Magnetocrystalline Anisotropy Energy Research Articles

Obtaining extremely low coercivity of high Bs FeCoBSiCPCu nanocrystalline alloys through modulation of magnetic anisotropy

Longitudinal magnetic field annealing is utilized for modifying the magnetic anisotropy and enhancing the magnetic softness of Fe75Co8(B10Si3C3P1)1-x/17Cux (x = 0.5, 0.75, 1, 1.25) nanocrystalline alloys. All of the magnetic field-annealed nanocrystalline alloys with Cu content more than 0.5 at.% exhibit significantly improved soft-magnetic properties, including high saturation magnetic flux density up to 1.87 T, effective permeability of 13000-16000 under the condition of 1 A/m and 1 kHz, coercivity as low as 1.6 A/m, and core loss of 0.11-0.45 W/kg under the condition of 1.0 T and 50 Hz. The application of a magnetic field promotes the nucleation and inhibits the growth of grains, leading to an increase in the number density of nanocrystals and the crystalline volume fraction, and a reduction in the grain size. The magnetic field annealing reduces the effective magneto-crystalline anisotropy energy to 2-4 J/m3, and induces longitudinal magnetic anisotropy with anisotropy energy density of 400-900 J/m3 which shows dependence on the crystalline volume fraction. The field-induced magnetic anisotropy dominates over the random local magnetic anisotropies, and results in the formation of regular magnetic domains aligned longitudinally, pinning-free domain wall displacement, and thus enhanced soft-magnetic properties.

The effects of V doping on the intrinsic properties of SmFe10Co2 alloys: A theoretical investigation

The present study focuses on the intrinsic properties of the SmFe10Co2-xVx (x = 0–2) alloys, which includes the SmFe10Co2 alloy, one of the most promising permanent magnets with the ThMn12 type of structure due to its large saturation magnetization (µ0Ms = 1.78 T), high Curie temperature (Tc = 859 K), and anisotropy field (µ0Ha = 12 T) experimentally obtained. Unfortunately, its low coercivity (<0.4 T) hinders its use in permanent magnet applications. The effect of V-doping on magnetization, magnetocrystalline anisotropy energy, and Curie temperature is investigated by electronic band structure calculations. The spin-polarized fully relativistic Korringa-Kohn-Rostoker (SPR-KKR) band structure method, which employs the coherent potential approximation (CPA) to deal with substitutional disorder, has been used. The Hubbard-U correction to local spin density approximation (LSDA + U) was used to account for the large correlation effects due to the 4f electronic states of Sm. The computed magnetic moments and magnetocrystalline anisotropy energies were compared with existing experimental data to validate the theoretical approach’s reliability. The exchange-coupling parameters from the Heisenberg model were used for obtaining the mean-field estimated Curie temperature. The magnetic anisotropy energy was separated into contributions from transition metals and Sm, and its relationships with the local environment, interatomic distances, and valence electron delocalization were analyzed. The suitability of the hypothetical SmFe10CoV alloy for permanent magnet manufacture was assessed using the calculated anisotropy field, magnetic hardness, and intrinsic magnetic properties.

Magnetization direction-controlled topological band structure in TlTiX (X = Si, Ge) monolayers

The quantum anomalous Hall (QAH) insulator is a vital material for the investigation of emerging topological quantum effects, but its extremely low working temperature limits experiments. Apart from the temperature challenge, effective regulation of the topological state of QAH insulators is another crucial concern. Here, by first-principles calculations, we find a family of stable two-dimensional materials TlTiX (X = Si, Ge) are large-gap QAH insulators. Their extremely robust ferromagnetic (FM) ground states are determined by both the direct- and super-exchange FM coupling. In the absence of spin–orbit coupling (SOC), there exist a spin-polarized crossing point located at each K and Kʹ points, respectively. The SOC effect results in the spontaneous breaking of C 2 symmetry and introduces a mass term, giving rise to a QAH state with sizable band gap. The tiny magnetocrystalline anisotropic energy (MAE) implies that an external magnetic field can be easily used to align magnetization deviating from z direction to the x–y plane, thereby leading to a transformation of the electronic state from the QAH state to the Weyl half semimetals state, which indicate monolayers TlTiX (X = Si, Ge) exhibit a giant magneto topological band effect. Finally, we examined the impact of stress on the band gap and MAE, which underlies the reasons for the giant magneto topological band effect attributed to the crystal field. These findings present novel prospects for the realization of large-gap QAH states with the characteristic of easily modifiable topological states.

