs. 4(b)–4(d). The anomalous Hall angle $\tan \left({\theta }_{{\rm{AHE}}}\right)$ was estimated as $\displaystyle \frac{{\rho }_{yx}}{{\rho }_{xx}},$ as shown in Fig. 4(e). Finally, we derived the transverse thermoelectric conductivity ${\alpha }_{yx},$ as shown in Fig. 4(f), using Eq. (1) and the measured parameters. It was found that ${\alpha }_{yx}$ had negative values and mostly the same Rh composition dependence as ${S}_{yx},$ with a maximum value at X = 48. This indicates that the transverse thermoelectric conductivity ${\alpha }_{yx}$ is an important component of the anomalous Nernst coefficient ${S}_{yx}.$

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To discuss the maximization of $| {\alpha }_{yx}|$ at X = 48, we refer to the band structure variation between the AFM and FM states across the phase transition in the Fe–Rh alloy. ^37,38) In particular, there is a difference in the AFM and FM density of states at the Fermi energy, which might be the cause of the change in ${\alpha }_{yx}.$ In addition, a previous study calculated the transverse thermoelectric conductivity. ⁴¹⁾ According to this, although $| {\alpha }_{yx}|$ is almost zero in the AFM state, $| {\alpha }_{yx}|$ is a finite value in the FM state. Focusing on ${\alpha }_{yx}$ at E_F, $| {\alpha }_{yx}|$ grows rapidly as Fe–Rh approaches the phase transition from the stable FM state, which corresponds to our experimental result that the sample with X = 48 had an FM state close to the phase transition. Additionally, there is a mixing phase of the AFM and FM states even below the phase transition temperature, indicating that the FM state is close to the phase transition state. Taking these into consideration, it is possible that $| {\alpha }_{yx}|$ is maximized at X = 48 because $| {\alpha }_{yx}|$ rapidly increases near the phase transition state at the Fermi energy. However, further investigation is necessary to clarify the mechanism.

The ANE of sputtered Fe_100−X Rh_X (X = 45, 48, 50, 52, 54, 60) films was investigated using the transverse thermoelectric conductivity ${\alpha }_{yx},$ which is an important factor for the anomalous Nernst coefficient ${S}_{yx}.$ The transverse thermoelectric conductivity ${\alpha }_{yx}$ had the same Rh composition dependence as the anomalous Nernst coefficient ${S}_{yx},$ with a maximum value at X = 48, indicating that ${S}_{yx}$ strongly depends on ${\alpha }_{yx}.$ The composition dependence of ${\alpha }_{yx}$ is consistent with $| {\alpha }_{yx}|$ calculated based on the band structure, which increases rapidly near the phase transition state. By realizing a single ferromagnetic state that is close enough to the phase transition state, we will able to obtain the further higher transverse thermoelectric conductivity ${\alpha }_{yx},$ and eventually anomalous Nernst coefficient ${S}_{yx}.$

We would like to thank Prof. Kimura and Dr. Ohnishi for the use of their VSM, and Prof. Kawae and Dr. Inagaki for support magnetization measurements using SQUID. We also thank Prof. Hihara for the measurement of magnetization dependence on temperature using VSM under the Nanotechnology Platform Project (Nagoya Institute of Technology, No. S-20-NI-0034). This study was supported by Thermal & Electric Energy Technology Inc. Foundation and Tanaka Noble Memorial Foundation.