Electric field tunable anisotropic magnetoresistance effect in an epitaxial ${\mathrm{Co}}_2\mathrm{Fe}\mathrm{Si}/\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_3$ interfacial multiferroic system

We study magnetic and magnetotransport properties of an epitaxial interfacial multiferroic system consisting of a ferromagnetic Heusler-alloy ${\mathrm{Co}}_2\mathrm{Fe}\mathrm{Si}$ and a ferroelectric-oxide $\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_3$. $L{2}_1$-ordered ${\mathrm{Co}}_2\mathrm{Fe}\mathrm{Si}$ epilayers on $\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_3\left(001\right)$ show an in-plane uniaxial magnetic anisotropy with strong temperature dependence, induced by the presence of the magnetoelastic effect via the spin-orbit interaction at the ${\mathrm{Co}}_2\mathrm{Fe}\mathrm{Si}/\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_3\left(001\right)$ interface. In the ${\mathrm{Co}}_2\mathrm{Fe}\mathrm{Si}$ Hall-bar devices, the anisotropic magnetoresistance (AMR) hysteretic curves depending on in-plane magnetization reversal processes on the $a$ and $c$ domains of $\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_3\left(001\right)$ are clearly observed at room temperature. Notably, the magnitude of the AMR ratio (%) for ${\mathrm{Co}}_2\mathrm{Fe}\mathrm{Si}$ Hall-bar devices can be tuned through the $a-c$ domain wall motion of $\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_3\left(001\right)$ by applying electric fields. We propose that the tunable AMR effect is associated with the modulation of the spin-orbit interaction, exchange interaction, and/or the electronic band structure near the Fermi level by applying electric fields in the epitaxial ${\mathrm{Co}}_2\mathrm{Fe}\mathrm{Si}/\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_3\left(001\right)$ interfacial multiferroic system.

Figure 1

Schematics of crystal structure and atomic arrangements of (001) plane for (a) ${\mathrm{Co}}_2\mathrm{Fe}\mathrm{Si}$ and (b) $\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_3$, respectively. (c) $\theta \text{−}2\theta$ measurements and (d) $\varphi$-scan measurements of (111) plane for an MBE-grown ${\mathrm{Co}}_2\mathrm{Fe}\mathrm{Si}$ layer. The gray data in Fig. 1 is the $\theta \text{−}2\theta$ XRD pattern for a $\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_3\left(001\right)$ substrate. The intensity of the $\theta \text{−}2\theta$ XRD pattern for the ${\mathrm{Co}}_2\mathrm{Fe}\mathrm{Si}/\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_3$ heterostructure is multiplied by a factor of 10. The inset in Fig. 1 shows a RHEED pattern of the surface after the growth of the ${\mathrm{Co}}_2\mathrm{Fe}\mathrm{Si}$ layer on $\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_3\left(001\right)$.

Figure 2

(a) HAADF-STEM image with EDX line profiles of an epitaxial ${\mathrm{Co}}_2\mathrm{Fe}\mathrm{Si}/\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_3\left(001\right)$ heterostructure. (b) Atomic resolution HAADF-STEM image of the ${\mathrm{Co}}_2\mathrm{Fe}\mathrm{Si}/\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_3$ interface, acquired along the $\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_3\left[110\right]$ and ${\mathrm{Co}}_2\mathrm{Fe}\mathrm{Si}\left[100\right]$ zone axes, respectively, showing the abrupt epitaxial growth of the ${\mathrm{Co}}_2\mathrm{Fe}\mathrm{Si}$ epilayer. (c) A high-field $M\text{−}H$ curve at 300 K for the ${\mathrm{Co}}_2\mathrm{Fe}\mathrm{Si}/\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_3$ heterostructure.

Figure 3

(a) $M\text{−}T$ curves for an epitaxial ${\mathrm{Co}}_2\mathrm{Fe}\mathrm{Si}/\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_3$ heterostructure under the application of an $H$ of 0.5 mT. The directions of $H$ under the measurements are also depicted in the inset. Schematics of structural phase transitions from tetragonal to orthorhombic phases at 278 K and from orthorhombic to rhombohedral phases at 183 K in $\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_3$ are also shown in the inset. (b) Polar plots of the normalized remanent magnetization ($M_r/M_s$) at 300 K (tetragonal phase), 230 K (orthorhombic phase), and 150 K (rhombohedral phase).

Figure 4

Low-field $M\text{−}H$ curves for an epitaxial ${\mathrm{Co}}_2\mathrm{Fe}\mathrm{Si}/\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_3$ heterostructure, measured under applying $H$ along (a) [100], (b) [110], and (c) [010] directions of $\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_3$ at 300 K.

Figure 5

(a) Schematic and (b) optical micrograph of a fabricated ${\mathrm{Co}}_2\mathrm{Fe}\mathrm{Si}$ Hall-bar device on $\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_3$. (c) Room-temperature $R_{xx}\text{−}H$ curves of device A for $H//\left[100\right]$ of $\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_3$ and $H\perp \left[100\right]$ of $\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_3$ at an $E$ of zero. (d) Schematics of the correlation between magnetization directions of the ${\mathrm{Co}}_2\mathrm{Fe}\mathrm{Si}$ epilayer and $a$ or $c$ domain of $\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_3$ under sweeping $H$. The dotted pink lines correspond to the magnetic easy axis of the ${\mathrm{Co}}_2\mathrm{Fe}\mathrm{Si}$ epilayers on each domain of $\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_3$.

Figure 6

Low-field MR curves for (a) device A and (b) device B under various $E$ from zero to $-1.8$ kV/cm at room temperature. Although there is no difference in the device fabrication process between device A and device B, the $E$ effect on the MR curves is different.

Figure 7

The angular ($\varphi$) dependence of the AMR ratio for (a) device A and (b) device B at $E=0$ and $-1.8\mathrm{kV}/\mathrm{cm}$ at room temperature under $H=0.4\mathrm{T}$. (c) EMR ratio versus $E$ for devices A and B at room temperature. The inset of (c) shows $R_{xx}$ versus $E$ for device A under $H=0.4\mathrm{T}$ at $\varphi =0^{\circ }$ (closed circles) and ${90}^{\circ }$ (open circles), respectively.