K.N. Martin

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 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.

Modelling magnetic exchange springs in 1D, 2D, and 3D

1D models of magnetic multilayers, with alternating hard and soft layers, are extended to 2D and 3D, and presented within a common framework of nearest neighbour interactions. Using 2D calculations, it is shown that the properties of magnetic exchange springs can be changed significantly by patterning the hard pinning layers. But, in certain cases the bending field BB is not significantly altered, even when half the pinning layer is removed. 3D calculations are used to probe the effects of defects on the properties of magnetic exchange springs, using epitaxial DyFe2/YFe2 superlattices as an example. It is shown that point defects such as Fe vacancies have little effect on the bending field transition. This is in marked contrast to the 1D model, where an Fe vacancy cuts the magnetic exchange spring into two. Finally, it is demonstrated that significant changes in the properties of magnetic exchange springs can be engineered, by placing rare-earth ions in the centre of the soft YFe2 springs. A new phenomenon, exchange spring collapse, is predicted.

The effect of inter-layer diffusion on magnetic exchange spring behaviour

The effect of inter-layer diffusion between the magnetically hard and soft layers in magnetic exchange spring systems is examined, using 1D and 2D models. It is shown that diffusion across the hard/soft interfaces leads to an increase in the bending field BB. This increase eventually saturates when the bending field BB and the coercivity BC merge. Moreover, if the increase in the bending field BB is large enough, the nature of the magnetic reversal can be affected. This behaviour is illustrated using a YFe2 dominated YFe2/DyFe2 exchange spring system. In this case the 1D model predicts that inter-layer diffusion can drive a magnetic phase change, from negative to positive coercivity. Discrete 2D model calculations of inter-layer diffusion are also presented and discussed. The latter support the predictions of the 1D model. Finally, while the emphasis is on atomic diffusion, some comments are made concerning interface roughness.

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.

Magnetic anisotropy basis sets for epitaxial (110) and (111) REFe2 nanofilms

Magnetic anisotropy basis sets for the cubic Laves phase rare earth intermetallic REFe2 compounds are discussed in some detail. Such compounds can be either free standing, or thin films grown in either (110) or (111) mode using molecular beam epitaxy. For the latter, it is useful to rotate to a new coordinate system where the z-axis coincides with the growth axes of the film. In this paper, three symmetry adapted basis sets are given, for multi-pole moments up to n = 12. These sets can be used for free-standing compounds and for (110) and (111) epitaxial films. In addition, the distortion of REFe2 films, grown on sapphire substrates, is also considered. The distortions are different for the (110) and (111) films. Strain-induced harmonic sets are given for both specific and general distortions. Finally, some predictions are made concerning the preferred direction of easy magnetization in (111) molecular beam epitaxy grown REFe2 films.

Magnetization reversal in micron-sized stripes of epitaxial (110)YFe2 films

In this paper, YFe2(110) single crystal films with Laves phase structure were grown on sapphire substrates by molecular beam epitaxy, and its magenization reversal was investigated by magneto-optical Kerr effect measurements. Results show that the films magnetic behavior is governed by the combined effect of induced shape anisotropy and intrinsic four-fold magneto-crystalline anisotropy. A dominant uniaxial in-plane anisotropy can be created by geometrical effects.