Giant crystalline anisotropic magnetoresistance in nonmagnetic perovskite oxide heterostructures

Anisotropic magnetoresistance (AMR) was observed by Lord Kelvin one-and-half centuries ago in iron and nickel. The resistance of these ferromagnetic conductors showed a few percent change when a magnetic field was applied along or across the current. Subsequently, a 20% AMR was demonstrated in alloys of nickel and iron (permalloys). Efforts have then been devoted to extend this effect in multifunctional materials. The oxide heterostructure exhibiting two-dimensional electron liquid is one of the potential candidates as it has shown to exhibit emergent magnetic ordering, strong spin-orbit interactions, and anisotropic magnetoresistance. Here we show a giant crystalline AMR as large as 57% to 104% in anisotropic quantum wells based on nonmagnetic perovskite oxides $\mathrm{LaAl}{\mathrm{O}}_3$ and $\mathrm{SrTi}{\mathrm{O}}_3$, providing an alternative way in tailoring AMR with an extremely large effect. The AMR maximum appears when the magnetic field points along the in-plane $\left[1\overline{1}0\right]$ direction, irrespective of the direction of current flow, which is consistent with the idea of crystalline AMR. Data analysis and density functional theory calculation show that the observed giant crystalline AMR mainly originates from the strong anisotropic spin-orbit field at the interface due to its unique elliptical Fermi surface related to its orbital configuration and reconstruction. This work demonstrates that perovskite oxide interface is a unique platform for orbital physics.

Figure 1

Transport properties and anisotropic magnetoresistance (AMR) at $\mathrm{LaAl}{\mathrm{O}}_3/\mathrm{SrTi}{\mathrm{O}}_3$ (LAO/STO) (110) heterostructures. (a) Resistance as a function of temperature measured in the annealed LAO/STO (110) sample in the current along $\left[1\overline{1}0\right]$-orientated Hall bar ($C_{[1-10]}$) and in the current along [001]-orientated Hall bar ($C_{\left[001\right]}$) geometries showing resistance upturn at low temperatures for $C_{[1-10]}$. Inset shows a sketch of stack and transport measurement geometries. (b) Resistance anisotropic defined by ${(R_{[1-10]}/R_{\left[001\right]}-1)}^{*}100\%$ as a function of temperature for data shown in (a). Inset shows a sketch of definition of angle θ, which is the angle between magnetic field and [001] direction. (c) Magnetoresistance measurement in an in-plane rotating magnetic field of 9 T in $\left[1\overline{1}0\right]$- and [001]-orientated Hall bars with the angles defiend in (b). (d) The $\ln \left(R_{[1-10]}/R_{\left[001\right]}\right)\mathrm{vs}{T}^{-1/3}$ plot for LAO/STO (110) sample and a 2D variable range hopping (VRH) fit.

Figure 2

Temperature dependent anisotropic magnetoresistance (AMR) signals of $\left[1\overline{1}0\right]$- and [001]-orientated Hall bars with an in-plane rotating magnetic field of 9 T. The angle is fixed according to the sample orientation. $\theta =0^{\circ }$ is for magnetic field along [001] and $\theta ={90}^{\circ }$ for $\left[1\overline{1}0\right]$. (a), (c), and (e) In $\left[1\overline{1}0\right]$-orientated Hall bar, we observe an increasing AMR signal up to 60% with decreasing temperature. The AMR signal is mostly positive and the maximum AMR always appears at θ close to or equal 90° or 270°, namely, when the magnetic field is parallel to [1, 2, 3, 4, 5, 6, 7, 8, 9, 10] direction. The maximum AMR appears at magnetic field parallel to current direction. The corresponding raw magnetoresistance data are shown in the right axis in each figure. (g) AMR map of $\left[1\overline{1}0\right]$-orientated Hall bar for the entire temperature range below 20 K. (b), (d), and (f) In [001]-orientated Hall bar, we observe an increasing AMR signal up to 20% with decreasing temperature. The AMR signal is mostly positive and the maximum AMR always appears at θ close to or equal 90° or 270°, namely, when the magnetic field is parallel to $\left[1\overline{1}0\right]$ direction. The maximum AMR appears at magnetic field perpendicular to current direction. The corresponding raw magnetoresistance data are shown in the right axis in each figure. (h) AMR map of [001]-orientated Hall bar for the entire temperature range below 20 K.

