Open AccessHeterogeneous ferromagnetic state in small particles and its connection with ferroelectricity
Author(s) -
T. S. Shaposhnikova,
Р. Ф. Мамин
Publication year - 2019
Publication title -
iop conference series. materials science and engineering
Language(s) - English
Resource type - Journals
eISSN - 1757-899X
pISSN - 1757-8981
DOI - 10.1088/1757-899x/699/1/012044
Subject(s) - condensed matter physics , vortex , ferromagnetism , physics , magnetization , connection (principal bundle) , polarization (electrochemistry) , vortex state , ferroelectricity , phenomenological model , homogeneous , quantum mechanics , magnetic field , superconductivity , geometry , statistical physics , mathematics , chemistry , mechanics , dielectric
PTs in spherical particles of a cubic ferromagnetic was considered in the framework of the Ginzburg-Landau phenomenological theory. Concentrating on depolarizing field effects, we study the competition between states with homogeneous magnetization and vortex structures. For large sphere radii (R>R c ), a PT to a vortex state is possible, while for R<R c it can be a homogeneous state. We obtain the inhomogeneous distribution of the ferromagnetic order parameter in the form of 2D and 3D vortices, for which the absolute value of the local magnetization depends on the distance from the centre of the vortex. This approach can be used for nano-sized particles. In our work, we compute the polarization caused by ferromagnetic 2D and 3D vortices within the phenomenological approach.