Linear colossal magnetoresistance and magnetic textures in ${\text{LaTiO}}_3$ thin films on ${\text{SrTiO}}_3$

Linear magnetoresistance (LMR) is of particular interest for memory, electronics, and sensing applications, especially when it does not saturate over a wide range of magnetic fields. Structural disorder, however, also tends to limit the mobility and hence the overall LMR amplitude. An alternative route to achieve large LMR is via nonstructural inhomogeneities which do not affect the zero field mobility, like magnetic domains. Here, we report a colossal positive linear magnetoresistance in $\mathrm{La}{\mathrm{TiO}}_3/\mathrm{Sr}{\mathrm{TiO}}_3$ heterostructures, with amplitude up to 6500% at 9T at low temperature. The colossal amplitude of the LMR, one of the largest in oxide heterostructure, stems from the unusual combination of a very high heterostructure mobility, up to 40 000 ${\mathrm{cm}}^2{\mathrm{V}}^{-1}{\mathrm{s}}^{-1}$, and a very large coverage of low-mobility regions. Low-temperature Lorentz transmission electron microscopy measurements further reveals a striped magnetic structure at the sub-$\mu \mathrm{m}$ scale in the $\mathrm{La}{\mathrm{TiO}}_3$ layer, compatible with in-plane spiral magnetism, with very high surface coverage. We propose that the low-mobility regions and striped magnetic regions are correlated, we model the increase in scattering induced by the magnetic texture, and we show that the non saturating LMR fits the Parish-Littlewood scenario. Our results provide a novel route for the engineering of large-LMR systems, using magnetic texture.

Figure 1

(a) Top: Schematic of the LTO/STO heterostructures patterned in a Hall bar shape and embedded in amorphous LTO (a-LTO). Bottom: Cross-sectional high resolution scanning TEM image of an LTO 3 u.c. (thickness 1.2 nm) thin film on STO. Scale bar: $1\mathrm{nm}$. (b) Optical image of a Hall bar, outlined with a dashed black line. Scale bar: 100 $\mu \mathrm{m}$. (c) Resistivity versus temperature for different Hall bars (HB) on the 3, 5, and 10 u.c. thick samples. (d) typical Hall effect measurements of the 3 u.c. sample (Hall bar 1) for temperatures ranging from 5 to 300 K. In our experimental configuration, this slope corresponds to electronlike charge carriers. (e) 2D Hall carrier density and (f) mobility of the 3, 5, and 10 u.c. thick samples versus temperature.

Figure 2

Magnetoresistance as a function of the perpendicular magnetic field for LTO thicknesses of 3, 5, and 10 u.c. (a) Linear magnetoresistance at $T=3\mathrm{K}$ for all three thicknesses and (b) a zoomed in view of only the 5 u.c. and the 10 u.c. samples. (c) Magnetoresistance MR (as defined in the main text) of the samples shown in panel (a) plotted in %. The dashed lines corresponds to a linear fit. Inset: the temperature dependence of the MR in a log-log scale for the three thicknesses at $B=9\mathrm{T}.$ (d) Linear slope of the MR at 8T as a function of the mobility of LTO thin films of different thicknesses. Solid lines correspond to linear fits. The areal coverage (in %) of the low mobility regions are extracted from the linear fit.

Figure 3

Temperature- and field-dependent Lorentz transmission electron microscopy (LTEM) of characteristic uniaxial magnetic modulation/texture. (a) Scattering and TEM specimen geometry employed for LTEM. Panels (b), (c) show LTEM images at $10\mathrm{K}$ without magnetic field and with an applied out-of-plane field of $200\mathrm{mT}$. The latter exhibits a magnetic texture (highlighted by red shaded areas and red lines) at bending contours (highlighted by green lines), where the direction of modulation agrees with a $\langle 100\rangle$ crystallographic axis of the cubic $\mathrm{Sr}{\mathrm{TiO}}_3$ substrate. Panels (d)–(h) show the evolution of LTEM images in a single area at selected temperatures between 10 K and 90 K. The gradual shrinkage and motion of the magnetic texture associated with bending contours I and II with increasing temperature until 90 K is highlighted. Panel (i) displays a line profile along the line scan over the uniaxially modulated region indicated as red arrow in panel (d) revealing a periodicity of about $200\mathrm{nm}$. (j) Schematic depiction of the LTEM contrast (one period) by the spin modulation of the Ti atoms.

