Thermodynamics of magnetic emergent crystals under coupled magnetoelastic fields

Magnetic fields and mechanical forces can change the deformation and stability of magnetic emergent crystals (MECs) such as Bloch skyrmion crystal (SkX), Néel SkX and Anti-SkX. Due to the tensor nature of strains, mechanical loads provide more fruitful ways to manipulate the MECs, while their effect on MECs other than the Bloch SkX is hitherto unclear. We construct a thermodynamic model for noncentrosymmetric ferromagnets in all possible point groups when subjected to coupled magnetoelastic fields. Compared with classic theories, we include terms coupling the elastic strains, the magnetization, and its derivatives in the free energy, which lead to strain-induced Dzyaloshinskii–Moriya interaction anisotropy. For epitaxial thin films in three types of point groups ( T , C 3 v , D 2 d ) hosting Bloch SkX, Néel SkX and Anti-SkX, we find the newly added terms always deform the MECs and eventually lead to their instability as the misfit strains increase. Specifically, for Bloch SkX in group T materials and Néel SkX in group C 3 v materials, a novel magnetic phase called paired-skyrmion crystal (pSkX) appears. Our theory lays the path to study deformation and phase transitions of different MECs, and to explore novel states of MECs in chiral magnets when subjected to magnetoelastic fields.