High-temperature large-gap quantum anomalous Hall insulating state in ultrathin double perovskite films

Santu Baidya, Umesh V. Waghmare, Arun Paramekanti, and Tanusri Saha-Dasgupta

Phys. Rev. B 94, 155405 – Published 5 October 2016

Abstract

Towards the goal of realizing topological phases in thin films of correlated oxide and heterostructures, we propose here a quantum anomalous Hall insulator (QAHI) in ultrathin films of double perovskites based on mixed $3 d - 5 d$ or $3 d - 4 d$ transition-metal ions, grown along the [111] direction. Considering the specific case of ultrathin ${Ba}_{2} {FeReO}_{6}$ , we present a theoretical analysis of an effective Hamiltonian derived from first principles. We establish that a strong spin-orbit coupling at the Re site, $t_{2 g}$ symmetry of the low-energy $d$ bands, polarity of its [111] orientation of perovskite structure, and mixed $3 d - 5 d$ chemistry results in room temperature magnetism with a robust QAHI state of Chern number $C = 1$ and a large band gap. We uncover and highlight a nonrelativistic orbital Rashba-type effect in addition to the spin-orbit coupling, that governs this QAHI state. With a band gap of $\sim 100$ meV in electronic structure and magnetic transition temperature $T_{c} \sim 300 K$ estimated by Monte Carlo simulations, our finding of the QAHI state in ultrathin ${Ba}_{2} {FeReO}_{6}$ is expected to stimulate experimental verification along with possible practical applications of its dissipationless edge currents.

Received 6 July 2016

DOI:https://doi.org/10.1103/PhysRevB.94.155405

Physics Subject Headings (PhySH)

Electrical properties Insulators Topological phases of matter

2-dimensional systems

Band structure methods

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Santu Baidya^1,*, Umesh V. Waghmare², Arun Paramekanti³, and Tanusri Saha-Dasgupta^4,†

¹Department of Physics and Center for Nanointegration Duisburg-Essen (CENIDE), University of Duisburg-Essen, Lotharstrasse 1, 47057 Duisburg, Germany
²Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur, Bangalore 560064, India
³Department of Physics, University of Toronto, Toronto, Ontario, Canada M5S 1A7 and Canadian Institute for Advanced Research, Toronto, Ontario, Canada M5G 1Z8
⁴Department of Condensed Matter Physics and Materials Science, S. N. Bose National Centre for Basic Sciences, Kolkata 700 098, India

^*Present address: Center for Correlated Electron Systems, Institute for Basic Science (IBS), Seoul 151-742, Republic of Korea; Department of Physics and Astronomy, Seoul National University (SNU), Seoul, 151-742, Republic of Korea.
^†t.sahadasgupta@gmail.com

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Vol. 94, Iss. 15 — 15 October 2016

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Images

Figure 1
(a) Bilayer of ${Ba}_{2} {FeReO}_{6}$ (BFRO), with the $c$ axis pointed along the [111] growth direction and terminated at the Fe layer. (b) Buckled honeycomb network of Re and Fe atoms, viewed along the growth direction. Ba, Re, Fe, and O atoms have been marked. In (b) Ba atoms have been omitted for clarity. (c) Spin-polarized GGA density of states projected onto Fe and Re $d$ states. (d) The GGA band structure in minority spin channel plotted in the hexagonal BZ. (e) Same as in (b), but plotted along high symmetry directions; the colors [cyan (light gray), black, red (dark gray)] show dominant orbital characters ( $d_{x y}, d_{x^{2} - y^{2}}, d_{3 z^{2} - r^{2}}$ ).
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Figure 2
(a) GGA+SO band structure in minority spin channel (top panel) and calculated Berry curvature (bottom panel) plotted along the high symmetry directions in the BZ. (b) Anomalous Hall conductivity of the band structure in (a), in units of $e^{2} / h$ . Quantized plateaus are highlighted. Inset: Frequency dependence of the real part of the optical AH conductivity $σ_{x y}^{AH} (ω)$ in units of $e^{2} / h$ .
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Figure 3
(a) The intraorbital ( $t_{0}, t_{1}$ ) and interorbital ( $t_{2}, t_{3}$ ) hoppings on the triangular Re lattice between $t_{2 g}$ orbitals with angular momenta $m_{ℓ} = 0$ and $m_{ℓ} = \pm 1$ . For $m_{ℓ} = \pm 1$ , the wheels depict opposite phase windings. (b) Decoupled $m_{ℓ} = 0$ and coupled $m_{ℓ} = \pm 1$ bands for $(Δ_{trg}, t_{0}, t_{1}, t_{2}) = (60, 45, 20, 80)$ meV, where all other terms in Hamiltonian have been set to zero (see text).
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Figure 4
Band structure obtained by setting (a) $(t_{R} = 0, λ \neq 0)$ , (b) $(t_{R} \neq 0, λ = 0)$ , and (c) $(t_{R} \neq 0, λ \neq 0)$ in the effective Hamiltonian (see text). (d) Berry curvature $Ω_{z} (k) / 2 π$ for the lowest band, with parameters as in (c), in units where the Re triangular lattice constant is set to unity. The Berry curvature is peaked slightly away from the $Γ$ point, and is asymmetric under $k \to - k$ due to broken inversion.
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Figure 5
(a), (b) Electron density for localized pseudospin states $m_{ℓ} = \pm 1$ shown at neighboring Re sites $r$ and $r + \hat{x}$ . (c)–(e) Bond electronic density obtained by superposing the electron density of the same orbital type (both $m_{ℓ} = + 1$ or both $m_{ℓ} = - 1$ ) for $k_{x} = 0$ and $k_{x} \neq 0$ , illustrating electric dipole $P_{y} \sim m_{ℓ}^{eff} sin k_{x}$ , which changes sign under reversing sign of $m_{ℓ}^{eff}$ or $k_{x}$ . (f) Triangular lattice structure of Re atoms and underlying Fe atoms. Arrows schematically indicate the in-plane electric fields, generated by symmetry breaking due to Fe atoms, which can linearly couple to $\vec{P}$ .
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Figure 6
Temperature dependence of (a) specific heat per unit cell of the honeycomb lattice (in units of $k_{B}$ ), and (b) magnetization per site of the honeycomb lattice (normalized to its value at $T = 0$ ), for the Heisenberg-Ising model in Eq. (1), for illustrative system sizes containing $2 L^{2}$ spins. We have plotted ${[\frac{m (T)}{m (0)}]}^{1 / β}$ to illustrate data collapse for an Ising order parameter exponent $β = 1 / 8$ . Using these simulations we determine the FM transition temperature $T_{c} / S_{F} J_{F R} \approx 0.975 (5)$ .
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