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In the field of micromagnetics, the calculation of long-range dipole–dipole interactions in non-uniformly magnetized bodies has long posed computational problems. In this paper, we present an inter and intra macro-cell point-dipole model, which can be used to speed-up the determination of dipole–dipole energies at the atomistic level. The model can be used to accurately compute the dipole–dipole energy, using macro-cells of any shape or size.

Exchange-coupled hard and soft magnetic layers find extensive use in data storage applications, for which their dynamical response has great importance. With bulk techniques, such as ferromagnetic resonance (FMR), it is difficult to access the behaviour and precise influence of each individual layer. By contrast, the synchrotron radiation-based technique of x-ray detected ferromagnetic resonance (XFMR) allows element-specific and phase-resolved FMR measurements in the frequency range 0.5–11 GHz. Here, we report the study of the magnetization dynamics of an exchange-coupled Ni _0.81Fe _0.19 (43.5 nm)/Co _0.5Fe _0.5 (30 nm) bilayer system using magnetometry and vector network analyser FMR, combined with XFMR at the Ni and Co L ₂ x-ray absorption edges. The epitaxially grown bilayer exhibits two principal resonances denoted as the acoustic and optical modes. FMR experiments show that the Kittel curves of the two layers cannot be t...

Irreversible exchange springs are experimentally observed in an antiferromagnetic (DyFe ₂ 40 Å/YFe ₂ 80 Å/DyFe ₂ 8 Å/YFe ₂ 80 Å) × 20 superlattice. Two irreversible exchange springs can be observed at 80 K with field along the [00 ] crystal direction. OOMMF micromagnetic simulation is employed to understand the underlying physics. It is confirmed that the induced anisotropy in the soft phase, by the 8 Å thick DyFe ₂ layer, is mainly responsible for the observed irreversibility, which corresponds to switching between energy minima of the thin hard inclusion in the soft phase. The qualitative agreement between experiment and simulation is satisfactory. This demonstrates the feasibility to control the irreversibility of exchange spring winding and unwinding processes in antiferromagnetically coupled superlattices. This additiona...

Ar ⁺ ions have been implanted into Laves phase epitaxial thin films of YFe ₂ and DyFe ₂. Magneto-optical Kerr effect and vibrating sample magnetometry experiments show that the easy and hard axes of magnetization in both materials rotate through an in-plane angle of 90°, whilst the strength of the magnetic anisotropy remains unaltered. This is supported by OOMMF computational modelling. Atomic force microscopy confirms that the film roughness is not affected by implanted ions. X-ray diffraction data show that the lattice parameter expands upon ion implantation, corresponding to a release of strain throughout the entire film following implantation with a critical fluence of 10 ¹⁷ Ar ⁺ ions cm ⁻². The anisotropy of the films is linked to the strain and from these data it is concluded that the source of anisotropy alters from one where magnetoelastic and magnetocrystalline effects compete to one which is governed solely b...

The current status of magnetic moments used in micro-magnetic modelling of the Laves phase rare earth iron REFe ₂ inter-metallic compounds is reviewed. In particular, it is argued that both the neutron scattering results and band structure calculations provide little support for the long-held view that the Fe 3d moments are constant across the REFe ₂ series, and for the oft-used rule of thumb that the ⁵⁷Fe hyperfine field is proportional to the Fe magnetic moment. Nevertheless, it is argued that it is acceptable to employ a simple ferrimagnetic model, in which the free-ion moment is ascribed to the RE ion and a moment of μ _d = μ _3d + μ _5d≈1.5 µ _B is used for the combined Fe(3d) and Fe-driven RE(5d) moments.

A system for classifying and quantifying entanglement in spin 1/2 pure states is presented based on simple images. From the image point of view, an entangled state can be described as a linear superposition of separable object wavefunction Ψ _O plus a portion of its own inverse image. Bell states can be defined in this way: . Using the method of images, the three-spin 1/2 system is discussed in some detail. This system can exhibit exclusive three-particle ν ₁₂₃ entanglement, two-particle entanglements ν ₁₂, ν ₁₃, ν ₂₃ and/or mixtures of all four. All four image states are orthogonal both to each other and to the object wavefunction. In general, five entanglement parameters ν ₁₂, ν ₁₃, ν ₂₃, ν ₁₂₃ and

Magnetic anisotropy basis sets for the cubic Laves phase rare earth intermetallic REFe ₂ 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 REFe ₂ 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 REFe ₂ films....

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 B _B. This increase eventually saturates when the bending field B _B and the coercivity B _C merge. Moreover, if the increase in the bending field B _B is large enough, the nature of the magnetic reversal can be affected. This behaviour is illustrated using a YFe ₂ dominated YFe ₂/DyFe ₂ 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, so...

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 B _B 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 DyFe ₂ /YFe ₂ 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 placin...

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 term , 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: