Magnetism and local structure in low-dimensional Mott insulating GdTiO${}_3$

Cation displacements, oxygen octahedral tilts, and magnetism of epitaxial, ferrimagnetic, insulating GdTiO${}_3$ films sandwiched between cubic SrTiO${}_3$ layers are studied using scanning transmission electron microscopy and magnetization measurements. With decreasing GdTiO${}_3$ film thickness, structural (GdFeO${}_3$-type) distortions are reduced, concomitant with a reduction in the Curie temperature. Ferromagnetism persists to smaller deviations from the cubic perovskite structure than is the case for the bulk rare-earth titanates. The results indicate that the ferromagnetic ground state is controlled by the narrow bandwidth, exchange and orbital ordering, and only to second order depends on the amount of the GdFeO${}_3$-type distortion.

Figure 1

(a) HAADF-STEM image of a 20-nm GdTiO${}_3$ film showing Gd displacements. The angle θ is measured between three successive Gd columns. A schematic of the unit cell is superimposed. (b)–(d) Representative images of 3.5-, 2.4-, and 2.0-nm-thick films.

Figure 2

Deviation angles for each $A$O plane across SrTiO${}_3$/GdTiO${}_3$/SrTiO${}_3$ interfaces with different GdTiO${}_3$ thicknesses. The angle for the 20-nm film is indicated by the dashed line and is an average over ∼100 GdO planes. Shaded regions indicate the extent of the GdTiO${}_3$ film for each sample, determined from the HAADF image intensities.

Figure 3

Simulated “GdTiO${}_3$” PACBED patterns for different Gd displacements and octahedral tilts (TEM foil thickness: 18.8 nm). The numbers indicate the degree of distortion, with 0 signifying no distortion, 1 the distortion in GdTiO${}_3$, and ½ corresponding to the intermediate distortion. The top-left panel corresponds to the cubic structure, while the bottom-right panel is bulk GdTiO${}_3$.

Figure 4

Experimental (top row) and simulated (bottom row) PACBED patterns of GdTiO${}_3$ and SrTiO${}_3$. White labels indicate the TEM foil thickness, and black ones the GdTiO${}_3$ layer thicknesses from which the experimental data was acquired. Simulated patterns use the expected octahedral tilts from measured deviation angles. Gd displacements were taken to be bulklike for both GdTiO${}_3$ simulations. The top half of simulated patterns include Gaussian convolution to account for detector point spread function, and show a better match to experimental patterns.

Figure 5

(a) Magnetization as a function of temperature for samples with GdTiO${}_3$ films of various thicknesses recorded on cooling under a field of 100 Oe. The arrows indicate $T_c$. The data from the 19-nm sample is from Ref. 20. (b) Magnetization as a function of magnetic field at 2 K.

Figure 6

Measured deviation angles (open diamonds, top graph) for GdTiO${}_3$ films with different film thicknesses. The FM stability region is indicated. The angles are an average of the center regions in the 3.5 and 2.4 nm quantum wells, and the peak value for the 2.0 nm quantum well. The arrow represents the estimated uncertainty of ±1°, estimated from the SrTiO${}_3$ deviation angle measurements, shown only on 20-nm film data for clarity, but applies to all measurements. The bottom graph (open circles) shows the deviation angles for bulk rare-earth titanates (Ref. 12) with different rare-earth ionic radii (Ref. 31). Filled triangles estimate the effects of coherent substrate strain and microscope scan asymmetry (∼2$\%$ difference between $x$ and $y$ directions, measured from cubic samples). Both change the measured lattice parameters and, hence, deviation angles. The FM and AFM stability regions are indicated.