Analytical studies of the magnetic domain wall structure in the presence of non-uniform exchange bias

The pinning phenomena of the domain wall in the presence of exchange bias are studied analytically. The analytic solution of the domain wall spin configuration is presented. Unlike the traditional solution, which is symmetric, our new solution could exhibit the asymmetry of the domain wall spin profile. Using the solution, the domain wall position, its width, its stability, and the depinning field are discussed analytically.