Calculating temperature-dependent properties of Nd${}_2$Fe${}_{14}$B permanent magnets by atomistic spin model simulations

Abstract

Temperature-dependent magnetic properties of Nd${}_2$Fe${}_{14}$B permanent magnets, i.e., saturation magnetization $M_{\text{s}}(T)$, effective magnetic anisotropy constants $K_i^{\text{eff}}(T)$ ($i=1,2,3$), domain wall width ${\delta }_w(T)$, and exchange stiffness constant $A_{\text{e}}(T)$, are calculated by using \textit{ab-initio} informed atomistic spin model simulations. We construct the atomistic spin model Hamiltonian for Nd${}_2$Fe${}_{14}$B 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, $M_{\text{s}}(T)$, ${\delta }_w(T)$, and $K_i^{\text{eff}}(T)$ agree well with the experimental results. $A_{\text{e}}(T)$ is estimated through a general continuum description of the domain wall profile by mapping atomistic magnetic moments to the macroscopic magnetization. $A_{\text{e}}$ is found to decrease more slowly than $K_1^{\text{eff}}$ with increasing temperature, and approximately scale with normalized magnetization as $A_{\text{e}}(T)\sim m^{1.2}$. This work provokes a scale bridge between \textit{ab-initio} calculations and temperature-dependent micromagnetic simulations of Nd-Fe-B permanent magnets.

arXiv comment11 pages, 6 figures

References in corpus (14)

• Atomistic spin model simulations of magnetic nanomaterials
• A method for atomistic spin dynamics simulations: implementation and examples
• Quantitative simulation of temperature dependent magnetization dynamics and equilibrium properties of elemental ferromagnets
• Constrained Monte Carlo Method and Calculation of the Temperature Dependence of Magnetic Anisotropy
• Micromagnetics of rare-earth efficient permanent magnets
• Monte Carlo analysis for finite temperature magnetism of Nd${}_2$Fe${}_{14}$B permanent magnet
• Anisotropy of exchange stiffness based on atomic-scale magnetic properties in rare-earth permanent magnet Nd${}_2$Fe${}_{14}$B
• Thermal activation in permanent magnets
• Reliability and applicability of magnetic force linear response theory: Numerical parameters, predictability, and orbital resolution
• Theoretical evaluation on the temperature dependence of magnetic anisotropy constants of Nd2Fe14B - Effects of exchange field and crystal field strength -
• Charge density functional plus $U$ theory of LaMnO${}_3$: Phase diagram, electronic structure, and magnetic interaction
• Multiscale examination of strain effects in Nd-Fe-B permanent magnets
• Calculating magnetic interactions in organic electrides
• Effects of trace elements on the crystal field parameters of Nd ions at the surface of Nd${}_2$Fe${}_{14}$B grains

Cited by in corpus (10)

• Temperature scaling of two-ion anisotropy in pure and mixed anisotropy systems
• Prediction of the Curie temperature considering the dependence of the phonon free energy on magnetic states
• Crucial role of Fe in determining the hard magnetic properties of Nd${}_2$Fe${}_{14}$B
• Machine Learning Predictions of High-Curie-Temperature Materials
• Calculated Curie temperatures for rare-earth permanent magnets: ab initio inspection on localized magnetic moments in d-electron ferromagnetism
• The effect of the surface magnetic anisotropy of the neodymium atoms on the coercivity in the neodymium permanent magnet
• Computation of magnetization, exchange stiffness, anisotropy, and susceptibilities in large-scale systems using GPU-accelerated atomistic parallel Monte Carlo algorithms
• Spin-wave dispersion and exchange stiffness in Nd${}_2$Fe${}_{14}$B and $R$Fe${}_{11}$Ti ($R$=Y, Nd, Sm) from first-principles calculations
• A multi-scale approach for magnetisation dynamics: Unraveling exotic magnetic states of matter
• Anisotropy at twin interfaces in $R{T}_{12}$ ($R$=rare earth, $T$=transition metal) magnets