Sensitivity of twin boundary movement to sample orientation and magnetic field direction in Ni-Mn-Ga

Abstract

When applying a magnetic field parallel or perpendicular to the long edge of a parallelepiped Ni-Mn-Ga stick, twin boundaries move instantaneously or gradullay through the sample. We evaluate the sample shape dependence on twin boundary motion with a micromagnetics computational study of magnetic domain structures and their energies. Due to the sample shape, the demagnetization factor varies with the direction of external magnetic field. When the external magnetic field is applied perpendicular to the long edge of the sample, i.e. in the direction in which the demagnetizing field is highest, the magnetic energy intermittently increases when the strength 2 of the applied magnetic field is low. This energy gain hinders the twin boundary motion and results in a gradual switching, i.e. a gradual magnetization reversal as the applied magnetic field is increased. The formation of 180⁰ magnetic domains offsets this effect partially. In contrast, when the applied magnetic field is parallel to the long edge of the sample, i.e. in the direction in which the demagnetizing field is lowest, the energy decreases with each subsequent magnetization domain reversal and the twin boundary moves instantaneously with ongoing switching. The actuation mode with the field parallel to the long sample edge lends itself for on-off actuators whereas the actuation mode with the field perpendicular to the long sample edge lends itself to gradual positioning devices.

3-D Meso-Scale Finite Element Calculations of Free Energy on Twin Boundaries in Magnetic Shape Memory Alloys

“…3 consists of 950,400 elements. Noticeably, for the chosen mesh size at the TB, each element had dimensions approximately an order of magnitude larger than the characteristic dimensions of computational domains typically considered in micromagnetics simulations [44], [45], [46], [47]. This emphasizes the fact that the simulations carried out in the present study represent a fundamentally different scale of consideration for MSM materials in comparison to typical micromagnetics calculations.…”

“…According to this approach, the distribution of the magnetization vector in the alloy is sought that minimizes the total free energy of the specimen, and dynamical processes of magnetization are described by the Landau-Lifshitz equation [43]. Examples using the micromagnetics approach to simulate the behavior of MSM alloys are reported in [44], [45], [46], [47]. Numerical codes based on either Finite Element (FE) or finite difference methods can be used for micromagnetics calculations [48], but fine discretization is needed to find the distribution of magnetic domains.…”

“…Numerical codes based on either Finite Element (FE) or finite difference methods can be used for micromagnetics calculations [48], but fine discretization is needed to find the distribution of magnetic domains. This requirement limits the practical size of the analyzed domains to be of micrometer scale, but even in this case, micromagnetics calculations typically require very large number of iterations to find a minimum energy state, e.g., [47] reports 380,000 iterations for one simulation. Also, special coupling techniques are needed to combine micromagnetics simulations performed only for small regions and magnetostatic calculations for the considered macro scale problem [49].…”

A tool to predict coercivity in magnetic materials

“…is the first variation of the free energy density with respect to m (ignoring the constraint), excluding the exchange energy. This form of the differential equation is widely used in the micromagnetics community to study domain formation (e.g., [46,47]), magnetic switching (e.g., [48]), and twin boundary movement [49] in ferromagnetic shape memory alloys. Eq.…”

A Tool to Predict Coercivity in Magnetic Materials

“…The effective field is H = − δψ δm = −2A∇ 2 m + h(m), in which, h(m) is the first variation of the free energy density with respect to m (ignoring the constraint), excluding the exchange energy. This form of the differential equation is widely used in the micromagnetics community to study domain formation (e.g., [46,47]), magnetic switching (e.g., [48]), and twin boundary movement [49] in ferromagnetic shape memory alloys. Eq.…”