Single-domain perpendicular magnetization induced by the coherent O $2p$-Ru $4d$ hybridized state in an ultra-high-quality $\mathrm{SrRu}{\mathrm{O}}_3$ film

We investigated the Ru $4d$ and O $2p$ electronic structure and magnetic properties of an ultrahigh-quality $\mathrm{SrRu}{\mathrm{O}}_3$ film on $\mathrm{SrTi}{\mathrm{O}}_3$ grown by machine-learning assisted molecular-beam epitaxy. The high itinerancy and long quantum lifetimes of the quasiparticles in the Ru $4d$ $t_{2g}$-O $2p$ hybridized valence band are confirmed by observing the prominent well-screened peak in the Ru $3d$ core-level photoemission spectrum, the coherent peak near the Fermi energy in the valence-band spectrum, and quantum oscillations in the resistivity. The element-specific magnetic properties and the hybridization between the Ru $4d$ and O $2p$ orbitals were characterized by Ru $M_{2,3}$-edge and O $K$-edge soft x-ray absorption spectroscopy and x-ray magnetic circular dichroism measurements. The ultrahigh-quality $\mathrm{SrRu}{\mathrm{O}}_3$ film with the residual resistivity ratio of 86 shows the large orbital magnetic moment of oxygen ions induced by the strong orbital hybridization of the O $2p$ states with the spin-polarized Ru $4d$ $t_{2g}$ states. The film also shows single-domain perpendicular magnetization with an almost ideal remanent magnetization ratio of 0.97. These results provide detailed insights into the relevance between orbital hybridization and the perpendicular magnetic anisotropy in $\mathrm{SrRu}{\mathrm{O}}_3/\mathrm{SrTi}{\mathrm{O}}_3$ systems.

Figure 1

RHEED patterns of a $\mathrm{SrRu}{\mathrm{O}}_3$ film taken along the (a) [100] and (b) [110] axes of the $\mathrm{SrTi}{\mathrm{O}}_3$ substrates. (c) HAADF-STEM and (d) ABF-STEM images of a $\mathrm{SrRu}{\mathrm{O}}_3$ film taken along the [100] axis of the $\mathrm{SrTi}{\mathrm{O}}_3$ substrates. The insets in (c) and (d) are magnified images near the interface.

Figure 2

(a) Temperature dependence of resistivity ρ of the $\mathrm{SrRu}{\mathrm{O}}_3$ film. The inset in (a) is a ρ vs $T^2$ plot with a linear fitting (black dashed line). We defined the Fermi liquid temperature range as the temperature range where the experimental ${\rho }_{\mathrm{xx}}$ and the linear fitting line in ${\rho }_{\mathrm{xx}}$ vs $T^2$ are close enough to each other $(<0.1\mu \mathrm{\Omega }\mathrm{cm})$. (b) SdH oscillation measured at 2 K with ${\mu }_{0}H$ $(3\mathrm{T}<{\mu }_{0}H<9\mathrm{T})$ applied in the out-of-plane [001] direction of the $\mathrm{SrTi}{\mathrm{O}}_3$ substrate for the $\mathrm{SrRu}{\mathrm{O}}_3$ film. The inset shows SdH oscillation observed at 0.1 K with ${\mu }_{0}H$ $(13\mathrm{T}<{\mu }_{0}H<14\mathrm{T})$ .

Figure 3

SX-PES spectra of the $\mathrm{SrRu}{\mathrm{O}}_3$ film. (a) Ru $3d$ and Sr $3p$ core-level spectrum taken with the photon energy (hν) of 1200 eV at 20 K. (b) Peak fitting for the Ru $3d$ spectrum. WS denotes the well-screened peak. Fitting functions are Voigt and asymmetric Gaussian. (c) Valence-band spectra taken with hν of 600 eV at 20 K.

Figure 4

(a) Ru $M_{2,3}$-edge XAS and XMCD spectra for the $\mathrm{SrRu}{\mathrm{O}}_3$ film at 6.5 K with a magnetic field ${\mu }_{0}H=0\mathrm{T}$ applied perpendicular to the film surface. The spectra were measured after the application of ${\mu }_{0}H=2\mathrm{T}$. (b) XMCD spectra and integrated XMCD signals from 450 eV taken at 6.5 K with a magnetic field ${\mu }_{0}H=2\mathrm{T}$ applied perpendicular to the film surface.

Figure 5

(a) Ru $M_{2,3}$-edge XMCD spectra for the $\mathrm{SrRu}{\mathrm{O}}_3$ film at 6.5 to 200 K with a magnetic field ${\mu }_{0}H=0$ or 2 T applied perpendicular to the film surface. Here, the zero magnetic field was set after the application of ${\mu }_{0}H=2\mathrm{T}$. (b) Ru $M_{2,3}$-edge XMCD spectra normalized at 484.7 eV for the $\mathrm{SrRu}{\mathrm{O}}_3$ film at 6.5 to 200 K with a magnetic field ${\mu }_{0}H=0$ or 2 T applied perpendicular to the film surface. Spectra measured at 6.5, 10, 20, 40, and 100 K are almost completely overlapped. (c) XMCD spectra and integrated XMCD signals from 450 eV at 200 K with a magnetic field ${\mu }_{0}H=2\mathrm{T}$ applied perpendicular to the film surface.

Figure 6

O $K$-edge XAS and XMCD spectra for the $\mathrm{SrRu}{\mathrm{O}}_3$ film at 6 K with a magnetic field ${\mu }_{0}H=2\mathrm{T}$ applied perpendicular to the film surface.

Figure 7

XMCD $H$ curves measured at the Ru $M_3$ edge (462.4 eV) for the $\mathrm{SrRu}{\mathrm{O}}_3$ film at 6.5 K. The vertical axis of the XMCD intensity at 2 T has been scaled so that it represents the sum of the total magnetic moment $M=m_{\mathrm{spin}}+m_{\mathrm{orb}}$ of the Ru ions estimated from Fig. 4.

Figure 8

Magnetic moment vs $H$ curves for the $\mathrm{SrRu}{\mathrm{O}}_3$ film measured by SQUID at 6 K with magnetic fields applied to the out-of-plane [001] (blue circles) and in-plane [100] (purple circles) directions of the $\mathrm{SrTi}{\mathrm{O}}_3$ substrate.