How La substitute doping affects the magnetic properties of the 2-14-1 magnets (Ce1-xLax)2Fe14B: Standard DFT and DFT + U studies

We investigated different amounts of La doping on the magnetic characterizations of the (Ce1-xLax)2Fe14B (x = 0, 0.125, 0.25, 0.375, 0.5, 0.625, 0.75, 0.875, 1) structures using standard density functional theory (DFT) and DFT plus U (DFT + U) methods. Substitutions of Ce atoms by La atoms increased the magnetic moment of Fe atoms. The absolute values of the magnetocrystalline anisotropy energy (MAE) calculated by standard DFT method gradually decreased with increasing amounts of La doping, while the MAE using DFT + U method exhibited non-monotonic dependence on La concentration. The optimal magnetic performance occurred within the range of x = 0.25 to 0.375. The DOS showed that the rare earth atomic magnetic moments were in the opposite direction to the magnetic moments of the Fe atoms, and the f-orbital electronic states of Ce atoms predicted by DFT + U method were generally larger than that predicted by standard DFT method.

Manipulation of magnetic anisotropy of 2D magnetized graphene by ferroelectric In2Se3

The capacity to externally manipulate magnetic properties is highly desired from both fundamental and technological perspectives, particularly in the development of magnetoelectronics and spintronics devices. Here, using first-principles calculations, we have demonstrated the ability of controlling the magnetism of magnetized graphene monolayers by interfacing them with a two-dimensional ferroelectric material. When the 3d transition metal (TM) is adsorbed on the graphene monolayer, its magnetization easy axis can be flipped from in-plane to out-of-plane by the ferroelectric polarization reversal of In2Se3, and the magnetocrystalline anisotropy energy (MAE) can be high to −0.692 meV/atom when adopting the Fe atom at bridge site with downward polarization. This may be a universal method since the 3d TM-adsorbed graphene has a very small MAE, which can be easily manipulated by the ferroelectric polarization. As a result, the inherent mechanism is analyzed by the second variation method.

Magnetic structures and magnetic anisotropy of Mn3−x Fe x Sn studied by first-principles calculations

Aiming at clarifying the structures and magnetic anisotropies of kagome Mn3−x Fe x Sn crystal over the wide range of x, we theoretically investigate the x-dependence of lattice parameters and bond lengths of their six magnetic phases by the first-principles calculations, and discuss their stabilities. Under the virtual crystal approximation at the Mn/Fe sites with a composition increment of Δx = 0.25, we find the following points. First, the lattice parameters and intra-plane first-neighbor bond lengths highly depend on the magnetic structures. Second, at x ≤ 0.25, the in-plane noncollinear antiferromagnetic (AFM) phase is most stable. Third, at x = 0.50, magnetic structures such as the out-of-plane spin canting structure, which are like superpositions of the AFM and ferromagnetic phases, are stable, and the magnetization easy axis is the c-axis. Finally, at x ≥ 1.00, the in-plane ferromagnetic phase is most stable, indicating that the easy axis is in the ab-plane, and the magnetocrystalline anisotropy energy reaches −1.60 MJ m−3 at x = 3.00.

