# Spin current and second harmonic generation in non-collinear magnetic systems: the hydrodynamic model

## TL;DR

This paper presents a theoretical model explaining how spin currents in non-collinear magnetic systems can generate second harmonic signals through a hydrodynamic approach, revealing a novel mechanism involving non-adiabatic spin polarization.

## Contribution

The study introduces a hydrodynamic model to explain second harmonic generation driven by spin currents in non-collinear magnetic systems, highlighting a new double frequency signal mechanism.

## Key findings

- Second harmonic signals arise from non-adiabatic spin polarization.
- Double frequency spin current is generated and converted to electric current.
- The inverse Spin Hall effect produces the second harmonic radiation.

## Abstract

We report a theoretical study of the second harmonic generation in a noncollinearly magnetized conductive medium with equilibrium spin current. The hydrodynamic model is used to unravel the mechanism of a novel effect of the double frequency signal generation due to the spin current. According to our calculations, this second harmonic response appears due to the "non-adiabatic" spin polarization of the conduction electrons induced by the oscillations in the non-uniform magnetization forced by the electric field of the electromagnetic wave. Together with the linear velocity response this leads to the generation of the double frequency spin current. This spin current is converted to the electric current via the inverse Spin Hall effect, and the double-frequency electric current emits the second harmonic radiation.