Figure 3

Comparison of the anisotropic magnetoresistance (AMR) in $\left[1\overline{1}0\right]$- and [001]-orientated Hall bars. (a) and (b) Polar plots corresponding to AMR experiments in a 9 T in-plane rotating field and temperature 5 K. The maximum AMR always appears at or close to $\left[1\overline{1}0\right]$ direction which is not expected in a normal AMR mechanism contributed by spin-orbit coupling. The AMR of both orientations show violation from sin(2θ) behavior and distinct higher harmonic or asymmetric component. (c) and (d) Field-rotation AMR maps demonstrating the AMR contribution moment dominating from $\left[1\overline{1}0\right]$ direction.

Figure 4

Field dependent magnetoresistance in $\left[1\overline{1}0\right]$- and [001]-orientated Hall bars at 5 K. (a) Magnetoresistance of $\left[1\overline{1}0\right]$-orientated Hall bar in applied magnetic field along $\theta =0^{\circ }$ and ${90}^{\circ }$. (b) Field-sweep magnetoresistance map of $\left[1\overline{1}0\right]$-orientated Hall bar for the entire range of field angles. (c) Magnetoresistance of [001]-orientated Hall bar in applied magnetic field along $\theta =0^{\circ }$ and 90°. (d) Field-sweep magnetoresistance map of [001]-orientated Hall bar for the entire range of field angles.

Figure 5

Longitudinal ADMR $R_{xx}(B,\theta )$ and $R_{yy}(B,\theta )$ and transverse ADMR $R_{xy}(B,\theta )$ and $R_{yx}(B,\theta )$ measurement in an in-plane rotating magnetic field of 3, 6, and 9 T in (a) and (b) [001]-orientated and (c) and (d) $\left[1\overline{1}0\right]$-orientated Hall bars with the angles at 5 K. $x$ direction is [001] and $y$ direction is $\left[1\overline{1}0\right]$.

Figure 6

Hybridized and polarized orbitals in LAO/STO(110) heterostructures calculated by DFT, spatial charge distribution, and Fermi surface of LAO/STO(110) heterostructure. Structural guidance for the model of LAO/STO(110) with spatial charge distribution along [001] (a) and along $\left[1\overline{1}0\right]$ (b). (c) Electronic band structure of LAO/STO(110). (d) and (e) The calculated total and interfacial density of states. (f) Charge density distribution at interfacial $\mathrm{Ti}{\mathrm{O}}_2$ layer of LAO/STO(110). (g) Calculated Fermi surface of the LAO/STO(110) in (110) plane.

Figure 7

AMR up to 104% observed in 10 unit cells LAO/STO(110) sample grown at oxygen partial pressure of $5\times {10}^{-5}\mathrm{Torr}$. Magnetoresistance measurement in an in-plane rotating magnetic field of 3, 6, and 9 T in (a) $\left[1\overline{1}0\right]$-orientated and (b) [001]-orientated Hall bars with the angles.

Figure 8

Charge density distribution and density of states in LAO/STO(110) heterostructures with interface oxygen vacancy calculated by DFT. Structural guidance for the model of LAO/STO(110) with spatial charge distribution along [001] (a) and along $\left[1\overline{1}0\right]$ (b). (c) Calculated total charge density of the LAO/STO(110). (d) Charge density of the LAO/STO(110) in the interface plane (110).

Figure 9

Origin of the noncrystalline and crystalline AMR in LAO/STO. (a) LAO/STO(001) with carrier density $n$ below the critical value $n_c$. (b) LAO/STO(001) with carrier density $n$ above the critical value $n_c$. (c) LAO/STO(110) with Fermi energy only occupying the degenerate lowest energy states $d_{xz}/d_{yz}$. (d) LAO/STO(110) with Fermi energy only occupying the undegenerate lowest energy states $d_{xz}/d_{yz}$ (for example splitting with large magnetic field).The top row is a scheme of energy level in $t_{2g}$ state with $d_{xy}$ and $d_{xz}/d_{yz}$ orbitals and the location of the Fermi energy. The second row is a scheme of Fermi surface at the Fermi energy. The bottom row is an AMR component.

Figure 10

Fitting of the (a)–(c) longitudinal and (d)–(f) transverse AMR to anisotropic AMR model. (a) and (d) 3 T, (b) and (e) 6 T, and (c) and (f) 9 T.