Large positive linear magnetoresistance in the two-dimensional t2g electron gas at the EuO/SrTiO3 interface

The development of novel nano-oxide spintronic devices would benefit greatly from interfacing with emergent phenomena at oxide interfaces. In this paper, we integrate highly spin-split ferromagnetic semiconductor EuO onto perovskite SrTiO3 (001). A careful deposition of Eu metal by molecular beam epitaxy results in EuO growth via oxygen out-diffusion from SrTiO3. This in turn leaves behind a highly conductive interfacial layer through generation of oxygen vacancies. Below the Curie temperature of 70 K of EuO, this spin-polarized two-dimensional t2g electron gas at the EuO/SrTiO3 interface displays very large positive linear magnetoresistance (MR). Soft x-ray angle-resolved photoemission spectroscopy (SX-ARPES) reveals the t2g nature of the carriers. First principles calculations strongly suggest that Zeeman splitting, caused by proximity magnetism and oxygen vacancies in SrTiO3, is responsible for the MR. This system offers an as-yet-unexplored route to pursue proximity-induced effects in the oxide two-dimensional t2g electron gas.


Supplementary Note 1
Supplementary Figure S6(a) displays XPS valence band spectra for the bare STO substrate (blue shading) and 10-nm-thick EuO film (red shading). Band offsets were calculated by both corelevel 1 and valence band 2,3 spectroscopy. The valence band maximum (EVBM) for each material was calculated using the linear extrapolation method. 4 By comparing energy offsets between the Ti 2p, Eu 3d, and valence band edge positions (as summarized in Table 1)  The VBO can also be determined directly from the valence band spectra. 2,3 For a heterostructure of 1 nm EuO/STO a contribution from the substrate is visible along with an attenuated contribution from the substrate (Supplementary Figure S6 (a), black open circles). We simulated a fit (purple solid line) to the heterostructure by scaling and offsetting the pure valence band spectra measured for the STO substrate and thick EuO film. This method uses an "all at once" fit minimizing χ 2 by the Levenberg-Marquardt algorithm implemented in Igor Pro software (WaveMetrics, Lake Oswego, OR). The difference between the measured and simulated spectra is also plotted (black line). Using this method, we calculate VBOsim = 2.26 eV, in good agreement with the offset calculated above by the core levels. The band profile is illustrated in Supplementary   Figure S6(b).

Supplementary Note 2
Our calculations follow Onose et al.'s work 5 , which is based on Boltzmann transport theory. In the present case, we have one interface (IF) ↑ band, and three unpolarized t2g bands for deep layers (we call them bulk t2g states). All these states are confined along the z direction. From abinitio calculations, the IF band is found to be split down by ∆ compared with the other bands and ∆ is about 0.15 eV. Thus, we can write the energy near the point for these bands 6 : Here, stands for light mass while ℎ stands for heavy mass. According to ARPES experiments 7 , * ≈ 0.7 , * ≈ 10~20 .
Without considering the spin degree of freedom, we can get the density of states (DOS) for the confined t 2g states: Taking the 3D conductivity tensor as a reference 8 , we get the 2D conductivity tensor for the three t 2g states: From this, we can see that the contribution of the state to is very small compared that of the state.
With an external magnetic field H, the majority band is shifted down and the minority band is shifted up. In our case, to first order, the change in the Fermi energy could be obtained by number conservation: where ∑ ( ) 2 takes the summation of DOS over all three bulk 2 bands at and ↑ ( + ∆) refers to the DOS of the IF ↑ band.
The conductivity without external magnetic field can be written as: The change of magnetoresistance is: To get a positive linear magnetoresistance (LMR), the sufficient conditions are: Considering strong scattering at the interface, it is highly possible that the above conditions could be satisfied. Therefore, we argue that the Zeeman effect is the likely origin of positive LMR in our system.

Supplementary Figures
Supplementary Figure S1: XPS Eu (a) 4d and (b) 3d core level measurements for varied substrate temperature and oxygen partial pressure.