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Higher order magnetoelasticity energy corrections in bcc and fcc systems

Jakub Šebesta, Ondřej Faiman, Dominik Legut

TL;DR

The paper addresses whether higher-order strain terms in the magnetoelastic energy substantially affect anisotropic magnetostriction in cubic bcc and fcc systems. It develops a theoretical framework by expanding the dipole-dipole interaction under strain to include higher-order terms, deriving $E_{me}^{III}$ and associated constants, then evaluates equilibrium strains for Fe (bcc) and Ni (fcc) using published ab initio values. The key finding is that quadratic higher-order terms have negligible influence on anisotropic magnetostriction in these cubic systems, while an extra linear term can shift isotropic magnetostriction and may affect $b_1$- and $b_2$-driven responses; the observed ab initio vs experiment discrepancies for $b_2$ are not resolved by these higher-order corrections. The results support using the linear ME energy for anisotropic effects in cubic materials and highlight the limited role of higher-order terms, with possible relevance for lower-symmetry cases future work could explore.

Abstract

Magnetoelastic properties play a vital role in industrial applications. Despite being hidden behind either purely magnetic or elastic behavior, magnetoelasticity takes place in a wide range of devices as transducers, acoustic actuators, or fast response sensors. In this work, we inspect the impact of higher-order terms on the anisotropic magnetostriction behavior. Regarding ab-initio calculations, the anisotropic magnetostriction can be related to the strain dependence of the magnetocrystaline energy. Commonly, the description is restricted to a linear strain dependence in the magnetoelastic energy. Here, we derive higher-order terms in strain for bcc and fcc crystal structures. Using a simple parametrization, we show that the influence of the higher-order strain terms is negligible for the studied cubic systems.

Higher order magnetoelasticity energy corrections in bcc and fcc systems

TL;DR

The paper addresses whether higher-order strain terms in the magnetoelastic energy substantially affect anisotropic magnetostriction in cubic bcc and fcc systems. It develops a theoretical framework by expanding the dipole-dipole interaction under strain to include higher-order terms, deriving and associated constants, then evaluates equilibrium strains for Fe (bcc) and Ni (fcc) using published ab initio values. The key finding is that quadratic higher-order terms have negligible influence on anisotropic magnetostriction in these cubic systems, while an extra linear term can shift isotropic magnetostriction and may affect - and -driven responses; the observed ab initio vs experiment discrepancies for are not resolved by these higher-order corrections. The results support using the linear ME energy for anisotropic effects in cubic materials and highlight the limited role of higher-order terms, with possible relevance for lower-symmetry cases future work could explore.

Abstract

Magnetoelastic properties play a vital role in industrial applications. Despite being hidden behind either purely magnetic or elastic behavior, magnetoelasticity takes place in a wide range of devices as transducers, acoustic actuators, or fast response sensors. In this work, we inspect the impact of higher-order terms on the anisotropic magnetostriction behavior. Regarding ab-initio calculations, the anisotropic magnetostriction can be related to the strain dependence of the magnetocrystaline energy. Commonly, the description is restricted to a linear strain dependence in the magnetoelastic energy. Here, we derive higher-order terms in strain for bcc and fcc crystal structures. Using a simple parametrization, we show that the influence of the higher-order strain terms is negligible for the studied cubic systems.
Paper Structure (7 sections, 33 equations, 1 figure, 3 tables)

This paper contains 7 sections, 33 equations, 1 figure, 3 tables.

Table of Contents

  1. Introduction
  2. Theory
  3. Results
  4. Conclusions
  5. Acknowledgemets
  6. High order expansion details
  7. Data availability

Figures (1)

  • Figure 1: Equilibrium strain as a function of the magnetization direction. (a) bcc Fe (b) fcc Ni. (solid lines) Equilibrium strain with the ME energy up to 2$^{nd}$ order in the strain (Eq. \ref{['Eq:2nd_ME']}). (dotted lines resp. dash-dotted lines) Behavior for experimental constants $b_{1}^{e}$ and $b_{2}^{e}$ resp. ab-initio one $b_{1}^{t}$ and $b_{2}^{t}$ with original ME energy formula (Eq. \ref{['Eq:MagelEng']}). (dotted lines) Equilibrium strain with only the linear strain terms in the Eq. \ref{['Eq:2nd_ME']}.