Figure 4

Schematic view of electronic transport in magnetic LTO/STO heterostructures in the Parish-Littlewood framework. Spiral magnetic domains (represented by stripes) are associated with increased magnetic scattering, leading to lower mobility. In LTO regions which are not in the spiral ground state (light green), or a possible 2DES (yellow), magnetic scattering is reduced, leading to higher mobility. Doped STO is also known to exhibit high mobility.

Figure 5

Film growth and characterization. (a) RHEED pattern of the bare substrate, (b) RHEED pattern of the completed 5 uc ${\mathrm{LaTiO}}_3$ sample, and (c) RHEED intensity of the specular spot during growth for a 3 u.c., a 5 u.c., and a 10 u.c. sample. Each oscillation corresponds to a completed unit cell layer. (d) LEED image of the film surface at a electron kinetic energy of 120 eV. The clean $1\times 1$ reconstruction is imposed by the STO substrate. (e) AFM image of the bare substrate. (f) AFM image of a 5 u.c. ${\mathrm{LaTiO}}_3$ film, with (g) a line profile. Large flat terraces with unit cell high steps of roughly 4 Å are visible.

Figure 6

X-ray photoemission spectroscopy. (a) X-ray photoemission spectrum of the valence band region with zoom in on the Ti $3\mathit{d}$ containing region just below the Fermi energy. The quasiparticle spectral weight indicates metallic behavior of LTO. (b) X-ray photoemission spectra of the Ti $2\mathit{p}$ core level, taken at emission angles $2.5^{\circ }$ and ${25}^{\circ }$ off normal emission and a photon energy of 850 eV. Intensity is normalized to integral of the Ti 2p spectral weight. The spectra at both emission angles are heavily dominated by the ${\mathrm{Ti}}^{4+}$ valency.

Figure 7

Photoemission spectroscopy. $\mathrm{\Gamma }$-X band map of the same sample as in Fig. 6 taken at 461.5 eV.

Figure 8

Sondheimer oscillations in 3 u.c. samples. (a) Raw longitudinal magnetoresistance at several temperatures. (b) Second derivative of the longitudinal magnetoresistance in panel (a), revealing oscillations around zero field at low temperature. (c) Indexed peak position of the oscillations. The linear dependence of the peak position with magnetic field reveals the Sondheimer origin.

Figure 9

Magnetoresistance in log-log scale for samples of all three thicknesses. For each thickness [(a) 3 u.c., (b) 5 u.c., (c) 10 u.c.], curves at different temperatures are shown. Dashed lines show linear fits of the lowest temperature data and the intersect with zero-field value.

Figure 10

Normalized magnetoresistance at various temperatures for samples of all three thicknesses, same as in Fig. 9. For each sample [(a) 3 u.c., (b) 5 u.c., (c) 10 u.c.]. Dashed lines are linear fit, and dotted lines are parabolic fits. The transition between linear and parabolic-like behavior occurs around $\sim 40\mathrm{K}$ for the 3 u.c. and the 5 u.c. samples.

Figure 11

LTEM images of LTO sample region depicted in Figs. 3 and 3, (a) underfocus, (b) in focus, and (c) overfocus. Stripe contrast is inverted going from under- to overfocus and consequently vanished in focus.

Figure 12

Perpendicular uniaxial stripe modulations aligned with crystal axis orientations of ${\mathrm{SrTiO}}_3$. The striped areas are highlighted with red shading and the stripes with red lines.

Figure 13

Magnetic moments (yellow arrows) on the four primitive ${\mathrm{Ti}}^{3+}$ ions in the ${\mathrm{LaTiO}}_3$ structure. They are labeled 1-2-3-4. Ti atoms are shown in blue, O atoms in red, and La atoms in green.