# Fermi Level Dependent Spin Pumping from a Magnetic Insulator into a Topological Insulator

## TL;DR

This study investigates how the Fermi level influences spin pumping in topological insulator/ferrimagnetic insulator bilayers, revealing that spin Hall conductivity remains constant across the bulk band gap, highlighting contributions from both bulk and surface states.

## Contribution

It demonstrates that spin-charge conversion efficiency in topological insulators depends on the Fermi level, emphasizing the combined role of bulk and surface states in spin pumping.

## Key findings

- Spin Hall conductivity is constant across the bulk band gap.
- Bulk states contribute significantly to spin-charge conversion.
- Surface states exhibit spin-momentum locking consistent with theoretical predictions.

## Abstract

Topological spintronics aims to exploit the spin-momentum locking in the helical surface states of topological insulators for spin-orbit torque devices. We address a fundamental question that still remains unresolved in this context: does the topological surface state alone produce the largest values of spin-charge conversion efficiency or can the strongly spin-orbit coupled bulk states also contribute significantly? By studying the Fermi level dependence of spin pumping in topological insulator/ferrimagnetic insulator bilayers, we show that the spin Hall conductivity is constant when the Fermi level is tuned across the bulk band gap, consistent with a full bulk band calculation. The results suggest a new perspective, wherein "bulk-surface correspondence" allows spin-charge conversion to be simultaneously viewed either as coming from the full bulk band, or from spin-momentum locking of the surface state.