Magnetic field controllable planar Hall effect in ${\mathrm{Sr}}_2\mathrm{Ir}{\mathrm{O}}_4$ films

The planar Hall effect (PHE) has remarkable advantages for applications to spintronic devices and the study of intrinsic magnetic properties because of its high signal-to-noise ratio and low thermal drift. Here, the magnetic field controllable PHE in ${\mathrm{Sr}}_2\mathrm{Ir}{\mathrm{O}}_4/\mathrm{SrTi}{\mathrm{O}}_3$ (001) films is presented. The PHE transforms from a “sinusoidal-shaped” twofold symmetry to fourfold oscillations with decrease in the magnetic field at 35 K. Furthermore, the PHE is approximately two to three orders of magnitude larger than the giant PHE associated with ferromagnetic semiconductors as the temperature decreases. Based on subsequent measurements of the magnetic transport properties and calculations of the angle between the magnetization and current, the unexpected fourfold-symmetric PHE can be attributed to magnetocrystalline anisotropy and spin-orbital coupling. These observations of PHE facilitate a deeper understanding of the magnetic interactions in ${\mathrm{Sr}}_2\mathrm{Ir}{\mathrm{O}}_4$ films and indicate potential applications in spintronic or magnetic-sensor devices.

Figure 1

(a) Mechanism for generating a net in-plane magnetic moment. The rotations of the $\mathrm{Ir}{\mathrm{O}}_6$ octahedra and the relation between the octahedral rotation angle δ and the isospin canting angle $\varphi \left(\delta \approx \varphi \right)$ are presented in the left panel. The red circles denote ${\mathrm{Ir}}^{4+}$, whereas the blue circles denote ${\mathrm{O}}^{2-}$. The red arrow indicates the net moment. The right panel shows the antiferromagnetic structure of ${\mathrm{Sr}}_2\mathrm{Ir}{\mathrm{O}}_4$. A weak ferromagnetic phase is induced by the isospin-flip transitions when an in-plane magnetic field is applied. (b) X-ray-diffraction patterns of the ${\mathrm{Sr}}_2\mathrm{Ir}{\mathrm{O}}_4/\mathrm{SrTi}{\mathrm{O}}_3$ (001) thin film. The asterisks indicate the diffraction peaks of the $\mathrm{SrTi}{\mathrm{O}}_3$ substrate. The inset shows the x-ray reflectivity patterns, and the Laue oscillations around the (0012) peak, based on which the thickness of the ${\mathrm{Sr}}_2\mathrm{Ir}{\mathrm{O}}_4$ thin film can be determined [25].

Figure 2

(a) θ dependence of $R_{\mathrm{PHE}}$ at different temperatures for the ${\mathrm{Sr}}_2\mathrm{Ir}{\mathrm{O}}_4$ film at 9 T. Black lines indicate fitting to Eq. (1). (b) Schematic of the PHE measurement setup, wherein a current $I$ is applied along the [100] direction and $H$ is rotated in plane. Here, θ is the angle between $H$ and $I$, and φ is the angle between the magnetization $M$ and $I$. (c) $R_{\mathrm{PHE}}\left(\theta \right)$ for different magnetic fields at 35 K. Black lines indicate fitting to the data obtained when a fourth-order term is added in Eq. (1).

Figure 3

(a) Percentage deviation of the PHE obtained from Eq. (1) vs the magnetic field. Inset: The double arrow represents the magnitude of the deviation obtained by considering 0.5 and 9 T as examples. (b) Temperature-dependent $R_{xy}$ for different magnetic fields at $\theta ={135}^{\circ }$. Inset: θ dependence of $R_{\mathrm{PHE}}$ at 0.2 T.

Figure 4

(a) Extracted φ vs θ. Solid points denote φ(θ) at 35 K for different magnetic fields, whereas hollow points denote φ(θ) at 9 T for different temperatures. The black dashed line is a guide for the eyes when $\phi \approx \theta$ (b) The RSS (see text) as a function of $H$ at 35, 45, and 100 K. The arrow marks the corresponding anisotropy field at 100 K.

Figure 5

In-plane magnetic field dependent $R_{xy}$ at 35 K and $\theta ={20}^{\circ }$. The black and red arrows indicate the sweep direction of the field. Insets show the spin configurations for the magnetic-reversal process, where the dashed lines denote the direction of the easy axis, the pink lines indicate the magnetic field direction, and the blue arrows denote the net magnetization.