Giant magnetic anisotropy energy and Os–Ir coupling driven variations in the physical properties of Y[formula omitted]NiIrO[formula omitted

Spintronics is a prosperous domain that comprises colossal applications executing both the charge and spin of the electrons. So double perovskite oxides (DPO) having unusual magnetism are very relevant for these objectives. Therefore, we systematically examine the effect of strong coupling between Ir and Os 5d orbitals on the structural stabilities, electronic structure, and magnetic properties of the Y2NiIrO6 DPO using ab-initio calculations by replacing Os with one of the Ir ion (Os@Ir). We predict that the antiferromagnetic spin–orbit coupling between half-filled Ni 3d and partially-filled Ir 5d in the pristine structure, results in a ferrimagnetic (FiM) Mott-insulating phase due to unusual Jeff=12 state of Ir+4 having an energy band gap (Eg) of 0.43 eV. The calculated partial spin moments (ms) on the Ni+2 and Ir+4 ions are 1.68 and −0.49μB with electronic configurations of t2g3↑t2g3↓eg2↑eg0↓ (S = 1) and t2g3↑t2g2↓eg0 (S =12), respectively. Furthermore, our estimated Curie temperature (TC) of 198 K employing the Heisenberg model is near to the experimentally examined value of 192 K. The easy magnetic axis yields to be the b-axis with a giant magnetocrystalline anisotropy energy (MAE) constant of 1.7×108 erg/cm3, which is the origin of a huge coercive field of 1.1 T. In the case of the Os@Ir motif, Eg closed where the filled Ir t2g and partially filled Os t2g orbitals are mainly responsible for conductivity. Surprisingly, the ms on the Ir ion almost becomes zero (+0.01μB), turns out to be in a +3 state with t2g3↑t2g3↓eg0 (S = 0) despite +4 along with 1.68/−1.55μB on the Ni+2/Os+5. Finally, MAE value and TC in Os-doped structure increase due to large structural distortions as compared to pristine one which makes the system technologically important.

Intraband terms of magnetocrystalline anisotropy energy in layered systems without inversion symmetry

Intraband terms of magnetocrystalline anisotropy energy in layered systems without inversion symmetry

Insulator-to-metal transition, magnetic anisotropy, and improved TC in a ferrimagnetic La2CoIrO6: strain influence.

The elegant interactions between Coulomb repulsion and spin-orbit coupling in Ir-based double perovskite oxides (DPO) normally induce peculiar magnetic behavior. Herein, we investigate the effect of the development of biaxial [110] strain on the formation energetics, and electronic and magnetic properties of the La2CoIrO6 DPO employing density functional theory calculations. Our results reveal that the unstrained motif is a Mott-insulator achieving an energy band gap of 0.35 eV with a ferrimagnetic (FiM) ground state, which essentially arises due to anti-ferromagnetic (AFM) coupling between the half-occupied Co t2g and partially occupied Ir t2g/empty eg orbitals via oxygen 2p states. Along with this, it is found that [001] (c-axis) is the easy magnetic axis, which results in 12.5 meV total energy per u.c., obtaining a large anisotropy constant of 0.8 × 108 erg cm-3. The computed partial spin-magnetic moments on the Co/Ir ion are 2.64/-0.46 μB, where the negative sign on the Ir ion moment confirms the AFM interactions between them. Additionally, the t2g/eg and t2g orbital characteristics of Co2+ and Ir4+ ions are visible in the spin-magnetization density isosurfaces plot, respectively. Likewise, the estimated Curie temperature (TC) using the Heisenberg model is 104 K, which is in agreement with the experimentally observed value of 94/97 K. Interestingly, an insulator-to-metal transition is achieved at a critical compressive strain of -6% with a robust FiM state, where the Co 3dxy and Ir 5dx2-y2 orbitals are mainly responsible for metallicity. Simultaneously, the magnetocrystalline anisotropy energy and TC can be sufficiently enhanced by applying compressive strain due to enhancement in the structural distortions. So this work suggested that the strain strategy is an efficient approach to tuning the properties of the compounds for their feasible realization in spintronics.

