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Correlation-driven eightfold magnetic anisotropy in a two-dimensional oxide monolayer

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Science Advances  10 Apr 2020:
Vol. 6, no. 15, eaay0114
DOI: 10.1126/sciadv.aay0114
  • Fig. 1 Structural characterizations of (SrRuO3)1/(SrTiO3)N superlattices.

    (A) Schematics of lattice structures of the N = 1 and N = 3 superlattices. (B) XRD ω-2θ scans of N = 1, 3, and 5 superlattices. (C) XRD reciprocal space maps of N = 1 to 5 superlattices taken around the (2 0 4) reflections of SrTiO3 substrates. (D) Average and the ideal c-axis lattice constants of the superlattices. (E) The (3/2 1/2 L) half-order diffraction peaks of the N = 1, 3, and 5 superlattices. The reciprocal lattice units (r.l.u.) in (B), (C), and (E) are calculated using the SrTiO3 substrate lattice. Error bars represent ±1 standard deviation.

  • Fig. 2 XMCD and SQUID magnetic characterizations of (SrRuO3)1/(SrTiO3)N superlattices.

    Ti L-edge (A) XAS and (B) XMCD of N = 1 to 5 superlattices. (C) SQUID magnetization (left axis) and MOKE Kerr rotation (right axis) measurements as a function of temperature of N = 1 to 5 superlattices. The measurements were taken during warming with 0.05-T field applied in the [001] direction. The magnetization versus magnetic field measured in the [001] and [111] directions of (D) N = 2, (E) N = 3, and (F) N = 4 superlattices at 5 K. The insets are the zoom-in view of the loops at low field.

  • Fig. 3 PNR of a 50-repeat (SrRuO3)1/(SrTiO3)3 superlattice.

    (A) Fitted PNR data. (B) Superlattice Bragg reflection fitted with Gaussian peaks to demonstrate the difference in peak height. (C) SA near the critical edge showing clear spin-dependent splitting of the reflectivities. All measurements were performed at 6 K under an applied field of 3 T. (D) Representative section of the nuclear and magnetic scattering length density (SLD) profiles used to generate the fits shown in (A) and (C). Error bars represent ±1 standard deviation.

  • Fig. 4 Magnetotransport properties of (SrRuO3)1/(SrTiO3)N superlattices.

    The MR at T = 5 K of N = 1 to 5 superlattices with the magnetic field applied parallel to (A) [001] and (B) [010] directions. The color correspondences are the same in (A) and (B). (C) Polar plots of MAR of N = 1 to 5 superlattices measured under a magnetic field of 9 T and at temperatures of 5, 25, and 50 K. The geometry of the MAR measurement is shown in the inset of (B). The sample rotates around the [100] direction, and the current is along the [100] direction, always being perpendicular to the magnetic field. θ is between the [001] direction and the field direction within the (100) plane. (D) Polar plots of MAR of N = 3 superlattice measured under a magnetic field of 9 T and at temperature of 5 K. The sample rotates around the [110] direction, and the current is along the [110] direction. θ is between the [001] direction and the field direction within the (110) plane. Both MAR with the sample rotating clockwise and anticlockwise are shown.

  • Fig. 5 DFT calculated crystal structure, DOS, and MA of (SrRuO3)1/(SrTiO3)N superlattices.

    Crystal structures of (A) N = 1 and (D) N = 3 superlattices. Near–Fermi-level DOS of (B) N = 1 and (E) N = 3 superlattices, calculated using DFT + U method with URu = 4 eV. The states in the upper (lower) half correspond to spin up (down). In (E), “LH” (“UH”) means a lower (upper) Hubbard band, which is filled (empty). Because of the orbital ordering described in the main text, in each RuO2 plane, there are two distinct Ru atoms (labeled as Ru1 and Ru2): For Ru1, LH is Ru (−) orbital, and UH is Ru (+); for Ru2, LH is Ru (+) orbital, and UH is Ru (−) orbital. The definition of Ru (+) and Ru (−) orbitals can be found in the main text. Total energy of (C) N = 1 and (F) N = 3 superlattices with different magnetic moment orientations, calculated using DFT + U + SOC method with URu = 4 eV. 〈001〉, 〈100〉, and 〈111〉 refer to the orientation of Ru magnetic moments. The energy of the 〈001〉 state is used as the reference. The twofold 〈001〉 MA is explicitly shown in the inset of (C). The eightfold 〈111〉 MA is explicitly shown in the inset of (F).

Supplementary Materials

  • Supplementary Materials

    Correlation-driven eightfold magnetic anisotropy in a two-dimensional oxide monolayer

    Zhangzhang Cui, Alexander J. Grutter, Hua Zhou, Hui Cao, Yongqi Dong, Dustin A. Gilbert, Jingyuan Wang, Yi-Sheng Liu, Jiaji Ma, Zhenpeng Hu, Jinghua Guo, Jing Xia, Brian J. Kirby, Padraic Shafer, Elke Arenholz, Hanghui Chen, Xiaofang Zhai, Yalin Lu

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