Magnetic anisotropy energy of ferromagnetic shape memory alloys Ni2X(X=Fe, Co)Ga by first-principles calculations

Wangqiang He,Yi Wang,Long-Qing Chen,Xingqiao Ma,Zhuhong Liu

doi:10.1063/1.4992138

Abstract

First-principles calculations were employed to explore magnetocrystalline anisotropy energy (MAE) of Ni2X(X=Fe, Co)Ga alloys. The MAE of Ni2FeGa is found to show a concave behavior as a function of tetragonal distortion and easy-axis of magnetization in martensitic phase is along long axis, which have been interpreted by the shift of Fe dxy+dyz peak in minority spin channel near Fermi level. The substitution of Ni by Co in Ni2FeGa alloys rotates magnetic easy axis from long axis to short axis in non-modulated phase while substitution of Fe by Co did not, which is in agreement with experiment. Magnetic anisotropy constant and magnetic stress have been estimated with calculated MAE of martensite phases. By comparing first-principles estimated values of magnetic and twinning stresses, we confirmed the condition, whether large magnetic field-induced strains in FSMAs could be obtained or not. This information can provide theoretical guidance in searching new types of FSMAs with large magnetic field induced strain.

Highlights

Magnetic-field-induced martensite variants reorientation (MIR) in ferromagnetic shape memory alloys (FSMAs), i.e. Ni2MnGa and Ni2FeGa have continuously been received attention for being potential smart materials for application in magnetomechanical sensors as well as actuators.[1,2] Ni2MnGa alloys showed the maximal value of 6%,3 9.5%2 and 12%4 magnetic-field induced strains (MFIS) in five-layered modulated martensite (10M, with lattice parameter ratio c/a < 1), seven-layered modulated martensite (14M, with a > b > c) and nonmodulated martensite (NM, with c/a > 1), respectively
The magnetocrystalline anisotropy energy (MAE) is important to understand the effect of the magnetic field which is moving twin boundary or rotation angle of magnetic moments, and the balance between MAE and energy to nucleate and propagate twin boundaries determines whether large MFIS at martensite state can be obtained.[11]
We obtained equilibrium austenite and martensite phases of the Ni2X(X=Fe, Co)Ga alloys and examined phase stability of Ni2FeGa with the effect of extra Co atoms. These alloys adopt a cubic L21 structure, Ni and extra Co atoms (CoC) occupy equivalent 4a (0.25, 0.25, 0.25) and 4c (0.75, 0.75, 0.75) in Wyckoff crystallographic positions whereas 4b (0.5, 0.5, 0.5) positions are occupied by X atoms and excess Co atoms (CoB), while 4d (0, 0, 0) positions are occupied by Ga atoms

Summary

INTRODUCTION

Magnetic-field-induced martensite variants reorientation (MIR) in ferromagnetic shape memory alloys (FSMAs), i.e. Ni2MnGa and Ni2FeGa have continuously been received attention for being potential smart materials for application in magnetomechanical sensors as well as actuators.[1,2] Ni2MnGa alloys showed the maximal value of 6%,3 9.5%2 and 12%4 magnetic-field induced strains (MFIS) in five-layered modulated martensite (10M, with lattice parameter ratio c/a < 1), seven-layered modulated martensite (14M, with a > b > c) and nonmodulated martensite (NM, with c/a > 1), respectively. The occurrence of MFIS is intimately linked to magnetic and twinning stresses relation[8] τM,max > σtw/2(where magnetic stress[9] τM,max = Ku/st, Ku is magnetocrystalline anisotropy energy (MAE) and st is the shear twin strain st = 1 − (c/a)[2] (c/a)) and may be achieved by tuning the value of two stresses.[4,10] The MAE is important to understand the effect of the magnetic field which is moving twin boundary or rotation angle of magnetic moments, and the balance between MAE and energy to nucleate and propagate twin boundaries determines whether large MFIS at martensite state can be obtained.[11] Several reports on microscopic origin of MAE in bulk[12,13] and magnetic anisotropies in films[14] have been carry out on Ni2MnGa alloys but theoretical explanation of only ∼ 0.02%-0.3% MFIS observed in Ni-Fe-Ga alloy have not been focused properly. The purpose of this letter is to investigate magnetic anisotropy properties of Ni2X(X=Fe, Co)Ga alloys and theoretically obtain the crucial parameter τM,max for FSMAs

COMPUTATION DETAILS

Structural properties

Magnetocrystalline anisotropy energy and magneto stress

Orbital moment and partial density of states

CONCLUSIONS