Buettner, F.; Krueger, B.; Eisebitt, S.; Kläui, M.: Accurate calculation of the transverse anisotropy of a magnetic domain wall in perpendicularly magnetized multilayers. Physical Review B 92 (2015), p. 054408/1-7
10.1103/PhysRevB.92.054408
Open Access Version (externer Anbieter)
Abstract:
Bloch domain walls are the most common type of transition between two out-of-plane magnetized domains (one magnetized upwards, one downwards) in films with perpendicular magnetic anisotropy. The rotation of the spins of such domain walls in the plane of the film requires energy, which is described by an effective anisotropy, the so-called transverse or hard axis anisotropy K⊥. This anisotropy and the related Döring mass density of the domain wall are key parameters of the one-dimensional model to describe the motion of magnetic domain walls. In particular, the critical field strength or current density where oscillatory domain wall motion sets in (Walker breakdown) is directly proportional to K⊥. So far, no general framework is available to determine K⊥ from static characterizations such as magnetometry measurements. Here, we derive a universal analytical expression to calculate the transverse anisotropy constant for the important class of perpendicular magnetic multilayers. All the required input parameters of the model, such as the number of repeats, the thickness of a single magnetic layer, and the layer periodicity, as well as the effective perpendicular anisotropy, the saturation magnetization, and the static domain wall width are accessible by static sample characterizations. We apply our model to a widely used multilayer system and find that the effective transverse anisotropy constant is a factor of seven different from that when using the conventional approximations, showing the importance of using our analysis scheme. Our model is also applicable to domain walls in materials with Dzyaloshinskii-Moriya interaction (DMI). The accurate knowledge of K⊥ is needed to determine other unknown parameters from measurements, such as the DMI strength or the spin polarization of the spin current in current-induced domain wall motion experiments.