Magnetic-Field-Induced Stresses and Magnetostrain Effect in Martensite

Abstract

An equivalence principle for mechanical and magnetoelastic stresses is used for the quantitative theoretical description of giant magnetostrain effect in ferromagnetic martensite. Field-induced strains are computed in the framework of phenomenological magnetoelastic model for two different orientations of magnetic field with respect to the crystal axes. Good agreement between the theoretical and experimental field dependencies of the strains in Ni-Mn-Ga alloys is achieved.

Interdependence between the magnetic properties and lattice parameters of Ni–Mn–Ga martensite

“…In accordance with our magnetoelastic model of ferromagnetic martensite [13][14][15][16], the interdependence between the magnetic subsystem and aforementioned large deformations in martensitic materials is determined by the spin-lattice magnetoelastic interaction that exists in all solids containing magnetic atoms. This interaction dominates in the formation of a large magnetic anisotropy of the martensitic phase that is proportional to the value of tetragonal distortion of the cubic crystal lattice arising in the course of MT [13][14][15][16] (this result of the magnetoelastic model is supported by first-principles calculations [17]). In view of the large value of the uniaxial magnetic anisotropy constant, the secondary deformation (twinning) results in the appropriate spatial distribution of the magnetic moments aligned with the principal axes of the tetragonal unit cells of the martensite variants forming the twin structure.…”

“…In figure 4, the structural results obtained from x-ray measurements are compared with those calculated from equation (3) using experimentally obtained saturation fields and magnetization values read at different temperatures. The previously reported values of δ = −23 (see [15,16]) and ρ = 8 g cm −3 (ρ is the mass density) were used for the calculations. The temperature dependences of the lattice distortion for both alloys can be approximated by a linear dependence.…”

“…This relationship corresponds to a linear approximation of the small lattice distortion 1 − c/a. It is convenient to present this relationship in the form of A = 6δ 1 (1 − c/a) (see [15,16]). When δ 1 < 0 the vector m of Ni-Mn-Ga martensite with c/a < 1 is parallel to the c-axis in zero magnetic field.…”

“…In view of the large value of the uniaxial magnetic anisotropy constant, the secondary deformation (twinning) results in the appropriate spatial distribution of the magnetic moments aligned with the principal axes of the tetragonal unit cells of the martensite variants forming the twin structure. A magnetic field application leads to the rotation of the magnetic moments from the initial crystallographic directions, and therefore the process of magnetization of ferromagnetic martensite provides information about the value of the magnetic anisotropy energy as well as about the volume fractions and orientations of the twin components (martensite variants) [1,2,7,15].…”

“…It was mentioned above that both the phenomenological magnetoelastic model [13][14][15][16] and ab initio calculations [17] predict a linear dependence of the magnetic anisotropy parameter of Ni-Mn-Ga martensite on the spontaneous strains ε ii which are proportional to the tetragonal distortion of a cubic crystal lattice occurring in the course of an MT (ε ii ∼ (c − a)/a 0 , where a and c are the lattice parameters of the tetragonal phase, and a 0 is the lattice parameter of the cubic phase). In the present work, this fundamental theoretical result is confirmed experimentally by the comparison of the temperature dependence of lattice parameters determined from the x-ray diffraction data with the dependence resulting from the theoretical treatment of magnetization curves taken for two different Ni-Mn-Ga ferromagnetic martensites.…”