Anisotropic superexchange through nonmagnetic anions with spin-orbit coupling
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THE EUROPEAN PHYSICAL JOURNAL B
Regular Article
Anisotropic superexchange through nonmagnetic anions with spin-orbit coupling Jun Chang 1,a , Jize Zhao 2 , and Yang Ding 3 1 2
3
College of Physics and Information Technology, Shaanxi Normal University, Xi’an 710119, P.R. China School of Physical Science and Technology&Key Laboratory for Magnetism and Magnetic Materials of the MoE, Lanzhou University, Lanzhou 730000, P.R. China Center for High-Pressure Science and Technology Advanced Research, Beijing 100094, P.R. China Received 18 March 2020 / Received in final form 16 June 2020 Published online 24 August 2020 c EDP Sciences / Societ`
a Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature, 2020 Abstract. Anisotropic superexchange interaction is one of the most important interactions in realizing exotic quantum magnetism, which is traditionally regarded to originate from magnetic ions and has no relation with the nonmagnetic ions. In our work, by studying a multi-orbital Hubbard model with spinorbit coupling on both magnetic cations and nonmagnetic anions, we analytically demonstrate that the spin-orbit coupling on nonmagnetic anions alone can induce antisymmetric Dzyaloshinskii-Moriya interaction, symmetric anisotropic exchange and single ion anisotropy on the magnetic ions and thus it actually contributes to anisotropic superexchange on an equal footing as that of magnetic ions. Our results promise one more route to realize versatile exotic phases in condensed matter systems, long-range orders in low dimensional materials and switchable single molecule magnetic devices for recording and manipulating quantum information through nonmagnetic anions.
1 Introduction Locking electron spin and momentum together, the relativistic spin-orbit coupling (SOC) plays a critical role in realizing a diversity of exotic phases in condensed matter systems, such as quantum spin liquid, spin-orbit coupled Mott insulator, Weyl semimetal and topological insulator [1–3]. In the absence of SOC, the magnetic interaction is isotropic with spin rotational invariance. However, SOC may lower the symmetry and lead to anisotropic interactions, which has been microscopically identified by Moriya by means of extending the Kramers-Anderson superexchange theory [4–7]. Importantly, the magnetic anisotropy is the key in bond-dependent Kitaev interaction and phase transition in low dimensional (D ≤ 2) systems, which has been argued to be a great promise for quantum computation and information processing in addition to the fundamental interest [8–10]. Recently, magnetic orders induced by magnetic anisotropy have been reported in experiments on some twodimensional (2D) materials or proposed by numerical simulations [11–16]. Since it is well known that the Hohenberg-Mermin-Wagner theorem forbids the spontaneous breaking of continuous symmetry at finite temperature in low dimensional systems [17], these findings are thus attributed to magnetic anisotropy in the materials. a
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Commonly, the magnetic
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