Magnetization spiral structure and high domain wall velocity induced by inertial effect

In ultrafast magnetism, i.e., the short time scales such as picosecond and femtosecond, we report that the spiral structure of magnetization can be formed by the inertial effect. Comparing with the case of fast magnetism in nanosecond time scale, we can obtain a higher velocity of domain wall in ultrafast magnetism due to the driving of inertial moment. There is a critical value tau(c) of angular momentum relaxation time tau for the inertial breakdown in uniaxial ferromagnet. Under the action of the inertial effect the domain wall width shows the characteristics of increases firstly as tau < tau(c), and then decreasing as tau > tau(c). It directly leads to the positive or negative mobility for the domain wall velocity as the inertia is less than or exceeds the critical value, respectively. In the high frequency mode (i.e., high field mode), we obtain the limit domain wall velocity, i.e., V -> 1/root alpha tau. The smaller the inertia or damping, the faster the domain wall moves. For the case of biaxial anisotropic ferromagnets, the domain wall width and velocity decreases with the increasing inertia term, respectively. In the presence of inertia effect, there is an another critical magnetic field h(c). The domain wall width decreases with the increase of the magnetic field as h < h(c), while increases as h > h(c). However, the domain wall velocity shows a nearly linear increase with the magnetic field. These results indicate that the ultrafast magnetism has more advantages than fast magnetism. It also provides a good control technique for rapid information processing in the future.