Effects of Anisotropy Field and easy axis dispersions on square-ness ratio for HDDR-processed NdFeB powders

NdFeB magnetic powders that are produced by a hydrogenation decomposition desorption recombination (HDDR) process consist of small grains with highly anisotropic energy [1]–[3]. Therefore, HDDR-processed NdFeB magnet powders are expected to have a high squareness ratio and high coercivity $(H_{c})$ to obtain the high maximum energy product $(BH _{max})$ that is required in highly efficient motors of hybrid or electric vehicles. The squareness ratio is defined as the value of the magnetic field at 90% of the remanent magnetization divided by $H_{c}$. However, the squareness ratio is much lower than the expected value of 1.0, and the $H_{c}$ is lower than a third of the average anisotropy fields. A previous study using a micromagnetic simulator has shown that when an anisotropy field $(H_{k})$ dispersion of grains was assumed to be a Gaussian distribution with a coefficient variation $(\sigma H_{k} {/\lt \mathrm {H}} _{k} \gt )$ of 30%, the squareness ratio corresponded with an experimental value [4]. However, Nishio et al. showed that the $H_{k}$ of a single crystal was 7600 kA/m [5]. Therefore, when the $\sigma H_{k} {/\lt \mathrm {H}} _{k} \gt$ is 30%, the $\lt H_{k} \gt + 3 \sigma H_{k}$ is unrealistically higher than the $H_{k}$ of a single crystal. In this study, the $H_{k}$ dispersion of the grains was assumed to be a horizontally flipped lognormal distribution, and the effects of the $H_{k}$ dispersion of the grains on the squareness ratio were investigated by using a micromagnetic simulator. Moreover, Nishio et al. showed that an easy axis (c-axis) inclination angle was distributed within ± 20° [6], so we also investigated the effects of the c-axis dispersion on the squareness ratio.