Extrinsic contribution to the anomalous Hall effect and Nernst effect in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>Fe</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:mi>Co</mml:mi></mml:mrow></mml:math> single-crystal thin films by Ir doping

Abstract

We report the effect of Ir doping on the anomalous Hall effect (AHE) and anomalous Nernst effect (ANE) in ${\mathrm{Fe}}_{3}\mathrm{Co}$ single-crystal thin films. ${({\mathrm{Fe}}_{3}\mathrm{Co})}_{100\text{--}x}{\mathrm{Ir}}_{x}$ $(x\ensuremath{\le}12%)$ composition-spread thin films are fabricated on MgO(100) substrates by a combinatorial sputtering technique for a high-throughput and systematic characterization. From a structural analysis using x-ray diffraction, the films are grown epitaxially on the substrates and B2-ordered phase is detected from $x=7.3%$ to 12%. The compositional dependence of the AHE, magnetoresistance, ANE, and Seebeck effect is measured to obtain anomalous Hall resistivity $({\ensuremath{\rho}}_{yx}^{A})$, longitudinal resistivity $({\ensuremath{\rho}}_{xx})$, anomalous Nernst coefficient $({S}_{\mathrm{ANE}})$, and Seebeck coefficient $({S}_{\mathrm{SE}})$, respectively. From these transport measurements, we calculate anomalous Nernst conductivity $({\ensuremath{\alpha}}_{xy}^{A})$. A large enhancement of the ${\ensuremath{\rho}}_{yx}^{A}$ value is observed upon Ir doping by a factor of \ensuremath{\approx} 9.2 for $x=12%$ at 300 K. By employing a scaling analysis to the AHE results, extrinsic contribution is found to be increased after Ir doping in the low-Ir concentration regime, while intrinsic contribution becomes more dominant in the high-Ir concentration regime. On the other hand, unlike the ${\ensuremath{\rho}}_{yx}^{A}$, the ${S}_{\mathrm{ANE}}$ does not show significant compositional dependence. We find that AHE-related contribution $(\ensuremath{-}{S}_{\mathrm{SE}}{\ensuremath{\rho}}_{yx}^{A}/{\ensuremath{\rho}}_{xx})$ is dominant to the ${S}_{\mathrm{ANE}}$ compared to the contribution from direct conversion of a temperature gradient to a transverse charge current by anomalous Nernst conductivity $({\ensuremath{\alpha}}_{xy}^{A}{\ensuremath{\rho}}_{xx})$. We also find that the ${\ensuremath{\alpha}}_{xy}^{A}$ value sharply changes from a positive to negative value immediately after Ir doping, showing a negative maximum at $x\ensuremath{\approx}1%$, followed by a decrease in magnitude to almost zero for $x=12%$. Based on the Mott's relation and the scaling analysis of the AHE, we suggest a possible connection between the ${\ensuremath{\alpha}}_{xy}^{A}$ and the extrinsic contribution of the AHE. These experimental results and analysis will provide insights into the relationship between the AHE and ANE in ferromagnetic alloys upon heavy metal doping.

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