# Notes on the gravitational, electromagnetic and axion memory effects

## TL;DR

This paper explores the connections between gravitational, electromagnetic, and axion memory effects, confirming their relation to soft theorems and proposing new ways to detect these effects through spin changes.

## Contribution

It explicitly demonstrates the equivalence of subleading and subsubleading memory effects with their corresponding soft theorems and introduces the detection of axion memory via spin changes.

## Key findings

- Memory effects correspond to soft theorems at various orders.
- Memory effects can be probed by spin displacements.
- Axion memory can be detected through spin changes.

## Abstract

We investigate the memory effects associated with the kicks of particles. Recently, the equivalence between the memory effect and soft theorem has been established. By computing the memory effect from the radiation solutions, we explicitly confirm that, in addition to the leading piece, the subleading and subsubleading soft theorems are equivalent to the subleading and subsubleading memory effects, respectively. It is known that the memory effects can be probed by the displacements or kicks of the test particles. We point out that the these memory effects are also probed by the permanent change of the direction of the spin. We also show that the axion memory effect, recently proposed by the current authors, can be detected as the change of the spin of the test particle. We discuss that if we consider the magnetic monopole as an external particle, the parity-odd electromagnetic memory appears.