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.

11 pages, 6 figures

References in corpus (4)

• Quantitative simulation of temperature dependent magnetization dynamics and equilibrium properties of elemental ferromagnets
• Micromagnetics of rare-earth efficient permanent magnets
• Theoretical evaluation on the temperature dependence of magnetic anisotropy constants of Nd2Fe14B - Effects of exchange field and crystal field strength -
• 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 (3)

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