Magnetoelastic modelling in soft nanocrystalline alloys

Geoffroy Olivier,Chazal Hervé,Porteseil Jean-Louis,Waeckerlé Thierry,Alves Francisco

doi:10.1016/j.jmmm.2006.02.123

Abstract

Magnetoelastic effects in ultra soft nanocrystalline alloys are investigated theoretically and experimentally. From H c measurements, extraction of magnetoelastic contribution is carried out using a formalism obtained revisiting random anisotropy model (RAM) in the light of domain walls (DW) displacements, our approach based on theoretical investigations on the way of a reversal of a correlated volume (CV) located in the vicinity of a DW. Modelling of magnetoelastic effects shows that even in perfectly relaxed samples, a magnetoelastic contribution exists due to elastic frustration experienced by a CV during its magnetization reversal. Magnitude of this energy is large enough to drive coercivity of samples featuring grain diameter D around 10 nm, which are of major interest for applications.

Highlights

Magnetoelastic effects in soft nanocrystalline alloys are of major importance
In part 2, an alternative formalism considering correlated volume (CV) reversal in a macroscopic scheme governed by domain wall (DW) displacement
=pm0–and related quantities–are determined by magnetostatics instead of anisotropy and are of unrealistically high magnitude. This paradox vanishes, noticing that, dealing with the magnetostatic energy, the crude assumption of uniformly magnetized regions leads to a high charges concentration and an overestimated evaluation calling upon m* effect [10], which leads to a reduction factor between 1 and 1 þ J2s =ð2m0KeÞ depending on the magnetizations of CV and surrounding medium

Summary

Introduction

Experimental data show that it is necessary to consider, apart from classical random anisotropy contribution, a second source of coercitivity usually attributed to magnetoelastic effects [1,2]. Tropy and leads to a negligible contribution compared with the magnetocrystalline one [6] This allows to consider the ribbon as isotropic and elastically homogeneous, with magnetostriction coefficient ls and Young Modulus E leading to a magnetoelastic energy density W me % El2s : With lsEseveral 10À6 and EE2 Â 1011 Pa, one obtains WmeEseveral J/m3, which, dealing with macroscopic properties, can play a role only if coherent at the scale of the CV. The part due to random anisotropy being not negligible, the extraction of magnetoelastic contribution to Hc involves dedicated formalism as proposed in Ref. Extraction of Kme from experiments will be carried out, allowing confrontation with modelling, marking the end of part 3

CV reversal and DW displacement

Annealing Temperatures

Modeling of Kme

Dlij j þ X Dlij2 þ 2 X gij2 5 j j

Conclusion