Quasi-Two-Dimensional Anomalous Hall Mott Insulator of Topologically Engineered ${J}_{\mathrm{eff}}=1/2$ Electrons

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Quasi-Two-Dimensional Anomalous Hall Mott Insulator of Topologically Engineered $J_{eff} = 1 / 2$ Electrons

Junyi Yang, Hidemaro Suwa, Derek Meyers, Han Zhang, Lukas Horak, Zhaosheng Wang, Gilberto Fabbris, Yongseong Choi, Jenia Karapetrova, Jong-Woo Kim, Daniel Haskel, Philip J. Ryan, M. P. M. Dean, Lin Hao, and Jian Liu

Phys. Rev. X 12, 031015 – Published 22 July 2022

Abstract

We investigate an experimental toy-model system of a pseudospin-half square-lattice Hubbard Hamiltonian in $[{({SrIrO}_{3})}_{1} / {({CaTiO}_{3})}_{1}]$ to include both nontrivial complex hopping and moderate electron correlation. While the former induces electronic Berry phases as anticipated from the weak-coupling limit, the latter stabilizes an antiferromagnetic Mott insulator ground state analogous to the strong-coupling limit. Their combined results in the real system are found to be an anomalous Hall effect with a nonmonotonic temperature dependence due to the competition of the antiferromagnetic order and charge excitations in the Mott state, and an exceptionally large Ising anisotropy that is captured as a giant magnon gap beyond the superexchange approach. The unusual phenomena highlight the rich interplay of electronic topology and electron correlation in the intermediate-coupling regime that is largely unexplored and challenging in theoretical modeling.

Received 9 November 2021
Revised 25 April 2022
Accepted 2 June 2022

DOI:https://doi.org/10.1103/PhysRevX.12.031015

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Anomalous Hall effect Dzyaloshinskii-Moriya interaction Magnetic anisotropy

Antiferromagnets Iridates Mott insulators Superlattices

Resonant elastic x-ray scattering X-ray resonant magnetic scattering

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Junyi Yang¹, Hidemaro Suwa ², Derek Meyers^3,4, Han Zhang¹, Lukas Horak ⁵, Zhaosheng Wang⁶, Gilberto Fabbris ⁷, Yongseong Choi ⁷, Jenia Karapetrova⁷, Jong-Woo Kim ⁷, Daniel Haskel⁷, Philip J. Ryan ^7,8, M. P. M. Dean ³, Lin Hao ^6,*, and Jian Liu ^1,†

¹Department of Physics and Astronomy, University of Tennessee, Knoxville, Tennessee 37996, USA
²Department of Physics, University of Tokyo, Tokyo 113-8656, Japan
³Department of Condensed Matter Physics and Materials Science, Brookhaven National Laboratory, Upton, New York 11973, USA
⁴Department of Physics, Oklahoma State University, Stillwater, Oklahoma 74078, USA
⁵Department of Condensed Matter Physics, Charles University, Ke Karlovu 5, 12116 Prague, Czech Republic
⁶Anhui Key Laboratory of Condensed Matter Physics at Extreme Conditions, High Magnetic Field Laboratory, HFIPS, Chinese Academy of Sciences, Hefei, Anhui 230031, China
⁷Advanced Photon Source, Argonne National Laboratory, Argonne, Illinois 60439, USA
⁸School of Physical Sciences, Dublin City University, Dublin 9, Ireland

^*To whom correspondence should be addressed. haolin@hmfl.ac.cn
^†To whom correspondence should be addressed. jianliu@utk.edu

Popular Summary

The strength of the correlation between electrons is often used to categorize quantum materials into three regimes: weak-coupling, strong-coupling, and the intermediate-coupling regime that connects the two limits. In the weak-coupling regime, electrons are free to move individually but are guided by symmetry. In contrast, in the strong-coupling limit, electrons are localized and only temporarily visit neighboring atoms, resulting in magnetic insulators. Such seemingly incompatible outcomes make it interesting but also challenging to understand how the two opposite limits are bridged by the intermediate regime. In this work, we realize a system where hallmarks of both the weak- and strong-coupling regime appear simultaneously, hinting at some of the complex physics that connects them.

We experimentally construct an artificial crystal to purposely remove all rotational symmetries but leave a glide symmetry for electrons with an intermediate coupling strength. The electrons not only form an insulator, as they do in the strong-coupling limit, but also spontaneously break the glide symmetry by ordering their spins magnetically to enable the anomalous Hall effect, a profound example of weak coupling. These behaviors suggest that the characters of the weak- and strong-coupling limits may be blended but in a nontrivial way: Neither the temperature dependence of the anomalous Hall effect nor the magnitude of the symmetry-breaking magnetic anisotropy can be simply understood from the two limits.

