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Register a new userAnomalous Hall and Nernst effects in ferrimagnetic Mn$_4$N films: possible interpretation and prospect for enhancement
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Ferrimagnetic Mn$_4$N is a promising material for heat flux sensors based on the anomalous Nernst effect (ANE) because of its sizable uniaxial magnetic anisotropy ($K_{rm u}$) and low saturation magnetization ($M_{rm s}$). We experimentally and theoretically investigated the ANE and anomalous Hall effect in sputter-deposited Mn$_4$N films. It was revealed that the observed negative anomalous Hall conductivity ($sigma_{xy}$) could be explained by two different coexisting magnetic structures, that is, a dominant magnetic structure with high $K_{rm u}$ contaminated by another structure with negligible $K_{rm u}$ owing to an imperfect degree of order of nitrogen. The observed transverse thermoelectric power ($S_{rm ANE}$) of $+0.5, mu{rm V/K}$ at $300, {rm K}$ gave a transverse thermoelectric coefficient ($alpha_{xy}$) of $+0.34, {rm A/(m cdot K)}$, which was smaller than the value predicted from first-principles calculation. The interpretation for $alpha_{xy}$ based on the first-principles calculations led us to conclude that the realization of single magnetic structure with high $K_{rm u}$ and optimal adjustment of the Fermi level are promising approaches to enhance $S_{rm ANE}$ in Mn$_4$N through the sign reversal of $sigma_{xy}$ and the enlargement of $alpha_{xy}$ up to a theoretical value of $1.77, {rm A/(m cdot K)}$.
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We study the anomalous Nernst effect (ANE) and anomalous Hall effect (AHE) in proximity-induced ferromagnetic palladium and platinum which is widely used in spintronics, within the Berry phase formalism based on the relativistic band structure calculations. We find that both the anomalous Hall ($sigma_{xy}^A$) and Nernst ($alpha_{xy}^A$) conductivities can be related to the spin Hall conductivity ($sigma_{xy}^S$) and band exchange-splitting ($Delta_{ex}$) by relations $sigma_{xy}^A =Delta_{ex}frac{e}{hbar}sigma_{xy}^S(E_F)$ and $alpha_{xy}^A = -frac{pi^2}{3}frac{k_B^2TDelta_{ex}}{hbar}sigma_{xy}^s(mu)$, respectively. In particular, these relations would predict that the $sigma_{xy}^A$ in the magnetized Pt (Pd) would be positive (negative) since the $sigma_{xy}^S(E_F)$ is positive (negative). Furthermore, both $sigma_{xy}^A$ and $alpha_{xy}^A$ are approximately proportional to the induced spin magnetic moment ($m_s$) because the $Delta_{ex}$ is a linear function of $m_s$. Using the reported $m_s$ in the magnetized Pt and Pd, we predict that the intrinsic anomalous Nernst conductivity (ANC) in the magnetic platinum and palladium would be gigantic, being up to ten times larger than, e.g., iron, while the intrinsic anomalous Hall conductivity (AHC) would also be significant.
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