Emergent elasticity of skyrmion lattice in chiral magnets

Yangfan Hu, Biao Wang

Published 2016-08-17Version 1

When exposed to uniaxial tension, the hexagonal lattice of skyrmions in FeGe is found to undergoes significant deformation, indicating an emergent elastic stiffness almost two orders of magnitude smaller than that of the underlying atomic lattice6. Meanwhile, the shape of skyrmion is sensitive to uniaxial tension, which provides an efficient control parameter to all the skyrmionic properties including the emergent electrodynamics and the shape and frequency of spin-wave modes. A thorough understanding of the physical underpinning of such emergent elastic phenomenon is vital for realization of tunable skyrmions through application of mechanical stresses. Here we show theoretically that the emergent elastic property of skyrmions stems from the magnetoelastic interaction of the underlying material. We introduce the emergent elastic strains (EES) as independent thermodynamic variables through the Cauchy-Born law to describe the deformation of the skyrmion lattice. Within a free energy functional of B20 compounds incorporating a comprehensive description of the magnetoelastic effects, we establish the thermodynamics of emergent elastic behavior of skyrmions, and derive the linear equations of state between the EES and the elastic strains and stresses. The emergent strain ratio tensor, which linearly relates the elastic strains to the EES, is analytically solved near the critical temperature. Through the theory, we reproduce the emergent elongation pattern of skyrmions suffering uniaxial distortion found in FeGe6, and further find that hydrostatic loading merely causes any emergent deformation of the skyrmion lattice for any B20 compounds since the emergent Poisson's ratio for the skyrmion lattice is always close to 1. Our theory can be used to obtain quantitative results of the emergent deformation pattern of skyrmions caused by any form of homogeneous mechanical loads.