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Terahertz (THz) quantum cascade lasers (QCLs) are technologically important laser sources for the THz range but are complex to model. An efficient extended rate equation model is developed here by incorporating the resonant tunneling mechanism from the density matrix formalism, which permits to simulate THz QCLs with thick carrier injection barriers within the semi-classical formalism. A self-consistent solution is obtained by iteratively solving the Schrödinger–Poisson equation with this transport model. Carrier–light coupling is also included to simulate the current behavior arising from stimulated emission. As a quasi-ab initio model, intermediate parameters, such as pure dephasing time and optical linewidth, are dynamically calculated in the convergence process, and the only fitting parameters are the interface roughness correlation length and height. Good agreement has been achieved by comparing the simulation results of various designs with experiments, and other models such as density matrix Monte Carlo and non-equilibrium Green's function method that, unlike here, require important computational resources. The accuracy, compatibility, and computational efficiency of our model enable many application scenarios, such as design optimization and quantitative insights into THz QCLs. Finally, the source code of the model is also provided in the supplementary material of this article for readers to repeat the results presented here, investigate, and optimize new designs. 

Spoke-type PMSMs were designed with commercial permanent magnets and theoretically designed hexaferrite: Nd-Fe-B (NdFe35, G1NH), Alnico (8B, 8H, 9), and La-CoSrM hexaferrite (NMF-15G). It was found that coercivity (Hc) plays a crucial role in determining motor performance. The ANSYS Maxwell software was used to characterize the designed motor performance. Commercial RE-free Alnico 9 holds a 10.5 MGOe of (BH)max, much higher than a 5.5 MGOe of RE-free Alnico 8B/8H and SrM (SrFe12O19) hexaferrite magnets. However, the Alnico 9 motor performance is not better than the other Alnico 8B/8H and hexaferrite motors. The spoke-type PMSM with our theoretically designed SrM hexaferrite simulated motor performance. A motor performs best when the Hc/Br ratio equals one with a high Hc. For instance, the motor torque and peak power increase to 189 Nm and 178 kW, respectively, as the Hc increases to 4.86 kOe from 2.43 kOe. However, the motor performance is not significantly changed with a fixed Hc and various Br. It was found that regardless of (BH)max, coercivity (Hc) plays a dominant role in motor performance. 

First-principles calculations were performed to calculate the electronic structures of low temperature phase (LTP) MnBi (Mn50Bi50) and substitutionally and interstitially Sn-doped MnBi [Mn50Bi25Sn25, (Mn0.5Bi0.5)66.7Sn33.3]. Brillouin function predicts the temperature dependence of saturation magnetization M(T). Sn substitution for Bi in MnBi (Mn50Bi25Sn25) changes the magnetocrystalline anisotropy constant (Ku) from −0.202 MJ/m3 (the in-plane magnetization) for LTP MnBi to 1.711 MJ/m3 (the out-of-plane magnetization). In comparison, the Ku remains negative but slightly decreases to −0.043 MJ/m3 when Sn is interstitially doped in MnBi [(Mn0.5Bi0.5)66.7Sn33.3]. The Curie temperature (TC) decreases from 716 K for LTP Mn50Bi50 to 445 K for Mn50Bi25Sn25 and 285 K for (Mn0.5Bi0.5)66.7Sn33.3. Mn50Bi25Sn25 has a lower magnetic moment of 5.034 μB/f.u. but a higher saturation magnetization of 64.2 emu/g than (Mn0.5Bi0.5)66.7Sn33.3 with a magnetic moment of 6.609 μB/f.u. and a saturation magnetization of 48.2 emu/g because the weight and volume of the substitutionally Sn-doped MnBi are smaller than the interstitially Sn-doped MnBi. The low Curie temperature and magnetization for Sn-doped MnBi are attributed to the high concentration of Sn. Thus, future study needs to focus on low Sn-concentrated MnBi.