# Magnetic hexadecapole order and magnetopiezoelectric metal in Ba$_{1-x}$K$_x$Mn$_2$As$_2$

## TL;DR

This paper investigates the magnetic hexadecapole order in Ba$_{1-x}$K$_x$Mn$_2$As$_2$, revealing novel electromagnetic responses and proposing it as a magnetopiezoelectric metal with potential for other materials.

## Contribution

It identifies a magnetic hexadecapole ordered state in BaMn$_2$As$_2$, demonstrating its unique electromagnetic responses and introducing the concept of a magnetopiezoelectric metal.

## Key findings

- Magnetic hexadecapole order breaks time-reversal and inversion symmetry.
- Electromagnetic responses include magnetoelectric and Edelstein effects.
- Current-induced nematic order in the metallic state.

## Abstract

We study an odd-parity magnetic multipole order in Ba$_{1-x}$K$_x$Mn$_2$As$_2$ and related materials. Although BaMn$_2$As$_2$ is a seemingly conventional Mott insulator with G-type antiferromagnetic order, we identify the ground state as a magnetic hexadecapole ordered state accompanied by simultaneous time-reversal and space-inversion symmetry breaking. A symmetry argument and microscopic calculations reveal the ferroic ordering of leading magnetic hexadecapole moment and admixed magnetic quadrupole moment. Furthermore, we clarify electromagnetic responses characterizing the magnetic hexadecapole state of semiconducting BaMn$_2$As$_2$ and doped metallic systems. A magnetoelectric effect and antiferromagnetic Edelstein effect are shown. Interestingly, a counter-intuitive currentinduced nematic order occurs in the metallic state. The electric current along the \textit{z}-axis induces the \textit{xy}-plane nematicity in sharp contrast to the spontaneous nematic order in superconducting Febased 122-compounds. Thus, the magnetic hexadecapole state of doped BaMn$_2$As$_2$ is regarded as a magnetopiezoelectric metal. The anomalous responses stem from the peculiar symmetry of the parity-violating magnetic order. Other candidate materials for magnetic hexadecapole order are proposed.