This work also demonstrates a controllable material platform for exploring emergent phenomena and rich physics of the intermediate regime by designing and implementing various symmetry configurations in artificial lattice structures.

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Vol. 12, Iss. 3 — July - September 2022

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Figure 1
Structure characterization. (a) Crystal structure of the $[{({SrIrO}_{3})}_{1} / {({CaTiO}_{3})}_{1}]$ SL grown on a ${S r TiO}_{3}$ substrate. (b) X-ray $θ − 2 θ$ scan pattern of the SL. (c),(d) Room-temperature (RT) synchrotron XRD measured around the (0.5 0.5 3) and (0.5 1.5 3) peaks.
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Figure 2
Magnetic structure and magnetoresistance effect. (a) $L$ scan across the (0.5 0.5 2) magnetic peak. Dashed line represents the background signal. Error bar represents statistical error. Inset shows the energy profile at 10 K, where a vertical dashed line indicates the Ir- $L_{3}$ absorption edge. (b) Integrated intensity of magnetic peak versus temperature. $T_{N}$ is denoted by a black arrow. (c) Temperature dependence of in-plane resistivity. Inset shows the relation between $d (\ln ρ) / d (1 / T)$ and temperature. (d) Temperature-dependent MR measured under an out-of-plane (red) or in-plane (green) 8 T magnetic field.
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Figure 3
Hall signatures of the topology. (a) Magnetic field dependence of Hall resistivity at different temperatures. The field sweeping directions are shown as gray arrows. (b) Temperature dependences of the saturated and remnant Hall conductivity. Inset shows the temperature dependences of $σ_{x y} / σ_{x x}$ and $S_{H}$ [53].
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Figure 4
Spin-dependent hopping of the Hubbard model. A perovskite square lattice with (a) octahedral rotations ( $p 4 g$ wallpaper group containing a fourfold rotational symmetry and a glide reflection), (b) octahedral tilts ( $p g$ wallpaper group containing a glide reflection), or (c) octahedral rotations and tilts ( $p g$ wallpaper group). Bottom panels show the modulation of $d_{i j}$ vectors (blue arrows). Octahedral rotation or tilts on neighboring sites are opposite. The finite $d_{□}$ (red arrow) in (b) and (c) is perpendicular to the mirror plane (gray) of the $b$ -glide symmetry. (d) Representative $U = 0$ band structure for a quasi-2D structure with two layers of square lattice (c) [53]. (e) Schematic diagram of Dzyaloshinskii–Moriya (DM) interactions on the square lattice (c) at the strong-coupling limit $U = \infty$ . The blank space with a question mark highlights the extensive and largely unexplored intermediate region among the two limits.
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Figure 5
Magnetic structure and low-energy magnetic excitations. (a) Temperature-dependent out-of-plane (red) and in-plane (blue) remnant magnetization ( $M_{remnant}$ ). Inset shows the temperature dependence of $R_{s}$ . (b) Extracted magnon peak dispersion across the Brillouin zone. The errors are statistical from the fitting with dashed line as a guide to the eye. Inset shows the ground-state magnetic pattern of the SL. The $J_{eff} = 1 / 2$ magnetic moments are represented as black arrows. (c) RIXS spectra at $Q = (π, π)$ of the SL (red) and $[{({SrIrO}_{3})}_{1} / {({SrTiO}_{3})}_{1}]$ (green) measured at 35 K. The magnon excitation feature is indicated by an ellipse. Inset shows the expanded view of the magnon feature.
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Physical Review X

Quasi-Two-Dimensional Anomalous Hall Mott Insulator of Topologically Engineered Jeff=1/2 Electrons

Junyi Yang, Hidemaro Suwa, Derek Meyers, Han Zhang, Lukas Horak, Zhaosheng Wang, Gilberto Fabbris, Yongseong Choi, Jenia Karapetrova, Jong-Woo Kim, Daniel Haskel, Philip J. Ryan, M. P. M. Dean, Lin Hao, and Jian Liu

Phys. Rev. X 12, 031015 – Published 22 July 2022

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Quasi-Two-Dimensional Anomalous Hall Mott Insulator of Topologically Engineered $J_{eff} = 1 / 2$ Electrons