Re/Ir@Os-doping induced insulator-to-metal transition in Mott-insulator Ca2FeOsO6: octahedral distortion effects.

Regardless of several investigations to elucidate the ground state of the strongly correlated electron systems in doped Mott-insulators (MIs), the origin of the doping-induced insulator-to-metal transition (IMT) remains a crucial and debatable subject in solid-state physics. Herein, we explore the consequences of Re/Ir-doping at the Os-site (Re/Ir@Os), on the physical properties of the MI ferrimagnetic (FiM) Ca2FeOsO6 double perovskite oxides using density functional theory calculations. The doped structures' solidity is analyzed by computing the defect formation energies in terms of the dopant-rich situation, which confirms their growth credibility at ambient conditions along with mechanical and dynamical stabilities. Various FiM spin-ordering is taken into account in the doped structures to analyze the magnetic ground state, which is FiM-I/FiM-II in the Re/Ir@Os-doped system. Remarkably, an IMT is predicted in the Re/Ir@Os-doped structures, which is due to the admixture of the partially occupied 5d orbitals of these ions. The calculated partial spin magnetic moments (ms) of +4.12, -1.58, -0.75 and +0.88μB on the Fe, Os, Re, and Ir ions, endorse the +3, +5, +5, and +4 states having electronic configurations of t32g↑t02g↓e2g↑e0g↓, t32g↑t02g↓e0g↑e0g↓, t22g↑t02g↓e0g↑e0g↓, t32g↑t22g↓e0g↑e0g↓, respectively. The "+" and "-" signs on the ions ms values, lead the systems into various FiM magnetic ordering. Moreover, the estimated Curie temperature (TC) using the Heisenberg model in the pristine structure is 334 K, which is close to the experimentally observed value of 320 K along with a colossal uniaxial magneto crystalline anisotropy energy constant (K) of 2.95 × 107 erg cm-3 having the easy magnetic axis of the ac-plane ([101]). It is established that TC/K reduces and enhances to 298 K/1.33 × 107 erg cm-3 and 365 K/4.71 × 107 erg cm-3 for the Re@Os and Ir@Os-doped motif due to an increase and decrease in the octahedral distortions compared to that of the pristine system, respectively.

Magnetic Anisotropy Tailoring by 5d-Doping in (Fe,Co)5SiB2 Alloys

Band-structure calculations were performed using the spin-polarized relativistic Korringa–Kohn–Rostoker (SPR-KKR) band-structure method, determining intrinsic magnetic properties, such as magnetic moments, magnetocrystalline anisotropy energy (MAE), and Curie temperatures, of Fe5−x−yCoxMySiB2 (M = Re, W) alloys. The general gradient approximation (GGA) for the exchange–correlation potential and the atomic sphere approximation (ASA) were used in the calculations. Previous studies have shown that for Fe5SiB2, the easy magnetization direction is in-plane, but it turns axial for Co-doping in the range 1 &lt; x ≤ 2.5 (y = 0). Furthermore, studies have shown that 5d-doping enhances the MAE by enabling the strong spin–orbit coupling of Fe–3d and M–5d states. The aim of the present theoretical calculations was to find the dependence of the anisotropy constant K1 for combined Co- and M-doping, building a two-dimensional (2D) map of K1 for 0 ≤ x ≤ 2 and 0 ≤ y ≤ 1. Similar theoretical 2D maps for magnetization and Curie temperature vs. Co and M content (M = W and Re) were built, allowing for the selection of alloy compositions with enhanced values of uniaxial anisotropy, magnetization, and Curie temperature. The magnetic properties of the Fe4.1W0.9SiB2 alloy that meet the selection criteria for axial anisotropy K1 &gt; 0.2 meV/f.u., Curie temperature Tc &gt; 800 K determined by the mean-field approach, and magnetization µ0Ms &gt; 1 T are discussed.

