Monte Carlo analysis for finite-temperature magnetism ofNd2Fe14Bpermanent magnet

Abstract

We investigate the effects of magnetic inhomogeneities and thermal fluctuations on the magnetic properties of a rare earth intermetallic compound, Nd2Fe14B. The constrained Monte Carlo method is applied to a Nd2Fe14B bulk system to realize the experimentally observed spin reorientation and magnetic anisotropy constants K A m (m = 1, 2, 4) at finite temperatures. Subsequently, it is found that the temperature dependence of K A 1 deviates from the Callen-Callen law,3 , even above room temperature, TR ∼ 300 K, when the Fe (Nd) anisotropy terms are removed to leave only the Nd (Fe) anisotropy terms. This is because the exchange couplings between Nd moments and Fe spins are much smaller than those between Fe spins. It is also found that the exponent n in the external magnetic field Hext response of barrier height FB = F 0 B (1 − Hext/H0) n is less than 2 in the low-temperature region below TR, whereas n approaches 2 when T > TR, indicating the presence of Stoner-Wohlfarth-type magnetization rotation. This reflects the fact that the magnetic anisotropy is mainly governed by the K A 1 term in the T > TR region.

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

“…The fourth term in Eq. 1 denotes the crystal-field (CF) Hamiltonian of Nd ions, which is the main source of large magnetic anisotropy in Nd 2 Fe 14 B and can be approximated as [24,25,33]…”

“…J z = J(s · e z ) denotes the z-component of the total angular momentum J which is 9/2 for Nd ions [34]. J = J 2 instead of J = J(J + 1) is used in the classical manner [24]. The reliable first-principles calculation of high-order CF parameters in Nd 2 Fe 14 B is still challenging.…”

“…Moreover, the evaluation of temperature-dependent macroscopic parameters for micromagnetic simulations is highly nontrivial. In this aspect, there are recent attempts to study temperaturedependent effective magnetic anisotropy, saturation magnetization, and reversal process in Nd 2 Fe 14 B by using atomistic spin model simulations [23][24][25][26][27], based on which arXiv:1902.05636v2 [cond-mat.mtrl-sci] 15 Jun 2019 the concept of a multiscale model approach for the design of advanced permanent magnets is proposed [28]. In general, an atomistic spin model is capable of calculating magnetic properties at different temperatures [29][30][31], in which the temperature effects can be taken into account by either Langevin-like spin dynamics or Monte Carlo simulations.…”

“…More efforts have to be made to either understand the gap between model simulations and experimental measurements or predict parameters over a broad range of temperatures, in order to establish the atomistic spin model as a readily available methodology for designing Nd-Fe-B magnets. In this work, following the similar framework in [24,25,32], we not only calculate the Curie temperature and the temperature dependent magnetization, magnetocrystalline anisotropy and domain wall width, but also add some additional new knowledge into the community of Nd-Fe-B magnets in terms of atomistic spin model simulations and temperature dependent intrinsic parameters. For example, considering the different description of spin states in the classical and quantum manner, such as the different availability of spin states in the classical atomistic spin model simulations and experiments, we determine the temperature rescaling parameter for Nd 2 Fe 14 B and figure out the difference between simulation and experimental temperatures.…”

Power law analysis for temperature dependence of magnetocrystalline anisotropy constants of Nd2Fe14B magnets

“…9,10 However, there remains a gap between our microscopic picture and the macroscopic aspects of MA since previous theoretical studies on the temperature dependence of MA for R 2 Fe 14 B magnets are based on complete diagonalization of the Hamiltonian 9,10 or numerical methods such as the Monte Carlo method. 4,11,12 An effective means of bridging this gap is to develop a power-law theory 5,6,[13][14][15][16][17][18] to establish the relationship between MACs and magnetization. The history of investigations on MA based on the power-law theory has been reviewed by Callen and Callen.…”