The metastable zero field magnetic states of elongated Permalloy islands on square lattices of different geometries are investigated by means of magnetic force microscopy and numerical calculations. Keeping the island shape L / w = 10 fixed while varying the interparticle distances a, it is demonstrated that the relative frequencies of observed magnetic configuration at remanence strongly depend on the packing density of an array and the magnetic history ͑i.e., in which direction the array has been saturated before measurement͒. From 16 possible arrangements, only two are experimentally observed. For small L / a, a mixture of configurations, i.e., a spin ice, is found in agreement with previous studies, while for large L / a, an onion state unexpectedly prevails independent of the direction of the previously applied field. The results are discussed within the framework of potential theory and general stray field interaction. The relative frequencies of metastable states as well as the absence of the true ground state are in good agreement with theory.

While the principal features of the exchange bias between a ferromagnet and an antiferromagnet are believed to be understood, a quantitative description is still lacking. We show that interface spin disorder is the main reason for the discrepancy of model calculations versus experimental results. Taking into account spin disorder at the interface between the ferromagnet and the antiferromagnet by modifying the well known Meiklejohn and Bean model, an almost perfect agreement can be reached. As an example this is demonstrated for the CoFe/IrMn exchange biased bilayer by analyzing the azimuthal dependence of magnetic hysteresis loops from MOKE measurements. Both, exchange bias and coercive fields for the complete 360• angular range are reproduced by our model. The exchange bias system refers to the shift of the ferromagnetic (F) hysteresis loop to positive or negative values when the F system is in contact with an antiferromagnetic (AF) system and cooled in an applied magnetic field through the Néel temperature of the AF system. The exchange bias (EB) phenomenon is associated with the interfacial exchange coupling between ferromagnetic and antiferromagnetic spin structures, resulting in a unidirectional magnetic anisotropy [1]. While the unidirectional anisotropy was successfully introduced by Meiklejohn and Bean (M&B), the origin of the enhanced coercive field is yet not well understood. The details of the EB effect depend crucially on the AF/F combination chosen and on the structure and thickness of the films [2,3]. However, some characteristic features apply to most systems: (1) H EB and H c increase as the system is cooled in an applied magnetic field below the blocking temperature T B ≤ T N of the AF layer, where T N is the Néel temperature of the AF layer; (2) the magnetization reversal can be different for the ascending and descending part of the hysteresis loop [4,5,6,7,8]; (3) thermal relaxation effects of H EB and H c indicate that a stable magnetic state is reached only at very low temperatures [9,10,11].Several theoretical models have been developed for describing possible mechanisms of the EB effect, including domain formation in the AF layer with domain walls perpendicular to the AF/F interface [12], creation of uncompensated excess AF spins at the interface [13], or the formation of domain walls in the AF layer parallel to the interface [14,15]. Another approach is the consideration of diluted antiferromagnets in an exchange field. In the work described in Ref. [16,17,18] the discussion about compensated versus uncompensated interfacial spins is replaced by a discussion of net magnetic moments within the antiferromagnetic layer. Depending on the complexity of the system, the models can explain some but not * florin.radu@bessy.de † Present address: BESSY GmbH, Albert-Einstein-Str. 15, D-12489 Berlin, Germany.all features of experimental hysteresis loops. Here we provide a new model which can describe all features, including the azimuthal dependence of H EB , H c , and the AF thickness dependence. In ...

We have investigated the magnetization arrangement in an in-plane stripe pattern with alternating exchangebias domains. The stripe pattern was produced by ion bombardment induced magnetic patterning, which changed locally the exchange-bias direction at the ferromagnet/antiferromagnet interface, but not the magnetic or antiferromagnetic properties of the Co 70 Fe 30 and Mn 83 Ir 17 layers, respectively. For the analysis of the magnetic domain structure evolution along the hysteresis loop we used a combination of experimental techniques: magneto-optical Kerr effect, Kerr microscopy, polarized neutron reflectometry, and off-specular scattering of polarized neutrons with polarization analysis. Instead of a perfect antiparallel alignment we found that the magnetization in neighboring stripes is periodically canted with respect to the stripe axis so that the net magnetization of the ferromagnetic film turns almost perpendicular to the stripes. At the same time the projection of the magnetization vector onto the stripe axis has a periodically alternating sign. The experimental observations are explained and quantitatively described within the frame of a phenomenological model, taking into account interfacial exchange bias, intralayer exchange energy, and uniaxial anisotropy. The model defines conditions which can be used for tailoring nano-and micro-patterned exchange-bias systems with different types of magnetic order.

Experimental and theoretical aspects of obtaining the magnetic information carried by laser beams diffracted from an array of micro- or nanosized magnetic objects are reviewed. We report on the fundamentals of vector magneto-optic Kerr effect (MOKE), Bragg-MOKE, and second-order effects in the Kerr signal in longitudinal Kerr geometry as well as on an experimental setup used for vector and Bragg-MOKE experiments. The vector and Bragg-MOKE technique in combination with micromagnetic simulation is a reliable tool for measuring the complete magnetization vector and for characterizing the reversal mechanism of lateral magnetic nanostructures. We discuss the Bragg-MOKE effect for three standard domain configurations during the magnetization reversal process and present the expected behavior of the magnetic hysteresis loops.

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A combination of experimental techniques, e.g. vector-MOKE magnetometry, Kerr microscopy and polarized neutron reflectometry, was applied to study the field induced evolution of the magnetization distribution over a periodic pattern of alternating exchange bias stripes. The lateral structure is imprinted into a continuous ferromagnetic/antiferromagnetic exchange-bias bi-layer via laterally selective exposure to He-ion irradiation in an applied field. This creates an alternating frozen-in interfacial exchange bias field competing with the external field in the course of the re-magnetization. It was found that in a magnetic field applied at an angle with respect to the exchange bias axis parallel to the stripes the re-magnetization process proceeds via a variety of different stages. They include coherent rotation of magnetization towards the exchange bias axis, precipitation of small random (ripple) domains, formation of a stripe-like alternation of the magnetization, and development of a state in which the magnetization forms large hyper-domains comprising a number of stripes. Each of those magnetic states is quantitatively characterized via the comprehensive analysis of data on specular and off-specular polarized neutron reflectivity. The results are discussed within a phenomenological model containing a few parameters which can readily be controlled by designing systems with a desired configuration of magnetic moments of micro-and nano-elements.

Artificial magnetic dipole arrays arranged on a square lattice exhibit a fascinating variety and complexity of configurations. Among the 16 possible configurations, six fulfill the spin ice rule of two dipoles pointing into a vertex and two point out. We present experimental realizations of magnetic dipole arrays and discuss the remanent state as well as the magnetization reversal in an external field.