Topological transition in spectrum of skyrmion crystal with uniaxial anisotropy

Abstract

The band structure of elementary excitations of skyrmion crystal in thin ferromagnetic film with Dzyaloshinskii-Moriya interaction and uniaxial magnetic anisotropy under external magnetic field is studied. In the absence of anisotropy there is a topological transition in the spectrum of skyrmion crystal: the gap between breathing and counter-clock-wise modes closes, which is accompanied by changes of Berry curvature sign of these bands. In this work we demonstrate that such topological transition exists in some range of the uniaxial anisotropy values. We present a phase diagram showing that the value of the field of topological transition is higher in the easy-plane domain and lower in the easy-axis domain of anisotropy.

Figures (2)

• Figure 1: Investigated region of the phase diagram of the model \ref{['eq:classicalenergy2']}. The black lines are borders of three phases: uniform magnetization, SkX and magnetic Helix. The red dashed line marks the topological transition in the spectrum, it corresponds to coincidence of frequencies of Br and CCW modes at the Brillouin zone center.
• Figure 2: Panels (a)-(e) demonstrate the evolution of Br and CCW bands for small easy-axis anisotropy, $a=-0.03$, and $b\in[0.58,0.64]$, with the band gap closure at $b=0.61$. The sign of the Berry curvature for each band is denoted by the color: blue points correspond to negative sign and yellow-red points correspond to positive sign. The similar picture of the Berry curvature sign change is observed at the whole red dashed line in Fig. \ref{['fig:phasediag']}.