Scaling of the anomalous Hall effect in Sr${}_{1-x}$Ca${}_x$RuO${}_3$

Abstract

The anomalous Hall effect (AHE) of ferromagnetic thin films of Sr${}_{1-x}$Ca${}_x$RuO${}_3$ (0 $\le x\le$ 0.4) is studied as a function of $x$ and temperature $T$. As $x$ increases, both the transition temperature $T_c$ and the magnetization $M$ are reduced and vanish near $x\sim$ 0.7. For all compositions, the transverse resistivity ${\rho }_H$ varies non-monotonously with $T$, and even changes sign, thus violating the conventional expression ${\rho }_H=R_{o}B+4\pi R_{s}M(T)$ ($B$ is the magnetic induction, while $R_o$ and $R_s$ are the ordinary and anomalous Hall coefficients). From the rather complicated data of ${\rho }_H$, we find a scaling behavior of the transverse conductivity ${\sigma }_{xy}$ with $M(T)$, which is well reproduced by the first-principles band calculation assuming the intrinsic origin of the AHE.

REVTeX 4 style; 5 pages, 3 figures; revised 23/2 and accepted for publication

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