Jürgen P. Zimmermann

Magnetic anisotropy in the cubic Laves REFe2 intermetallic compounds

In the past, the Callen–Callen (1965 Phys. Rev. 139 A455–71; 1966 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 REFe2 compounds. In this paper, we show that it is possible to replicate the values of the phenomenological parameters K1, K2 ,a ndK3 given by Atzmony and Dariel (1976 Phys. Rev. B 13 4006–14), by extending the Callen– Callen model to second order in HCF .I n particular, explanations are provided for (i) the unexpected changes in sign of K1 and K2 in HoFe2 and DyFe2, respectively, and (ii) the origin and behaviour of the K3 term. In addition, it is demonstrated that higher order terms are required,and that K4 exceeds K3 at low temperatures. Revised estimates of K1, K2, K3, K4 ,a ndK5 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

Micromagnetic simulation studies of ferromagnetic part spheres

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<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.

Micromagnetic simulation of the magnetic exchange spring system DyFe2∕YFe2

Magnetic measurements of [110] [50ADyFe2∕200AYFe2] 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 (LTs). For high temperatures (HTs), 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.

Exchange spring driven spin flop transition in ErFe2∕YFe2 multilayers

Magnetization loops for (110) ErFe2∕YFe2 multilayer films grown by molecular beam epitaxy are presented and discussed. The direction of easy magnetization for the Er layers is out of plane, near a ⟨111⟩-type crystal axis. For fields applied along the (110) crystal growth axis, out-of-plane magnetic exchange springs are set up in the magnetically soft YFe2 layers. For multilayer films that display negative coercivity at low temperatures, there is a crossover temperature above which the coercivity becomes positive, with additional transitions at high fields. These features are interpreted using micromagnetic modeling. 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 ErFe2 layers switches into a nominally hard in-plane ⟨111⟩ axis, perpendicular to the applied field.

Analysis of Magnetoresistance in Arrays of Connected Nano-Rings

We study the anisotropic magnetoresistance (AMR) of a 2-D periodic square array of connected permalloy rings with periodicity of 1 mum combining experimental and computational techniques. The computational model consists of two parts: 1) the computation of the magnetization and 2) the computation of the current density. For 1), we use standard micromagnetic methods. For 2), 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

Numerical studies of demagnetizing effects in triangular ring arrays

We study the effect of the magnetostatic field in a two-dimensional periodic square array of Permalloy triangular rings by means of micromagnetic simulations. The rings have a lateral size of 50nm, an edge width of 8nm, and the thickness is 10nm. Applying an external field to one of the elements and assuming the rest of the array to be in the remanent state, we show how the remanent magnetization and coercive field are affected by the magnetostatic field of the array, both as a function of the distance between the elements and as a function of the number of elements used to model the periodic array. We provide an estimate of the minimum distance for an independent behavior of the elements, and we show that a model with the first and second nearest neighbors of an element can accurately approximate the effect of a much larger array.

Micromagnetic Modelling of the Dynamics of Exchange Springs in Multi-Layer Systems

Exchange springs are formed in multilayers of alternating hard and soft ferromagnetic materials which are exchange coupled at their interfaces. These systems are rich of interesting physical properties, which can be tuned by selecting suitable geometries and compositions. In this paper, we present a computational study of the dynamics of a tri-layer DyFe2/YFe2/DyFe2 exchange spring system near the bending field (the field required to twist the magnetization of the soft YFe2 layer out of the aligned state). The dynamical reaction of the system to small variations of the applied field is studied and its oscillatory nature is analyzed numerically. The behaviors of the decay times, the frequencies, and amplitudes reveal enhanced responses of the system near the bending field

Numerical investigation of domain walls in constrained geometries

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=490kA∕m) with a weak in-plane anisotropy (K1=2000J∕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 Neel 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 11nm is found (where the ...

Spin-flop transition driven by exchange springs in ErFe2∕YFe2 multilayers

Magnetization loops for (110) ErFe2∕YFe2 multilayer films grown by molecular beam epitaxy are presented and discussed. The easy axis for the hard ErFe2 layers is near an out of plane ⟨111⟩-type crystal axis. At low temperatures there is just one irreversible switch of the hard layers, accompanied by the formation of magnetic exchange springs in the soft YFe2 layers. However, above a certain temperature the coercivity changes sign and there are additional high field transitions. This crossover temperature, TCO, depends on the composition of the multilayers. In sufficiently high fields, perpendicular to the multilayer film plane, the energy is minimized by an exchange spring driven multilayer spin-flop state. The composition dependence of TCO is explained with a simple energy argument.