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.

Hard-soft multilayer a b s t r a c tThe magnetization reversal processes of ½10 nm ErFe 2 =nYFe 2 =4 nm DyFe 2 =nYFe 2 multilayer films with a (11 0) growth axis and a variable YFe 2 layer thickness n are investigated. The magnetically soft YFe 2 compound acts as a separator between the hard rare earth (RE) ErFe 2 and DyFe 2 compounds, each of them bearing different temperature dependent magnetic anisotropy properties. Magnetic measurements of a system with n ¼ 20 nm reveal the existence of three switching modes: an independent switching mode at low temperatures, an ErFe 2 spin flop switching mode at medium high temperatures, and an YFe 2 dominated switching mode at high temperatures. The measurements are in qualitative agreement with the findings of micromagnetic simulations which are used to illustrate the switching modes. Further simulations for a varied YFe 2 layer thickness n ranging from 2 to 40 nm are carried out. Quantitative criteria are defined to classify the reversal behavior, and the resultant switching modes are laid out in a map with regard to n and the temperature T. A new coupled switching mode emerges above a threshold temperature for samples with thin YFe 2 separation layers as a consequence of the exchange coupling between the magnetically hard ErFe 2 and DyFe 2 layers. It reflects the increasing competition of the two conflicting anisotropies to dominate the magnetic switching states of both RE compounds under decreasing n.

The magnetic anisotropy parameters in [110] MBE-grown films of REFe 2 (RE, rare earth) compounds are not the same as those in the bulk. This is due to the presence of a shear strain ε xy , frozen-in during crystal growth. In this paper, magnetic anisotropy parameters for [110] MBE-grown REFe 2 films, that directly involve the shear strain ε xy , are presented and discussed. In addition to the usual first-order Callen and Callen termK 2 , there are nine second-order terms, six of which involve cross-terms between ε xy and the cubic crystal field terms B 4 and B 6 . Two of the second-order cross-terms are identified as being important:K 242 (T ) andK 264 (T ). Of these, the rank-two termK 242 (T ) dominates over a large temperature range. It has the same angular dependence as the first-order termK 2 , but with a more rapid temperature dependence. The correction at T = 0 K for TbFe 2 , DyFe 2 , HoFe 2 , ErFe 2 and TmFe 2 , amounts to ∼+9.2%, −13.9%, −11.6%, +14.3%, and 27.1%, respectively. Similar comments are made concerning the rank-fourK 264 (T ) term.

In recent years, magnetic domain wall structures in ferromagnetic nanowires have attracted growing attention, opening paths to develop novel devices which exploit magnetoresistive effects. A reduction of the domain wall length in geometrically constrained areas has been predicted and observed. In this article, we consider a rectangular constriction (width s0, length 2d0) in form of a thin film, attached to a rectangular pad (width s1) on either side. The material considered is Ni (Ms = 490 kA/m) with a weak in-plane anisotropy (K1 = 2000 J/m3 ). We investigate the dependence of the domain wall length as a function of the constriction geometry. Micromagnetic simulations are used to systematically study the head-to-head domain walls between head-to-head domains (case A) and Néel walls between sidewise domain orientations (case B). We present the resulting domain wall length w as a function of 2d0 and s0 and analyze the magnetization patterns. A reduction of the domain wall length to below 11 nm is found (where the corresponding unconstrained domain wall length is 69 nm). For constriction lengths above a critical value (case B only), the single 180• domain wall splits into two 90• domain walls.