Anisotropy of exchange stiffness and its effect on the properties of magnets

Abstract

Using the spin-spiral formulation of the tight-binding linear muffin-tin orbital method, the principal components of the exchange stiffness tensor are calculated for typical hard magnets including tetragonal CoPt-type and hexagonal YCo5 alloys. The exchange stiffness is strongly anisotropic in all studied alloys. This anisotropy makes the domain wall surface tension anisotropic. Competition between this anisotropic surface tension and magnetostatic energy controls the formation and dynamics of nanoscale domain structures in hard magnets. Anisotropic domain wall bending is described in detail from the general point of view and with application to cellular Sm-Co magnets. It is shown that the repulsive cell-boundary pinning mechanism in these magnets is feasible only due to the anisotropic exchange stiffness if suitably oriented initial pinning centers are available. In polytwinned CoPt-type magnets the exchange stiffness anisotropy controls the orientation of macrodomain wall segments. These segments may reorient both statically during microstructural coarsening and dynamically during the macrodomain wall splitting in external field. Reorientation of segments may facilitate their pinning at antiphase boundaries.

Anisotropy of exchange stiffness based on atomic-scale magnetic properties in the rare-earth permanent magnetNd2Fe14B

“…10 (a) blue line) is the most suitable conditions in our modelings. Most strong permanent magnets, Nd 2 Fe 14 B, YCo 5 and also L1 0 -type magnet (CoPt, FePd, FePt) cannot reproduce the same condition because A x > A z [24], whereas Sm(Fe,Co) 12 would do because the anisotropy as A x < A z [25]. Therefore, Sm(Fe,Co) 12 and other R(Fe,Co) 12 -type compounds (R is a rare-earth element) may have higher potential to realize strong performance exchange spring magnet rather than the other magnets.…”

Influence of the lattice discreteness on magnetic ordering in nanostructures and nanoarrays

“…It has recently been demonstrated [119] that an anisotropy of the exchange stiffness tensor can lead to the anisotropic orientation of domain walls in bulk orthorhombic materials. At first sight this theory is not applicable to the case of double layers with lattices of perfect cubic symmetry.…”

Effects of anisotropic exchange on the micromagnetic domain structures

“…The coefficients of this tensor can be determined experimentally, for example by the long-wavelength part of the magnon spectrum [11]. Although for some selected tetragonal and hexagonal crystals the principal components of the exchange stiffness tensor have been calculated using a spin-spiral formulation of the tight-binding linear muffin-tin orbital method [12], the experimental and theoretical determination of the components are not commonly performed. Moreover, the effects of anisotropic exchange on the micromagnetic domain structure have not been explored yet and are the focus of this paper.…”

“…In this case, i.e., the direction normal to the domain wall perpendicular to both the direction of the stiffest exchange and the magnetocrystalline easy axis, the respective energies are minimum. However, in case the direction of the stiffest coupling is not parallel to the magnetocrystalline easy axis, the energy minimum of a domain transition is non-trivial [12]. A domain wall along the stiffest coupling decreases the exchange energy by simultaneously increasing the magnetocrystalline anisotropy energy and or the demagnetization energy.…”