Correlating magnetic structure and magnetotransport in semimetal thin films of ${\mathrm{Eu}}_{1-x}{\mathrm{Sm}}_x{\mathrm{TiO}}_3$

We report on the evolution of the average and depth-dependent magnetic order in thin-film samples of biaxially stressed and electron-doped ${\mathrm{EuTiO}}_3$ for samples across a doping range $<0.1$ to $7.8\times {10}^{20}{\mathrm{cm}}^{-3}$. Under an applied in-plane magnetic field, the $G$-type antiferromagnetic ground state undergoes a continuous spin-flop phase transition into in-plane, field-polarized ferromagnetism. The critical field for ferromagnetism slightly decreases with an increasing number of free carriers, yet the field evolution of the spin-flop transition is qualitatively similar across the doping range. Unexpectedly, we observe interfacial ferromagnetism with saturated ${\mathrm{Eu}}^{2+}$ moments at the substrate interface at low fields preceding ferromagnetic saturation throughout the bulk of the degenerate semiconductor film. We discuss the implications of these findings for the unusual magnetotransport properties of this compound.

Figure 1

Magnetic neutron diffraction: raw diffraction scans along $l$ are shown both at base temperature (blue) and at the 10 K “background” (gold). Inset: the background-subtracted scan (black) reveals the $G$-type AFM ${\mathrm{Sm}}_x{\mathrm{Eu}}_{1-x}{\mathrm{TiO}}_3$ peak. This is fit to a simple Gaussian (red) with fixed width and fixed center to extract the area. Widths were fixed to the instrumental resolution; in the case of (103), 0.018 r.l.u. along $l$ ($7\text{nm}=9c$).

Figure 2

Order parameters: AFM peaks in green and FM peaks in red are shown for (a) metallic, (b) semimetallic, and (c) parent ${\mathrm{Sm}}_x{\mathrm{Eu}}_{1-x}{\mathrm{TiO}}_3\setminus \mathrm{LSAT}$(001) samples. Data are shown in symbols, and lines are error function fits to the data. In (b), the black symbols are magnetoresistance taken at 2 K with $I\left|\right|H\perp c$ for a similarly doped sample $n=3.4\times {10}^{20}{\mathrm{cm}}^{-3}$ which is 50 nm thick. Diffraction samples are 100 nm thick. Details are in the text.

Figure 3

Field-concentration phase diagram based on diffraction measurements of the parent, intermediate, and metallic samples. Label abbreviations are “AFM” antiferromagnetism and “FM” saturated ferromagnetism. The applied field is in-plane, perpendicular to the tetragonal $c$ axis. Error bars are from fit uncertainties in Fig. 2. Colored regions are speculative guides to the eye. Inset: Sketch of one predicted pair of conduction band crossings, projected on the spin $z$ component. Horizontal dashed lines indicate the Fermi energy at different carrier concentrations. DFT calculations predict Weyl nodes for $n\approx 4\times {10}^{20}{\mathrm{cm}}^{-3}$ near ($\pm 0.24\pi /a$, 0, 0). Adapted from Ref. [12].

Figure 4

Polarized neutron reflectometry: (a) data for the semimetallic intermediate doping sample ($n=4.0\times {10}^{20}{\mathrm{cm}}^{-3}$) at various applied fields at 0.35 K along with refined fits for magnetically uniform (dashed line) and interfacial magnetism (solid lines) models. (b) Magnetic scattering length density models from which the fits to the data were calculated. Gray data points are the best-fit refined magnetization value for each slab in the two-slab model with error plotted as the 95% confidence interval.