Structural control of magnetic anisotropy in a strain-driven multiferroic EuTiO${}_3$ thin film

Octahedral distortion plays a key role in engineering the physical properties of heterostructures composed of perovskite oxides. We observe a strong in-plane uniaxial magnetic anisotropy in a strain-enabled multiferroic EuTiO${}_3$ thin film epitaxially grown on a (110)${}_{\mathrm{o}}$ DyScO${}_3$ substrate. First-principles calculations show that the magnetic anisotropy is closely correlated with the uniaxial TiO${}_6$ octahedral tilting and the ferroelectric polarization of the film, indicating potential strong magnetoelectric coupling in the strain-engineered multiferroic system.

Figure 1

(a) Reflectivity as a function of $Q$ measured at $T$ = 2.8 K after the 25 nm thick EuTiO${}_3$/(110)${}_{\mathrm{o}}$ DyScO${}_3$ sample is cooled down in a 100 Oe magnetic field applied along the [001]${}_{\mathrm{o}}$ direction of the (110)${}_{\mathrm{o}}$ DyScO${}_3$ substrate. A measurement field of 10 Oe is applied to maintain the neutron polarization direction. The inset shows the $Q$ dependence of reflectivity of non-spin-flip scattering measured at $T$ = 10 K. Symbols are experimental data and solid curves are the fits; error bars correspond to ±1 σ. (b) Depth profile of the magnitude and angle of the magnetization of the sample calculated from the data fitting. Inset shows the schematics of the film with nonuniform magnetization through the film thickness. Blue, violet, and red colors represent the top surface, the intermediate layer, and the interface, respectively.

Figure 2

(a) Schematic of the crystal structure of EuTiO${}_3$ under biaxial tensile strain with pseudocubic indices. (b) Temperature dependence of the magnetization of the EuTiO${}_3$/DyScO${}_3$ thin film with a 100 Oe magnetic field applied along various principle axes while cooling down from 10 to 1.8 K. Measurements were performed at zero field during the warm up process. The inset shows the directions measured. Note that the pseudocubic directions of the epitaxial EuTiO${}_3$ film are aligned with the pseudocubic directions of the DyScO${}_3$ substrate.

Figure 3

(a) Calculated energies as a function of in-plane biaxial strain for polar structures with two different tilt symmetry patterns: $a^{-}$$b^{-}$$c^0$ and $a^0$$b^0$$c^{-}$. (b) Calculated enthalpies of antiferromagnetic (AFM) and ferromagnetic (FM) states as a function of the ferroelectric polarization for EuTiO${}_3$ with 1.1$\%$ tensile strain, corresponding to commensurate EuTiO${}_3$/(110)${}_{\mathrm{o}}$ DyScO${}_3$.

Figure 4

Schematic illustrating that the calculated directions of the TiO${}_6$ octahedral rotation axis (RA) and ferroelectric polarization (P) are perpendicular to the magnetic easy axis (M) of the EuTiO${}_3$ film. The directions given refer to the pseudocubic unit cell. Note that the demagnetization energy term was not taken into account in the DFT calculations, leading to the out-of-plane magnetization component.