On the wave-nature of skyrmion lattice in chiral magnets

Yangfan Hu

Published 2017-02-03Version 1

A magnetic skyrmion is a topologically protected spin texture with particle-like properties stabilized in magnetic system without inversion symmetry. In most bulk materials and thin films where they are detected, skyrmions spontaneously form crystalline state with long range order. Despite tremendous achievements made in this area over the last few years, a fundamental problem of how to interpret this so-called "skyrmion lattice phase" is still under debate. The key issue refers to the "wave-particle duality" of the skyrmion lattice. The particle side describes a skyrmion in lattice with an axial symmetric core and a disturbed edge region, while the wave side expresses the magnetization as superposition of a constant vector and three helical waves. Here, we show by variational analysis that the skyrmion lattice with long range crystalline order has a wave-nature. To be a solution of the variational problem that minimizes the free energy funcitonal, the magnetization of the skyrmion lattice phase as well as its gradient field and curl field are proved to be all continuous within the unit cell. It means the magnetization vector can be expressed as Fourier series, which destroy local axial symmetry regardless of the expansion order. We formulate the nth order Fourier representation of the skyrmion lattice, which reduces to the "triple-Q" representation for n=1. Based on the Fourier representation, the equilibrium magnetization is obtained by solving a set of algebraic equations at any given temperature and magnetic field. We find that nth order Fourier representation explains well the variation of the skyrmion lattice constant with the magnetic field for n>4. Our finding implies that a phase transition occurs which breaks the local axial symmetry of isolated skyrmions when they condense into the skyrmion lattice.