Exploitable magnetic anisotropy and half-metallicity controls in multiferroic van der Waals heterostructure

Two-dimensional (2D) XY ferromagnets have drawn pronounced interest in recent years, but the characteristic of easy-plane magnetization restricts their application in spintronics to some extent. Here, we propose a general strategy for constructing multiferroic van der Waals heterostructures, aiming to achieve electrical control over the magnetic anisotropy in 2D XY ferromagnets. The validity of this strategy is verified by the heterostructure composed of ferromagnetic VBi2Te4 and ferroelectric In2Se3 monolayers. By manipulating the polarized states of In2Se3, the VBi2Te4 can be reversibly transformed between 2D XY and Heisenberg ferromagnets, characterized by the switching of easy magnetization axis between in-plane and out-of-plane directions. More interestingly, accompanied by the changes in magnetic anisotropy, the VBi2Te4 also demonstrates a phase transition from a semiconductor to a half-metal state, which can be ascribed to the band alignment and interfacial charge transfer. The switchable magnetic and electronic properties enable the heterostructure to be utilized in nonvolatile memory and logic devices. Additionally, the half-metallicity and magnetocrystalline anisotropy energy of the heterostructure can be effectively tuned by biaxial strain. These findings not only pave the way for electrically nonvolatile control of 2D XY ferromagnet, but also facilitate the development of interfacial magnetoelectric physics and applications.

Accelerating Nature: Induced Atomic Order in Equiatomic FeNi.

The production of locally atomically ordered FeNi (known by its meteoric mineral name, tetrataenite) is confirmed in bulk samples by simultaneous conversion X-ray and backscattered γ-ray 57 Fe Mössbauer spectroscopy. Up to 22 volume percent of the tetragonal tetrataenite phase is quantified in samples thermally treated under simultaneous magnetic- and stress-field conditions for a period of 6 weeks, with the remainder identified as the cubic FeNi alloy. In contrast, all precursor samples consist only of the cubic FeNi alloy. Data from the processed alloys are validated using Mössbauer parameters derived from natural meteoritic tetrataenite. The meteoritic tetrataenite exhibits a substantially higher degree of atomic order than do the processed samples, consistent with their low uniaxial magnetocrystalline anisotropy energy of ≈1 kJ·m-3 . These results suggest that targeted refinements to the processing conditions of FeNi will foster greater atomic order and increased magnetocrystalline anisotropy, leading to an enhanced magnetic energy product. These outcomes also suggest that deductions concerning paleomagnetic conditions of the solar system, as derived from meteoritic data, may warrant re-examination and re-evaluation. Additionally, this work strengthens the argument that tetrataenite may indeed become a member of the advanced permanent magnet portfolio, helping to meet rapidly escalating green energy imperatives.

Modulating the ferromagnetism of Fe3GeTe2 with 3d transition metal adsorption and strain-engineering

Two-dimensional ferromagnetic materials hold great promise to develop energy-efficient magnetoelectric memory devices and next-generation spintronics. However, one of the crucial challenges for these materials is the realization of tunable magnetocrystalline anisotropy (MCA) to balance thermal stability and energy efficiency. Here, we systematically study the adsorption effects of 3d transition metals (3d-TMs) on the electronic structure and magnetic property of the Fe3GeTe2 (FGT) monolayer. The adsorption systems exhibit different ground state configurations depending on the adatoms, while the controlled perpendicular magnetic anisotropy has also been achieved. Notably, the Mn/FGT system can maintain the out-of-plane magnetic orientation with a changing amplitude of MCA energy up to 3.057 erg/cm2 as the external strain varies from −4% to 1%. In contrast, the Fe/FGT structure undergoes spin reorientation from in-plane to out-of-plan magnetization with a distinct modification behavior of MCA. We elucidate that the underlying atomistic mechanism mainly arises from the alteration of Fe-derived 3d-orbital states in response to the strain effect, leading to competitive changes in the different coupling states. These findings can not only provide useful guidance to optimize two-dimensional magnets for fundamental research but also reveal the promising potential of TMs/FGT materials for the development of ultra-low energy spintronic devices.

