Analytical and numerical calculations of the magnetic force microscopy response: A comparison

We investigate the domain structure of submicrometer sized ferromagnetic stripes exhibiting in-plane and out-of-plane magnetized areas with magnetic force microscopy (MFM). Two simulation approaches are used to calculate the observed MFM response. The first relies on an analytical solution for the stray field of a bar magnet and the subsequent modeling of the sample as an arrangement of bar magnets. The MFM response is calculated for a realistic tip shape incorporating a distribution of magnetic dipoles. The second, numerical approach is based on a discretization scheme, breaking the tip-sample problem up into cells and then calculating the energy of the magnetic tip-sample interaction. The MFM responses obtained for the ferromagnetic stripe structure are compared. A discussion of the advantages and limitations of the two methods is given in terms of precision, computing time, and flexibility. The numerical method offers shorter computing times and greater flexibility, opening the door for realistic three-dimensional MFM response simulations. The advantage of the analytical method is the investigation of small structures, as its precision is higher for the comparable computational effort. © 2006 American Institute of Physics

Three-dimensional micromagnetic domain structure of MnAs films on GaAs(001): Experimental imaging and simulations

The micromagnetic domain structure of MnAs films on GaAs(001) has been systematically investigated by micromagnetic imaging and simulations. The magnetic force microscopy (MFM) contrast resulting from the stray field of the simulated three-dimensional domain patterns was calculated and found to be in excellent agreement with MFM experiments. By combining three-dimensional stray-field imaging by MFM with surface sensitive probing and micromagnetic simulations, we were able to derive a consistent picture of the micromagnetic structure of MnAs. For example, the origin of the comblike contrast observed through MFM was identified as a metastable domain configuration exhibiting a cross-tie wall. © 2007 The American Physical Society

Three-dimensional magnetic flux-closure domain patterns in MnAs thin films on GaAs(001)

The magnetic microstructure of single-crystalline MnAs films on GaAs(001) has been investigated. Magnetic force microscopy (MFM) reveals a three-dimensional magnetization pattern that is in disagreement with the simple domain picture observed by surface-sensitive magnetic imaging. Here, we present a consistent micromagnetic picture of MnAs thin films in the ferromagnetic stripe phase, which appears in the course of the phase transition. A number of equilibrium magnetization patterns of the stripes are found that are, in fact, based on flux-closure domain patterns in the basal plane of MnAs. The simulation of a stripe array yields excellent agreement with the measured surface magnetization. The experimentally observed stray field contrast was confirmed by MFM contrast simulations based on these equilibrium magnetization patterns. © 2007 American Institute of Physics

Micromagnetic properties of epitaxial MnAs films on GaAs surfaces

We present a systematic study of the micromagnetic properties of MnAs deposited by molecular-beam epitaxy on GaAs(001) and GaAs(111)B surfaces. In epitaxial MnAs films, the strain state in MnAs-on-GaAs(001) (anisotropic) and MnAs-on-GaAs(111)B (isotropic) has a strong influence on the magneto-structural phase transition and thus the micromagnetic properties. The ferromagnetic α and the β phase coexist over a wide temperature range exhibiting self-organized, magnetically coupled nanostructures. Independent of the substrate orientation, magnetic flux-closure domain patterns are formed in the basal plane of MnAs. The spatial distribution of the phases in equilibrium (stripes and quasi-hexagonal islands, respectively) stabilizes various magnetic states, which were found experimentally and confirmed by micromagnetic simulations. © 2007 WILEY-VCH Verlag GmbH and Co. KGaA