[Paper Review] Higher order magnetoelasticity energy corrections in bcc and fcc systems

Jakub Šebesta, Ondřej Faiman+1 more|arXiv (Cornell University)|Jan 10, 2026

Magnetic Properties and Applications0 citations

TL;DR

The paper derives higher-order strain terms in the magnetoelastic energy for cubic bcc Fe and fcc Ni, and shows these terms have negligible impact on anisotropic magnetostriction within cubic symmetry, while isotropic magnetostriction can be notably affected by an extra linear term.

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.

Motivation & Objective

• Motivate the importance of magnetoelasticity in devices like transducers and sensors.
• Extend magnetoelastic energy descriptions beyond linear strain terms for cubic systems.
• Parametrize higher-order terms using dipole-dipole interactions to assess their impact on magnetostriction.
• Compare theoretical predictions with ab-initio and experimental constants to evaluate accuracy.

Proposed method

• Derive higher-order strain terms in the magnetoelastic energy for bcc and fcc structures by expanding the dipole-dipole interaction under strain.
• Express magnetoelastic constants b_i and b_i'' as functions of l(r) and its derivative L = r0 dl/dr|_{r0} (Table 1).
• Minimize the sum of magnetoelastic and elastic energies to obtain equilibrium strains (Eqs. 3, 7-9).
• Compute equilibrium strains for Fe (bcc) and Ni (fcc) using published constants and the extended energy formulation (Fig. 1).
• Compare results with linear-term model and with ab-initio/experimental constants to assess impact of higher-order terms.

Experimental results

Research questions

• RQ1 Do higher-order strain terms in the magnetoelastic energy significantly modify anisotropic magnetostriction in cubic bcc and fcc systems?
• RQ2 How do the extended magnetoelastic constants derived from dipole-dipole interactions compare with ab-initio and experimental values for Fe and Ni?
• RQ3 Does inclusion of higher-order terms shift isotropic magnetostriction predictions, and under what conditions?
• RQ4 Are quadratic terms in strain negligible for cubic symmetry but potentially more important for lower-symmetry systems?

Key findings

• Higher-order strain terms introduce additional b_i' and b_i'' terms in the magnetoelastic energy (Eq. 16).
• For cubic bcc Fe and fcc Ni, the quadratic terms have negligible influence on anisotropic magnetostriction.
• The extended model yields a constant shift in the ε_xx curve due to an extra linear term b1' (Fig. 1).
• The quadratic magnetoelastic constants b_i'' are small relative to corresponding elastic constants, limiting their impact.
• Isotropic magnetostriction can be substantially modified by the extra linear term, but anisotropic magnetostriction remains largely unaffected in cubic systems.