Theory of magnetic skyrmion glass

Skyrmions and skyrmion crystal (SkX) discovered in chiral magnets show unique physical properties due to their nontrivial topology such as the stability against the annihilation and the motion driven by the ultralow current density, which can be advantageous for the device applications such as magnetic memories. Especially, the chiral dynamics, i.e., the velocity perpendicular to the force acting on a skyrmion, is a key to avoid the impurity potential and enhances its mobility. However, the collective pinning of SkX occurs by the disorder, which is crucial for its low energy properties. Here, we study theoretically the low energy dynamics of SkX in the presence of disorder effects in terms of replica field theory, and reveal nonreciprocal collective modes and their electromagnetic responses along the direction of external magnetic field. The physical quantities such as the relaxation rate of $\mu$SR/NMR and the pinning frequency show a dramatic change associated with the topological phase transition from the helical state to SkX. These results provide a firm basis to explore the glassy state of SkX.