Field-induced reorientation of helimagnetic order in Cu$_2$OSeO$_3$ probed by magnetic force microscopy

TL;DR

This study uses magnetic force microscopy to observe how helimagnetic order in Cu$_2$OSeO$_3$ reorients under magnetic fields, revealing domain formation, phase transitions, and the link to electric polarization, supported by theoretical modeling.

Contribution

First direct imaging of helimagnetic reorientation and domain formation in Cu$_2$OSeO$_3$ under magnetic fields, linking magnetic structure changes to electric polarization.

Findings

Helimagnetic order reorients to a conical phase at higher fields.

Magnetic domains form during reorientation process.

Electric polarization depends on helimagnetic reorientation.

Abstract

Cu$_2$OSeO$_3$ is an insulating skyrmion-host material with a magnetoelectric coupling giving rise to an electric polarization with a characteristic dependence on the magnetic field $\vec H$. We report magnetic force microscopy imaging of the helical real-space spin structure on the surface of a bulk single crystal of Cu$_2$OSeO$_3$. In the presence of a magnetic field, the helimagnetic order in general reorients and acquires a homogeneous component of the magnetization, resulting in a conical arrangement at larger fields. We investigate this reorientation process at a temperature of 10~K for fields close to the crystallographic $\langle 110\rangle$ direction that involves a phase transition at $H_{c1}$. Experimental evidence is presented for the formation of magnetic domains in real space as well as for the microscopic origin of relaxation events that accompany the reorientation process. In addition, the electric polarization is measured by means of Kelvin-probe force microscopy. We show that the characteristic field dependency of the electric polarization originates in this helimagnetic reorientation process. Our experimental results are well described by an effective Landau theory previously invoked for MnSi, that captures the competition between magnetocrystalline anisotropies and Zeeman energy.