CrP2Se6 monolayer: Two-dimensional intrinsic ferromagnetic half-metal with large magnetic anisotropy and high Curie temperature

Low Curie temperature (TC) and small magnetocrystalline anisotropy energy (MAE) are the main obstacle limiting the application of two-dimensional (2D) ferromagnetic (FM) materials. Here, by using first-principles calculations and Monte Carlo method, we predicted a 2D intrinsic FM CrP2Se6 monolayer with high TC and large MAE. The result shows that the TC of CrP2Se6 monolayer is about 440 K based on Monte Carlo simulations, and this monolayer possesses desired out-of-plane (z axis) easy magnetic axis with large MAE (∼1.2 meV/Cr). Interestingly, CrP2Se6 monolayer is intrinsically half-metallic with the spin filtering reaching 100 % and a wide spin gap of 3.09 eV under Heyd–Scuseria–Ernzerhof (HSE06) level. In addition, the dynamic, thermal, and mechanical stabilities of CrP2Se6 monolayer were confirmed by our phonon dispersion calculations, ab initio molecular dynamics simulations, and elastic constants, respectively. These outstanding magnetic properties make 2D CrP2Se6 monolayer a promising candidate for high efficiency spintronic devices.

Influence of substitutional defects on the structural and magnetic properties of barium hexaferrites

A computational analysis is conducted to understand the impact of Al and Sr substitutions on the structural and magnetic properties of M-type barium hexaferrite (BaFe12O19 or BFO). Al substitutions in BFO led to concentration-dependent increases in lattice parameters and magnetocrystalline anisotropy energy (), while the magnetic moment showed a decline. In contrast, Sr substitutions influenced the lattice differently, reducing parameters but enhancing both and the spin magnetic moment, especially under varying Coulomb interaction () conditions. It’s noteworthy that the value reached approximately 1.03 meV with full Sr substitution. Furthermore, SrFe12O19 (SFO) consistently outperformed BFO in terms of exchange interaction parameters. These findings offer valuable insights for the development and optimization of next-generation magnetic materials.

Tuning the magnetocrystalline anisotropy of rare-earth free L10-ordered Mn1-xTMxAl magnetic alloy (TM = Fe, Co, or Ni) with transition elements

Tuning of the magnetocrystalline anisotropy of MnAl was studied by substituting Mn of MnAl with transition elements (Fe, Co, or Ni). The Brillouin function and semi-empirical Callen and Callen relation predicted the thermal behaviors of saturation magnetization and magnetocrystalline anisotropy energy. First-principles calculations based on density functional theory (DFT) were performed to calculate the electronic structures of Mn0.5TM0.5Al, where TM = Mn, Fe, Co, and Ni. The estimated total magnetic moment of Mn0.5TM0.5Al decreases as the number of valence electrons (n) of TM (e.g., 7 for Mn (3d5 4 s2), 8 for Fe (3d6 4 s2), 9 for Co (3d7 4 s2), and 10 for Ni (3d8 4 s2)) increases. Ni-substituted MnAl becomes ferrimagnetic, while other TM-substituted MnAl retain a ferromagnetic state. Curie temperature rapidly decreases with increasing the valence electrons from 685 K for MnAl to 20 K for Ni-substituted MnAl. Thermomagnetic behaviors of Mn0.5TM0.5Al (TM = Mn, Fe, Co, or Ni) are reported. Our magnetocrystalline anisotropy energy (MAE) calculations demonstrate that the magnetocrystalline anisotropy changes to the in-plane from the out-of-plane (uniaxial) direction for Co– and Ni-substituted MnAl. The K reaches a maximum of 2.98 MJ/m3 at n = 8, i.e., Fe substitution.

