Domain Walls in Helical Magnets: Elasticity and Pinning

Recently completely new types of domain walls (DWs) have been discovered in helical magnets, consisting generically of a regular array of {\it pairs} of magnetic vortex lines \cite{Li+12}. Only for special orientations DWs are free of vortices. In this article we calculate their elastic and pinning properties, using the pitch angle $\theta$ as a small parameter. In particular we show that vortex free DWs exhibit long range elasticity which makes them very stiff and suppresses their pinning by impurities. Their roughening transition temperature is of the order of the N\'eel temperature. DWs including vortices (either by orientation or due to step formation above their roughening transition) show short range elasticity and strong pinning by impurities. These results apply both to centro-symmetric as well as to non-centrosymmetric systems. The application to chiral liquid crystals is briefly discussed.