Hidden orbital polarization in diamond, silicon, germanium, gallium arsenide and layered materials

Ji Hoon Ryoo,Cheol-Hwan Park

doi:10.1038/am.2017.67

Abstract

It was previously believed that the Bloch electronic states of non-magnetic materials with inversion symmetry cannot have finite spin polarizations. However, since the seminal work by Zhang et al. (Nat. Phys. 10, 387–393 (2014)) on local spin polarizations of Bloch states in non-magnetic, centrosymmetric materials, the scope of spintronics has been significantly broadened. Here, we show, using a framework that is universally applicable independent of whether hidden spin polarizations are small (e.g., diamond, Si, Ge and GaAs) or large (e.g., MoS2 and WSe2), that the corresponding quantity arising from orbital—instead of spin—degrees of freedom, the hidden orbital polarization is (i) much more abundant in nature since it exists even without spin–orbit coupling and (ii) more fundamental since the interband matrix elements of the site-dependent orbital angular momentum operator determine the hidden spin polarization. We predict that the hidden spin polarization of transition metal dichalcogenides is reduced significantly upon compression. We suggest experimental signatures of hidden orbital polarization from photoemission spectroscopies and demonstrate that the current-induced hidden orbital polarization may play a far more important role than its spin counterpart in antiferromagnetic information technology by calculating the current-driven antiferromagnetism in compressed silicon.

Highlights

Electronic states at a given Bloch wavevector in non-magnetic materials with inversion symmetry are degenerate
To illustrate the idea that the current-induced hidden orbital polarization can play a more important role than the hidden spin polarization, we looked into the current-driven antiferromagnetism of silicon under a 2% uniaxial compressive strain along the [001] direction, achievable in real experiments.[25,26] (Because silicon has many point group symmetries, an electric current in silicon does not generate site-dependent magnetization; a strain can result in current-induced magnetization by breaking some symmetries.20) silicon may not be the best material for antiferromagnetic information technology applications, it is one of the simplest and most well-known materials, a good candidate for supporting our hypothesis
In centrosymmetric group IV materials such as diamond, Si and Ge, the hidden spin polarization is very small, but the hidden orbital polarization is on the order of ħ

Summary

Introduction

Electronic states at a given Bloch wavevector in non-magnetic materials with inversion symmetry are degenerate. It was believed that there is no spatial spin distribution if averaged over these two spin-degenerate states. It has been found that even in centrosymmetric, non-magnetic crystals, the degenerate Bloch states can have local spin polarization if atoms are not at an inversion center.[1] Zhang et al.[1] reported that the lack of the local inversion symmetry at atomic sites leads to hidden, or site-dependent, spin polarization, expanding the scope of spintronics significantly, even to bulk materials with global inversion symmetry. The important role of orbital polarization in Rashba-split bands[7,8,9] and quantum anomalous Hall phases[10] of systems without inversion symmetry has been explored

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Conclusion