Antisymmetric contribution to the planar Hall effect of ${\mathrm{Fe}}_3\mathrm{Si}$ films grown on $\mathrm{GaAs}\left(113\right)A$ substrates

The planar Hall effect (PHE) in ferromagnets is believed to result from the anisotropic magnetoresistance (AMR) and hence does not change the sign by reversing the direction of the applied in-plane magnetic field. Our studies of the ferromagnetic Heusler alloy ${\mathrm{Fe}}_3\mathrm{Si}$ films grown on low-symmetric GaAs(113)A substrates however show a change in the sign of the PHE by reversing the direction of the applied field, indicating the existence of an additional antisymmetric component superimposed with the usual symmetric AMR term. This antisymmetric component shows a maximum along the major in-plane $⟨33\overline{2}⟩$ axes and vanishes along the other major in-plane $⟨\overline{1}10⟩$ axes. A phenomenological model based on the symmetry of the crystal provides a good explanation of the observed antisymmetric contribution to the PHE. The model shows that this component arises from the antisymmetric part of the magnetoresistivity tensor and is basically a second order Hall effect. It is shown that the observed effect can be ascribed to the Umkehr effect, which refers to the coexistence of even and odd terms in the component of magnetoresistivity tensor. A sign reversal of this antisymmetric component is also found for a Si content above 21 at. % and at temperatures below a certain critical temperature which increases with increasing Si content.

Figure 1

(a) Optical microscopy image of the Hall bar structure employed for the magnetotransport studies. The contacts are labeled and the crystallographic directions of the (113) plane are shown. (b) Planar Hall effect response from ${\mathrm{Fe}}_{3+x}{\mathrm{Si}}_{1-x}$ films grown on GaAs(113)A at 300 K for a sample with $x=0.07$ and magnetic field applied along $\left[33\overline{2}\right]$. (c) Separation of the symmetric and antisymmetric contribution of PHE.

Figure 2

(Color online) (a) Planar Hall effect response from the ${\mathrm{Fe}}_{3+x}{\mathrm{Si}}_{1-x}$ $(x=0.07)$ film grown on GaAs(113)A with magnetic field applied in-plane along $\left[\overline{1}10\right]$ at 300 K showing the vanishing antisymmetric component. (b) Angular dependence of ${\rho }_{xy}$ at 300 K with a saturating in-plane magnetic field so that ${\theta }_{\mathrm{H}}={\theta }_{\mathrm{M}}$. Open circles represent experimental data and solid line (in red color) is a fit using Eq. (3) (see text). (b) Separation of the symmetric and antisymmetric part of the PHE. Open circles represent experimental data and solid lines (in red color) are fitted curves using a $\sin 2{\theta }_{\mathrm{M}}$ behavior for symmetric part and ${\rho }_{\mathrm{SATM}}^0\cos {\theta }_{\mathrm{M}}+{\rho }_{\mathrm{SATM}}^1{\cos }^3{\theta }_{\mathrm{M}}$ type behavior for antisymmetric part. The major in-plane crystallographic directions for the (113) plane are also shown with 0° along $\left[33\overline{2}\right]$.

Figure 3

(Color online) (a) Planar Hall effect response from ${\mathrm{Fe}}_{3+x}{\mathrm{Si}}_{1-x}\left(113\right)$ $(x=0.07)$ film at 77 K with magnetic field applied in-plane along $\left[33\overline{2}\right]$. (b) Corresponding angular dependence of ${\rho }_{xy}$ at 77 K with a saturating in-plane magnetic field so that ${\theta }_{\mathrm{H}}={\theta }_{\mathrm{M}}$. (c) Separation of the symmetric and antisymmetric part of the PHE. Open circles represent experimental data and solid lines (in red color) are fitted curves as explained in Fig. 2.

Figure 4

(a) Temperature and composition dependence of the ${\rho }_{\mathrm{SATM}}={\rho }_{xy}(H>+H_{\mathrm{sat}})-{\rho }_{xy}(H<-H_{\mathrm{sat}})$ measured with a saturating field applied near to the $\left[33\overline{2}\right]$ direction. (b) Temperature dependence of ${\rho }_{\mathrm{AHE}}$ for two typical samples with $x=0.07$ and 0.15.

Figure 5

(Color online) (a) Field dependence of the AMR $\left({\rho }_{xx}\right)$ from the ${\mathrm{Fe}}_{3+x}{\mathrm{Si}}_{1-x}\left(113\right)$ film with $x=0.07$ at 300 K for different in-plane orientations. The open circles represent the easy axis of magnetization, for which the AMR signal does not change. Angular dependence of ${\rho }_{xx}$ at a fixed saturating field of $H=1\mathrm{kOe}$ obtained at (b) 300 K and (c) 77 K. For comparison, the amplitude of AMR is kept fixed for the three figures.