Anisotropic ferroelectric distortion effects on the RKKY interaction in topological crystalline insulators

Abstract

Manipulation of electronic and magnetic properties of topological materials is a topic of much interest in spintronic and valleytronic applications. Perturbation tuning of multiple Dirac cones on the (001) surface of topological crystalline insulators (TCIs) is also a related topic of growing interest. Here we show the numerical evidence for the ferroelectric structural distortion effects on the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between two magnetic impurity moments on the SnTe (001) and related alloys. The mirror symmetry breaking between Dirac cones induced by the ferroelectric distortion could be divided into various possible configurations including the isotropically gapped, coexistence of gapless and gapped, and anisotropically gapped phases. Based on the retarded perturbed Green’s functions of the generalized gapped Dirac model, we numerically find the RKKY response for each phase. The distortion-induced symmetry breaking constitutes complex and interesting magnetic responses between magnetic moments compared to the pristine TCIs. In the specific case of coexisted gapless and gapped phases, a nontrivial behavior of the RKKY interaction is observed, which has not been seen in other Dirac materials up until now. For two impurities resided on the same sublattices, depending on the distortion strength, magnetic orders above of a critical impurity separation exhibit irregular ferromagnetic ⇔ antiferromagnetic phase transitions. However, independent of the impurity separation and distortion strength, no phase transition emerges for two impurities resided on different sublattices. This essential study sheds light on magnetic properties of Dirac materials with anisotropic mass terms and also makes TCIs applications relatively easy to understand.

RKKY interaction in helical higher-order topological insulators

“…The RKKY interaction has been extensively investigated in various systems such as low-dimensional quantum structures, [29,30] graphene and Dirac semimetals, [31,32] topological insulators, [33,34] Weyl semimetals, [35,36] and topological crystalline insulators. [37][38][39] The boundary effects in topological materials are predicted to be highly intriguing. HOTIs possess 1D topological hinge states that may offer a unique RKKY interaction resilient to perturbations.…”

Non-Hermitian indirect exchange interaction in a topological insulator coupled to a ferromagnetic metal

“…Indirect exchange interaction between magnetic impurities mediated by carriers of host material, known as Ruderman–Kittel–Kasuya–Yosida (RKKY) interaction 32 – 34 has been investigated in systems having definite chirality, such as graphene 35 – 44 , 3D topological insulators 45 – 47 , topological crystalline insulators 48 , 49 , and Weyl quasi-particles 50 , 51 . The effects of superconducting correlations 52 , temperature, and Zeeman field 53 on the RKKY interaction have also been explored in topological insulators.…”