Abstract
An unexpected finding two decades ago demonstrated that Shockley electron states in noble metal surfaces are spin-polarized, forming a circulating spin texture in reciprocal space. The fundamental role played by the spin degree of freedom was then revealed, even for a non-magnetic system, whenever the spin-orbit coupling was present with some strength. Here, we demonstrate that, similarly to electrons in the presence of spin-orbit coupling, the propagating vibrational modes are also accompanied by a well-defined magnetic oscillation even in non-magnetic materials. Although this effect is illustrated by considering a single layer of the WSe2 dichalogenide, the phenomenon is completely general and valid for any non-magnetic material with spin-orbit coupling. The emerging phonon-induced magnetic oscillation acts as an additional effective flipping mechanism for the electron spin and its implications in the transport and scattering properties of the material are evident and profound.
Highlights
An unexpected finding two decades ago demonstrated that Shockley electron states in noble metal surfaces are spin-polarized, forming a circulating spin texture in reciprocal space
In a solid with spin–orbit coupling, electron states are described by two-component spinor wave functions for each k point spanning the Brillouin zone (BZ), Ψk;iðrÞ 1⁄4
An alternative and more transparent way to see whether an overall magnetic property emerges is to consider the effect of the perturbation on each electron spinor wave function and integrate over the BZ
Summary
An unexpected finding two decades ago demonstrated that Shockley electron states in noble metal surfaces are spin-polarized, forming a circulating spin texture in reciprocal space. Under these conditions the balance of the electron spin-polarizations within the BZ is broken and the BZ integral gives a finite value and, a net real-space magnetic oscillation with the same wave number as the phonon q.
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