First-principles study of magnetic interactions and excitations in antiferromagnetic van der Waals material MPX3 (M=Mn, Fe, Co, Ni; X=S, Se)

Transition metal phosphorus trichalcogenides MPX3 (M = Mn, Fe, Co, Ni; X = S, Se), as layered van der Waals antiferromagnetic (AFM) materials, have emerged as a promising platform for exploring two-dimensional (2D) magnetism. Based on density functional theory, we present a comprehensive investigation of the electronic and magnetic properties of MPX3. We calculated the spin exchange interactions as well as magnetocrystalline anisotropy energy. The numerical results reveal that J 3 is AFM in all cases, and J 2 is significantly smaller compared to both J 3 and J 1. This behavior can be understood with regard to exchange paths and electron filling. Compared to other materials within this family, FePS3 and CoPS3 demonstrate significant easy-axis anisotropy. Using the obtained parameters, we estimated the Néel temperature T N and Curie-Weiss temperature , and the results are in good agreement with the experimental observations. We further calculated the magnon spectra and successfully reproduce several typical features observed experimentally. Finally, we give helpful suggestions for the strong constraints about the range of non-negligible magnetic interactions based on the relations between magnon eigenvalues at high-symmetry k points in honeycomb lattices.

Electronic structure and magnetothermal properties of strongly-correlated compound NpB2 via first-principles and Monte Carlo study

The electronic structure and magnetic properties of strongly-correlated compound neptunium boride (NpB2) were investigated by first-principles calculation together with Monte Carlo simulations. Our results showed that NpB2 can exist stably in terms of mechanical stability and thermodynamic stability. From the band structure and spin magnetic moment, it can be judged that the material exhibits obvious metallic properties, and the magnetism is mainly caused by the 5f orbitals of Np. We also provide a more detailed distribution of electrons by electron localization function. Through Monte Carlo simulation, we not only obtain the magnetic moment and magnetic susceptibility of NpB2 at different temperatures, but also found the competitive relationship between the crystal field (D) and magnetic field (h) in affecting the magnetothermal properties, where the critical temperature (TC = 116 K) is in good agreement with the experimental data. In addition, the magnetocrystalline anisotropy energy of NpB2 is calculated and the contributions of different orbitals to spin–orbit coupling (SOC) effect are provided. For relatively complex f orbitals, fx3 and fy3x2 orbitals are coupled to the greatest degree in the direction of the inner layer, while other f orbitals (such as fzx2 and fy3x2, fyz2 and fzx2, fxz2 and fz3) show a considerable degree of coupling outside the plane. Our work not only helps to understand the internal physical mechanism of NpB2, but also helps to explore the potential applications of such magnetic materials.

Revisiting Néel 60 years on: The magnetic anisotropy of L10 FeNi (tetrataenite)

The magnetocrystalline anisotropy energy of atomically ordered L10 FeNi (the meteoritic mineral tetrataenite) is studied within a first-principles electronic structure framework. Two compositions are examined: equiatomic Fe0.5Ni0.5 and an Fe-rich composition, Fe0.56Ni0.44. It is confirmed that, for the single crystals modeled in this work, the leading-order anisotropy coefficient K1 dominates the higher-order coefficients K2 and K3. To enable comparison with experiment, the effects of both imperfect atomic long-range order and finite temperature are included. While our computational results initially appear to undershoot the measured experimental values for this system, careful scrutiny of the original analysis due to Néel et al. [J. Appl. Phys. 35, 873 (1964)] suggests that our computed value of K1 is, in fact, consistent with experimental values, and that the noted discrepancy has its origins in the nanoscale polycrystalline, multivariant nature of experimental samples, that yields much larger values of K2 and K3 than expected a priori. These results provide fresh insight into the existing discrepancies in the literature regarding the value of tetrataenite’s uniaxial magnetocrystalline anisotropy in both natural and synthetic samples.