Low-temperature skyrmions and spiral reorientation processes in chiral magnets with cubic anisotropy: Guidelines for bridging theory and experiment

We revisit the phenomenological Dzyaloshinskii framework, a central theoretical approach for describing magnetization processes in bulk chiral magnets, and demonstrate how magnetocrystalline cubic anisotropy reshapes the phase diagrams of states and provides the key mechanism stabilizing low-temperature skyrmion phases. We show that, for magnetic field directions along the easy anisotropy axes, the phase diagrams feature stable skyrmion pockets for both signs of the anisotropy constant. We further analyze the nature of the transitions at the critical field <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:msub> <a:mi>H</a:mi> <a:mrow> <a:mi>c</a:mi> <a:mn>1</a:mn> </a:mrow> </a:msub> </a:math> , associated with the reorientation of stable and metastable spirals along the field. We also examine the transition at <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:msub> <b:mi>H</b:mi> <b:mrow> <b:mi>c</b:mi> <b:mn>2</b:mn> </b:mrow> </b:msub> </b:math> , where the conical state closes into the homogeneous state accompanied by a deviation of the wave vector from the field direction. By mapping characteristic anisotropy-dependent parameters in the theoretical phase diagrams, we provide guidelines for connecting theory with experiment and for estimating the cubic anisotropy constant in <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mrow> <c:msub> <c:mi>Fe</c:mi> <c:mrow> <c:mn>1</c:mn> <c:mo>−</c:mo> <c:mi>x</c:mi> </c:mrow> </c:msub> <c:msub> <c:mi>Co</c:mi> <c:mi>x</c:mi> </c:msub> <c:mi>Si</c:mi> </c:mrow> </c:math> and MnSi. Our results indicate that samples <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:mrow> <d:msub> <d:mi>Fe</d:mi> <d:mrow> <d:mn>1</d:mn> <d:mo>−</d:mo> <d:mi>x</d:mi> </d:mrow> </d:msub> <d:msub> <d:mi>Co</d:mi> <d:mi>x</d:mi> </d:msub> <d:mi>Si</d:mi> </d:mrow> </d:math> with small <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"> <e:mrow> <e:mi>x</e:mi> <e:mo>∼</e:mo> <e:mn>0.1</e:mn> </e:mrow> </e:math> possess sufficiently strong cubic anisotropy to stabilize a low-temperature skyrmion phase. Overall, these theoretical findings establish a quantitative framework for predicting and interpreting skyrmion stability in other cubic helimagnets as well.