In the past, the Callen-Callen (1965 Phys. Rev. 139 A455-71; J. Phys. Chem. Solids 27 1271-85) model has been highly successful in explaining the origin and temperature dependence of the magneto-crystalline anisotropy in many magnetic compounds. Yet, despite their high ordering temperatures of ∼650 K, the Callen-Callen model has proved insufficient for the REFe 2 compounds. In this paper, we show that it is possible to replicate the values of the phenomenological parameters K 1 , K 2 , and K 3 given by Atzmony and Dariel (1976 Phys. Rev. B 13 4006-14), by extending the CallenCallen model to second order in H CF . In particular, explanations are provided for (i) the unexpected changes in sign of K 1 and K 2 in HoFe 2 and DyFe 2 , respectively, and (ii) the origin and behaviour of the K 3 term. In addition, it is demonstrated that higher order terms are required,and that K 4 exceeds K 3 at low temperatures. Revised estimates of K 1 , K 2 , K 3 , K 4 , and K 5 are given. Finally, an alternative 'multipolar' approach to the problem of magnetic anisotropy is also provided. It is shown that the latter confers significant advantages over the older phenomenological method. In particular, all the multipolar coefficients (K N , N = 4, 6, 8, 10, 12) decrease monotonically with increasing temperature, withK N decreasing faster thanK N −2 etc. These observations are in accord with expectations based on the original Callen-Callen model.

Magnetic measurements of ͓110͔ ͓50 Å DyFe 2 / 200 Å YFe 2 ͔ reveal a rich switching behavior: the formation of exchange springs in this system of alternating hard and soft layers can be observed for low temperatures ͑LTs͒. For high temperatures ͑HTs͒, the appearance of the hysteresis loop changes significantly, implying a more complicated reversal process. In this article, we reproduce hysteresis loops for net and compound-specific magnetizations by means of micromagnetic simulations and assess the quality by a direct comparison to recent x-ray magnetic circular dichroism measurements. The HT switching characteristics, showing a magnetization reversal of the hard magnetic layer before the soft magnetic layer, are investigated and understood on the basis of detailed magnetic configuration plots. The crossover of LT to HT switching patterns is explained by energy considerations, and the dependence on different parameters is outlined.

Abstract-We study the Anisotropic Magneto-Resistance (AMR) of a two-dimensional periodic square array of connected permalloy rings with periodicity of 1µm combining experimental and computational techniques.The computational model consists of two parts: (i) the computation of the magnetization and (ii) the computation of the current density. For (i), we use standard micromagnetic methods. For (ii), we start from a potential difference applied across the sample, compute the resulting electric potential and subsequently the corresponding current density based on a uniform conductivity. We take into account the backreaction of the magnetoresistive effects onto the current density by self consistently computing the current density and conductivity until they converge.We compare the experimentally measured AMR curve (as a function of the applied field) with the numerically computed results and find good agreement. The numerical data provides insight into the characteristics of the AMR data.Finally, we demonstrate the importance of taking into account the spatial variation of the current density when computing the AMR.

Self-assembly techniques can be used to produce periodic arrays of magnetic nanostructures. We have developed a double-template technique using electrochemical deposition. This method produces arrays of dots which are of spherical shape, as opposed to those prepared by standard lithographic techniques, which are usually cylindrical. By varying the amount of material that is deposited electrochemically, spheres of diameter d can be grown up to varying heights h Ͻ d. Thus different spherical shapes can be created ranging from shallow dots to almost complete spheres. Using micromagnetic modeling, we calculate numerically the magnetization reversal of the soft part spherical particles. The observed reversal mechanisms range from single domain reversal at small radii to vortex movement in shallow systems at larger radii and vortex core reversal, as observed in spheres at larger heights. We present a phase diagram of the reversal behavior as a function of radius and growth height. Additionally, we compare simulation results of hybrid finite element/boundary element and finite difference calculations for the same systems.

Abstract.Magnetization loops for (110) MBE grown ErFe 2 /YFe 2 multilayer films are presented and discussed. The magnetocrystalline easy axis for the Er layers is parallel to a <111> type crystal axis, with the out of plane <111> axes favoured by the strain. For fields applied along the (110) crystal growth axis, out-of-plane magnetic exchange springs are set up in the magnetically soft YFe 2 layers. For multilayer films that display exchange spring dominated reversal at low temperatures, there is a cross-over temperature above which there are additional transitions at high fields. These features are interpreted using micro-magnetic modelling. At sufficiently high fields, applied perpendicular to the multilayer film plane, the energy is minimized by an exchange spring driven multilayer spin flop. In this state, the average magnetization of the ErFe 2 layers switches into a nominally hard in-plane <111> axis, perpendicular to the applied field.