Multiscale Calculations of Intrinsic and Extrinsic Properties of Permanent Magnets

Permanent magnets with high coercivity Hc and maximum energy product (BH)max are indispensible for the modern technologies in which electric energy is efficiently converted to motion, or vice versa. Modelling and simulation play an important role in mechanism understanding and optimization of Hc and (BH)max and uncovering the associated coercivity mechanism. However, both Hc and (BH)max are extrinsic properties, i.e., they depend on not only the intrinsic magnetic properties of the constituent phases but also the microstructures across scales. Therefore, multiscale simulations are desirable for a mechanistic and predictive calculation of permanent magnets. In this thesis, a multiscale simulation framework combining first-principles calculations, atomistic spin model (ASM) simulations, and micromagnetic simulations is demonstrated for the prediction of temperature-dependent intrinsic magnetic properties as well as the microstructure-related extrinsic properties in permanent magnets, with a focus on Nd-Fe-B and rare-earth free exchange-spring magnets. The main contents and results are summarized in the following. (1) The intrinsic temperature-dependent magnetic properties of the main phase Nd2Fe14B in Nd-Fe-B permanent magnets are calculated by ab-initio informed ASM simulations. The ASM Hamiltonian for Nd2Fe14B is constructed by using the Heisenberg exchange of Fe–Fe and Fe–Nd atomic pairs, the uniaxial single-ion anisotropy of Fe atoms, and the Nd ion crystal-field energy. The calculated temperature-dependent saturation magnetization Ms(T ), effective magnetic anisotropy constants Keff i (T ) (i = 1, 2, 3), domain-wall width δw(T ), and exchange stiffness constant Ae(T) are found to agree well with the experimental results. This calculation framework enables a scale bridge between first-principles calculations and temperature-dependent micromagnetic simulations of permanent magnets. (2) The intrinsic bulk exchange stiffness Ae in Nd2Fe14B and the extrinsic interface exchange coupling strength Jint between Nd2Fe14B and grain boundary (GB), as well as their influences on Hc, are explored by combining the first-principles calculations, ASM simulations, and micromagnetic simulations. Both Ae and Jint are found to be anisotropic. Ae is larger along crystallographic a/b axis than along c axis of Nd2Fe14B. "Double anisotropy" phenomenon regarding to GB is discovered, i.e., in addition to GB magnetization anisotropy, Jint is also strongly anisotropic even when GB possesses the same magnetization. It is found that Jint for (100) interface is much higher than that for (001) interface. The discovered anisotropic exchange is shown to have profound influence on Hc. These findings allow new possibilities in designing Nd-Fe-B magnets by tuning exchange. (3) Hc of Nd-Fe-B permanent magnets with featured microstructure are calculated by combining ASM and micromagnetic simulations. With the intrinsic properties from ASM results as input, finite-temperature micromagnetic simulations are performed to calculate the magnetic reversal and Hc at high temperatures. It is found that apart from the decrease of anisotropy field with increasing temperature, thermal fluctuations further reduce Hc by 5–10% and β (temperature coefficient of Hc) by 0.02–0.1% K−1 when a defect layer exists. Both Hc and β can be enhanced by adding the Dy-rich shell, but they saturate at a shell thickness (tsh) around 6–8 nm after which further increasing tsh or adding Dy into the core is not essential. (4) The microstructural influence in rare-earth free permanent magnet candidates, in particular the α′′-Fe16N2/SrAl2Fe10O19 composite and MnBi/FexCo1−x bilayer are investigated in collaboration with the experimental and theoretical partners. For the former, pure micromagnetic simulations show that the design criterion for the magnetically hard/softphase composite is invalid for the hard/semi-hard-phase composite. α′′-Fe16N2 nanoparticle diameter less than 50 nm and an interface exchange in the order of 0.01–0.1 pJ/m enable the Hc enhancement, while less surface oxides and higher volume fraction of α′′-Fe16N2 nanoparticles are decisive for enhancing the composite’s (BH)max. For the latter, DFTinformed micromagnetic simulations show that the interface roughness could deteriorate the interface exchange coupling and induce premature magnetic reversal in FeCo layer. A 1-nm thick FeCo layer and an interface exchange parameter around 2 pJ/m could improve (BH)max by 10% when compared to the pure MnBi layer. The presented multiscale simulation framework across scales from the electronic level, atomistic classic spin to microstructure in this thesis is demonstrated to be of the capability towards a powerful and predicative computational design of high-performance permanent magnets, even though there is still a long way to go for its direct application to the real product design