Influence of fourfold anisotropy form on hysteresis loop shape in ferromagnetic nanostructures

Abstract

The dependence of the form of different mathematical depictions of fourfold magnetic anisotropies has been examined, using a simple macro-spin model. Strong differences in longitudinal and transverse hysteresis loops occur due to deviations from the usual phenomenological model, such as using absolute value functions. The proposed possible models can help understanding measurements on sophisticated magnetic nanosystems, like exchange bias layered structures employed in magnetic hard disk heads or magnetic nano-particles, and support the development of solutions with specific magnetization reversal behavior needed in novel magneto-electronic devices.

Asymmetric Hysteresis Loops in Co Thin Films

“…Such minor loops can be used, e.g., to measure first order reversal curves (FORC), which allow for calculating reversible and irreversible loop components and contain additional information about the investigated system [10][11][12]. On the other hand, it is possible to measure minor loops erroneously, since a hysteresis loop seems to be closed, but parts of the sample are not fully reversed, or a hard axis in a thin film sample is not yet crossed [3,[13][14][15]. Harres et al gave some criteria to avoid such undesired minor loops: Singularities in the magnetization should be observed by successive derivations of the magnetization with respect to the external magnetic field; by finding the maximum positive field which is sufficient to acquire the remanent 2 of 10 magnetization; and by measuring zero field cooling/field cooling curves, allowing for estimating the anisotropy field [14].…”

Influence of shape and dimension on magnetic anisotropies and magnetization reversal of Py, Fe, and Co nano-objects with four-fold symmetry

“…In a former study based on a macrospin model, this ratio was equal to 3.28 for the usual phenomenological approach most often used for fourfold systems, 3.54 for a fourfold anisotropy of the form cos(4ϕ), or 1.87 if the macroscopic approach of an absolute value function |sin ϕ · cos ϕ| is used, 19 which was motivated by results of exchange bias systems. The values of 0.30 / 0.28 / 0.53 could also be achieved since the orientations of hard and easy axes may be exchanged.…”

“…Additionally it should be mentioned that more than half of the nanostructures exhibit ratios that cannot be explained by previous calculations based on a macrospin model. 19 Thus in future simulations and experiments, the anisotropies of these new nanostructures will be examined to support understanding the new configurations and thus tailoring their magnetic properties.…”

“…Due to the significant competition between demagnetization and exchange fields as well as shape anisotropies in such structures of dimensions reduced to nanoscale, different overall magnetic anisotropies can be expected to occur which cannot be described by common phenomenological or macroscopic approaches, 18,19 resulting in unusual magnetic states and magnetization reversal processes.…”