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

Monolayer polar metals with large piezoelectricity derived from MoSi2_2N4_4

The advancement of two-dimensional polar metals tends to be limited by the incompatibility between electric polarity and metallicity as well as dimension reduction. Here, we report polar and metallic Janus monolayers of MoSi$_2$N$_4$ family by breaking the out-of-plane (OOP) structural symmetry through Z (P/As) substitution of N. Despite the semiconducting nature of MoSi$_2$X$_4$ (X=N/P/As), four Janus MoSi$_2$N$_{x}$Z$_{4-x}$ monolayers are found to be polar metals owing to the weak coupling between the conducting electrons and electric polarity. The metallicity is originated from the Z substitution induced delocalization of occupied electrons in Mo-d orbitals. The OOP electric polarizations around 10$-$203 pC/m are determined by the asymmetric OOP charge distribution due to the non-centrosymmetric Janus structure. The corresponding OOP piezoelectricity is further revealed as high as 39$-$153 pC/m and 0.10$-$0.31 pm/V for piezoelectric strain and stress coefficients, respectively. The results demonstrate polar metallicity and high OOP piezoelectricity in Janus MoSi$_2$N$_{x}$Z$_{4-x}$ monolayers and open new vistas for exploiting unusual coexisting properties in monolayers derived from MoSi$_2$N$_4$ family

Emerging versatile two-dimensional MoSi2_2N4_4 family

The discovery of two-dimensional (2D) layered MoSi$_2$N$_4$ and WSi$_2$N$_4$ without knowing their 3D parents by chemical vapor deposition in 2020 has stimulated extensive studies of 2D MA$_2$Z$_4$ system due to its structural complexity and diversity as well as versatile and intriguing properties. Here, a comprehensive overview on the state-of-the-art progress of this 2D MA$_2$Z$_4$ family is presented. Starting by describing the unique sandwich structural characteristics of the emerging monolayer MA$_2$Z$_4$, we summarize and anatomize their versatile properties including mechanics, piezoelectricity, thermal transport, electronics, optics/optoelectronics, and magnetism. The property tunability via strain engineering, surface functionalization and layered strategy is also elaborated. Theoretical and experimental attempts or advances in applying 2D MA$_2$Z$_4$ to transistors, photocatalysts, batteries and gas sensors are then reviewed to show its prospective applications over a vast territory. We further discuss new opportunities and suggest prospects for this emerging 2D family. The overview is anticipated to guide the further understanding and exploration on 2D MA$_2$Z$_4$.Comment: 29 pages, 21 figure

Modeling and simulation of sintering process across scales

Sintering, as a thermal process at elevated temperature below the melting point, is widely used to bond contacting particles into engineering products such as ceramics, metals, polymers, and cemented carbides. Modelling and simulation as important complement to experiments are essential for understanding the sintering mechanisms and for the optimization and design of sintering process. We share in this article a state-to-the-art review on the major methods and models for the simulation of sintering process at various length scales. It starts with molecular dynamics simulations deciphering atomistic diffusion process, and then moves to microstructure-level approaches such as discrete element method, Monte--Carlo method, and phase-field models, which can reveal subtle mechanisms like grain coalescence, grain rotation, densification, grain coarsening, etc. Phenomenological/empirical models on the macroscopic scales for estimating densification, porosity and average grain size are also summarized. The features, merits, drawbacks, and applicability of these models and simulation technologies are expounded. In particular, the latest progress on the modelling and simulation of selective and direct-metal laser sintering based additive manufacturing is also reviewed. Finally, a summary and concluding remarks on the challenges and opportunities are given for the modelling and simulations of sintering process.Comment: 45 pages, 38 figure

