Calculating temperature-dependent properties of Nd2Fe14B permanent magnets by atomistic spin model simulations

Abstract

Temperature-dependent magnetic properties of Nd2Fe14B permanent magnets, i.e., saturation magnetization Ms(T ), effective magnetic anisotropy constants K eff i (T ) (i = 1, 2, 3), domain wall width δw(T ), and exchange stiffness constant Ae(T ), are calculated by using ab-initio informed atomistic spin model simulations. We construct the atomistic spin model Hamiltonian for Nd2Fe14B by using the Heisenberg exchange of Fe−Fe and Fe−Nd atomic pairs, the uniaxial single-ion anisotropy of Fe atoms, and the crystal-field energy of Nd ions which is approximately expanded into an energy formula featured by second, fourth, and sixth-order phenomenological anisotropy constants. After applying a temperature rescaling strategy, we show that the calculated Curie temperature, spin-reorientation phenomenon, Ms(T ), δw(T ), and K eff i (T ) agree well with the experimental results. Ae(T ) is estimated through a general continuum description of the domain wall profile by mapping atomistic magnetic moments to the macroscopic magnetization. Ae is found to decrease more slowly than K eff 1 with increasing temperature, and approximately scale with normalized magnetization as Ae(T ) ∼ m 1.2 . Especially, the possible domain wall configurations at temperatures below the spin-reorientation temperature and the associated δw and Ae are identified. This work provokes a scale bridge between ab-initio calculations and temperature-dependent micromagnetic simulations of Nd-Fe-B permanent magnets.

Anisotropic exchange in Nd–Fe–B permanent magnets

“…M s (T) is the temperature-dependent saturation magnetization. Both F( , T) and M s (T) have been determined previously [37,40]. In Equation (2), the additional term regarding to M s is originated from the demagnetization energy in the Néel wall.…”

“…The temperature-dependent A e of Nd 2 Fe 14 B is evaluated through ASM simulation by using VAMPIRE [36] based on the atomistic spin Hamiltonian which is proposed and parameterized previously [37][38][39][40][41]. Detailed formulations for the ASM of Nd 2 Fe 14 B are provided in the Supplemental Material.…”

Atomistic simulations of α-Fe/Nd2Fe14B magnetic core/shell nanocomposites with enhanced energy product for high temperature permanent magnet applications

“…With these, we are able to perform a secondary fit to the experimental data to determine α. Using this method gives re-scaling constants α Fe ¼ 2:876 23 and α NdFeB ¼ 1:756, 24,25 which we apply to the α-Fe and Nd 2 Fe 14 Bs u blattices, respectively, allowing the temperature dependence of the saturation magnetization and energy product of the composite system to be compared to experiment. This is important to accurately assess the changes in magnetic properties with temperature, not achievable with a simple classical model.…”

“…5] gives values for T c of 584.3 K and 1040.0 K for Nd 2 Fe 14 B and α-Fe, respectively, in agreement with previous atomistic simulations on the pure materials. 23,25 Having aligned our model with the experimental parameters, we now investigate the temperature dependence of the composite nanoparticle properties.…”

Temperature scaling of two-ion anisotropy in pure and mixed anisotropy systems

“…However, at the Curie temperature the magnetic anisotropy has to tend to zero due to the loss of magnetic ordering, and so the effective anisotropy shows a maximum around T /T c ≈ 0.7. [30,31] was applied to better approximate the temperature dependence of a realistic ferromagnet at low temperature, where the classical spin model overestimates the fluctuations. The negative exponent corresponds to an initial increase of the magnetic anisotropy with increasing temperature, turning into a decrease as T → T c , where the anisotropy tends to zero due to the loss of magnetic ordering.…”