Six-fold crystalline anisotropic magnetoresistance in the (111) ${\mathbf{LaAlO}}_{3}/{\mathbf{SrTiO}}_{3}$ oxide interface

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Six-fold crystalline anisotropic magnetoresistance in the (111) ${LaAlO}_{3} / {SrTiO}_{3}$ oxide interface

P. K. Rout, I. Agireen, E. Maniv, M. Goldstein, and Y. Dagan

Phys. Rev. B 95, 241107(R) – Published 9 June 2017

Abstract

We measured the magnetoresistance of the 2D electron liquid formed at the (111) ${LaAlO}_{3} / {SrTiO}_{3}$ interface. The hexagonal symmetry of the interface is manifested in a six-fold crystalline component appearing in the anisotropic magnetoresistance (AMR) and planar Hall data, which agree well with symmetry analysis we performed. The six-fold component increases with carrier concentration, reaching 15% of the total AMR signal. Our results suggest the coupling between higher itinerant electronic bands and the crystal as the origin of this effect and demonstrate that the (111) oxide interface is a unique hexagonal system with tunable magnetocrystalline effects.

Received 1 January 2017

DOI:https://doi.org/10.1103/PhysRevB.95.241107

Physics Subject Headings (PhySH)

Anisotropic magnetoresistance

Interfaces Oxides Two-dimensional electron gas

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

P. K. Rout, I. Agireen, E. Maniv, M. Goldstein, and Y. Dagan^*

Raymond and Beverly Sackler School of Physics and Astronomy, Tel-Aviv University, Tel Aviv, 69978, Israel

^*yodagan@post.tau.ac.il

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Vol. 95, Iss. 24 — 15 June 2017

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Figure 1
(a) Left: Schematic depiction of ${SrTiO}_{3}$ unit cell showing (111) ( ${SrO}_{3})^{4 -}$ planes. Right: Top view of three consecutive (111) ${Ti}^{4 +}$ planes showing various in-plane crystal directions. The Ti atoms in three different planes are marked as Ti(1) (orange), Ti(2) (green), and Ti(3) (blue). (b) Schematic of different $100 μ m \times$ $260 μ m$ Hall bar devices oriented along $[1 \bar{1} 0]$ (device 1A) and $[11 \bar{2}]$ (device 2B). Device 1C lies at an angle of $45^{\circ}$ to the other two. (c) Temperature dependent sheet resistance $R_{S} (T)$ at $V_{g} = 0 V$ . (d),(e) Gate dependence of the inverse Hall coefficient $1 / |e R_{H}|$ and sheet resistance $R_{S}$ at $T = 5$ K.
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Figure 2
Magnetoresistance for device 1A. (a) perpendicular ( $\vec{H}$ perpendicular to $\vec{J}$ and interface) and transverse ( $\vec{H}$ perpendicular to $\vec{J}$ and parallel to interface) magnetoresistance, MR = [R(H)-R(0)]/R(0), at 5 K and 50 K ( $V_{g} = 0$ V). (b) MR as a function of $H$ at 5 K for different gate voltages. (c) MR at 12 T and 5 K as a function of $V_{g}$ .
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Figure 3
AMR for device 1A. (a) Out-of-plane ${AMR}_{O P} (ψ) = [R (ψ) - R (0)] / R (0)$ , at 5 K and 50 K for $V_{g} = 0 V$ . $ψ$ is the angle between $\vec{H}$ and the interface. (b) In-plane ${AMR}_{I P} (θ) = [R (θ) - R_{mean}] / R_{mean}$ at 5 K and 50 K for $V_{g} = 0 V$ . $R_{mean}$ is the angle-averaged resistance and $θ$ is the angle between $\vec{H}$ and $\vec{J}$ . (c),(d) Gate dependence of ${AMR}_{O P} (ψ)$ and ${AMR}_{I P} (θ)$ at 5 K. For high temperatures (e.g., 50 K) and low gates (e.g., $- 20$ V), ${AMR}_{I P}$ is maximal when $\vec{H} ∥ \vec{J}$ . The corresponding angle is taken as $θ = 0^{\circ}$ .
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Figure 4
${AMR}_{I P}$ at 5 K for $V_{g} =$ 40 V (a) and 0 V (b) measured on device 1A. The panels also include the two-fold and four-fold contributions, along with their sum, ${AMR}_{Fit}$ . (c),(d) The same data after subtracting ${AMR}_{Fit}$ are shown along with six-fold fit. (e),(f) Gate voltage (at 5 K) and temperature (at 0 V, sample I4 [29]) dependence of the AMR coefficients $C_{2}$ , $C_{4}$ , and $C_{6}$ [Eq. (1)].
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Figure 5
(a)–(c) ${AMR}_{I P}$ for device 1A (a) measured at 5 K while for devices 1C (b) and 2B (c) at 2 K. The applied gate voltage is $V_{g} = 50 V$ . The solid line shows the ${AMR}_{Fit}$ , which is composed of two-fold and four-fold AMR contributions (dashed lines). The values of fitting parameter $C_{2}$ are $7.7 %$ , $12.2 %$ , and $9.4 %$ for devices 1A, 1C, and 2B, respectively, while the corresponding $C_{4}$ values are $0.56 %$ , $0.87 %$ , and $3.45 %$ . The data and fits are adjusted such that $θ = 0^{\circ}$ corresponds to the $[1 \bar{1} 0]$ direction. (d)–(f) The residual data ( ${AMR}_{I P} - {AMR}_{Fit}$ ) for devices 1A (d), 1C (e), and 2B (f) along with six-fold AMR fits (solid line). The vertical black line represents the $[1 \bar{1} 0]$ direction while the current direction is shown by vertical blue line. (g)-(i) Schematic of (111) ${Ti}^{4 +}$ planes showing the $[1 \bar{1} 0]$ crystal axis (black arrow), current direction (blue arrow), and extra uniaxial anisotropy direction (red arrow) for the three devices.
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Physical Review B

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Six-fold crystalline anisotropic magnetoresistance in the (111) ${LaAlO}_{3} / {SrTiO}_{3}$ oxide interface

P. K. Rout, I. Agireen, E. Maniv, M. Goldstein, and Y. Dagan

Phys. Rev. B 95, 241107(R) – Published 9 June 2017

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Physical Review B

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Six-fold crystalline anisotropic magnetoresistance in the (111) LaAlO3/SrTiO3 oxide interface

P. K. Rout, I. Agireen, E. Maniv, M. Goldstein, and Y. Dagan

Phys. Rev. B 95, 241107(R) – Published 9 June 2017

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Six-fold crystalline anisotropic magnetoresistance in the (111) ${LaAlO}_{3} / {SrTiO}_{3}$ oxide interface