In Situ

“Smaller is stronger,” sub-, micro-, and nanomaterials exhibit high strength, ultralarge elasticity and unusual plastic and fracture behaviors which originate from their size effect and the low density of defects, different from their conventional bulk counterparts. To understand the structural evolution process under external stress at atomic scale is crucial for us to reveal the essence of these “unusual” phenomena and is momentous in the design of new materials. Our review presents the recent developments in the methods, techniques, instrumentation, and scientific progress of atomic scale in situ deformation dynamics on single crystalline nanowires. The super-large elasticity, plastic deformation mechanism transmission, and unusual fracture behavior related to the experimental mechanics of nanomaterials are reviewed. In situ experimental mechanics at the atomic scale open a new research field which is important not only to the microscopic methodology but also to the practice

Giant magnetocaloric effect in magnets down to the monolayer limit

Two-dimensional magnets could potentially revolutionize information technology, but their potential application to cooling technology and magnetocaloric effect (MCE) in a material down to the monolayer limit remain unexplored. Herein, we reveal through multiscale calculations the existence of giant MCE and its strain tunability in monolayer magnets such as CrX$_3$ (X=F, Cl, Br, I), CrAX (A=O, S, Se; X=F, Cl, Br, I), and Fe$_3$GeTe$_2$. The maximum adiabatic temperature change ($\Delta T_\text{ad}^\text{max}$), maximum isothermal magnetic entropy change, and specific cooling power in monolayer CrF$_3$ are found as high as 11 K, 35 $\mu$Jm$^{-2}$K$^{-1}$, and 3.5 nWcm$^{-2}$ under a magnetic field of 5 T, respectively. A 2% biaxial and 5% $a$-axis uniaxial compressive strain can remarkably increase $\Delta T_\text{ad}^\text{max}$ of CrCl$_3$ and CrOF by 230% and 37% (up to 15.3 and 6.0 K), respectively. It is found that large net magnetic moment per unit area favors improved MCE. These findings advocate the giant-MCE monolayer magnets, opening new opportunities for magnetic cooling at nanoscale

Calculating temperature-dependent properties of Nd2Fe14 B permanent magnets by atomistic spin model simulations

Temperature-dependent magnetic properties of Nd2Fe14B permanent magnets, i.e., saturation magnetization Ms(T), effective magnetic anisotropy constants Kieff(T)(i=1,2,3), domain-wall width δw(T), and exchange stiffness constant Ae(T), are calculated by using ab initio informed atomistic spin model simulations. We construct the atomistic spin model Hamiltonian for Nd2Fe14B 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, Ms(T),δw(T), and Kieff(T), agree well with the experimental results. Ae(T) is estimated through a general continuum description of the domain-wall profile by mapping atomistic magnetic moments to the macroscopic magnetization. Ae is found to decrease more slowly than K1eff with increasing temperature and approximately scale with normalized magnetization as Ae(T)∼m1.2. Specifically, the possible domain-wall configurations at temperatures below the spin-reorientation temperature and the associated δw and Ae are identified. This work provokes a scale bridge between ab initio calculations and temperature-dependent micromagnetic simulations of Nd-Fe-B permanent magnets

On the origin of incoherent magnetic exchange coupling in MnBi/Fex_xCo1−x_{1-x} bilayer system

In this study we investigate the exchange coupling between the hard magnetic compound MnBi and the soft magnetic alloy FeCo including the interface structure between the two phases. Exchange spring MnBi-Fe$_x$Co$_{1-x}$ (x = 0.65 and 0.35) bilayers with various thicknesses of the soft magnetic layer were deposited onto quartz glass substrates in a DC magnetron sputtering unit from alloy targets. Magnetic measurements and density functional theory (DFT) calculations reveal that a Co-rich FeCo layer leads to more coherent exchange coupling. The optimum soft layer thickness is about 1 nm. In order to take into account the effect of incoherent interfaces with finite roughness, we have combined a cross-sectional High Resolution Transmission Electron Microscopy (HR-TEM) analysis with DFT calculations and micromagnetic simulations. The experimental results can be consistently described by modeling assuming a polycrystalline FeCo layer consisting of crystalline (110) and amorphous grains as confirmed by HR-TEM. The micromagnetic simulations show in general how the thickness of the FeCo layer and the interface roughness between the hard and soft magnetic phases both control the effectiveness of exchange coupling in an exchange spring system