Giant Uniaxial Magnetocrystalline Anisotropy in SmCrGe 3
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Xu, Mingyu↗
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Robustness of magnetocrystalline anisotropy and coercivity in Fe–Co–B
As a potential candidate for critical chemical element free permanent magnet, (Fe 0.7 Co 0.3 ) 2 B, shows promising intrinsic magnetic properties, including large magnetization, high Curie temperature and moderate magnetocrystalline anisotropy (MCA). Still, the coercivity that has been achieved is relatively low. To understand and improve coercivity, here we study the robustness of MCA related to the fluctuation of chemical composition and the structural distortion and its effect on coercivity in (Fe 0.7 Co 0.3 ) 2 B from first principles DFT (density functional theory) calculation and micromagnetic simulation. A fluctuation of cobalt content of 10%, or 1% isotropic lattice strain, or 2% tetragonal distortion reduces MCA energy up to 30%. By considering randomly distributed local MCA energy reduction up to 30%, the calculated coercivity of anisotropic bulk magnets reduced from 3.6 kOe to 2.2 kOe. Rational microstructure design, such as grain size refinement and development of strong crystal texture of MCA easy-axis (i.e., degree of alignment for (Fe 0.7 Co 0.3 ) 2 B grains), can enhance coercivity and mitigate the effect of local MCA reduction. In addition to acceptable intrinsic magnetic properties, the promising hard magnetic phase needs good MCA robustness to facilitate the development of practical magnets.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Highly tunable magnetocrystalline anisotropy energy in Fe3+-doped BaTiO3
Magnetic dopants in ferroelectric oxide host materials provide a platform for electric field control of isolated spins, facilitated by tuning of the magnetocrystalline anisotropy energy (MCAE). We present first-principles calculations of the MCAE experienced by isolated Fe3+ dopants in the tetragonal, orthorhombic, and rhombohedral phases of the prototypical ferroelectric BaTiO3. We identify an order-of-magnitude decrease in the MCAE in the rhombohedral phase relative to the tetragonal and orthorhombic phases. We explain this dramatic decrease, as well as the formation of a spin-easy plane in the tetragonal phase and spin-easy axes in the orthorhombic and rhombohedral phases, using crystal field theory arguments. Building a superposition model from crystal field theory, we show how a set of simple criteria based on crystalline environment can be used to estimate the MCAE. We suggest this as a route to rapidly screen candidate ferroelectric hosts and magnetic dopants that possess phases with spin-easy axes and maximal MCAE tunability.
Barker, Bradford A↗
Importance of enforcing Hund’s rules in density functional theory calculations of rare earth magnetocrystalline anisotropy
Density functional theory (DFT) and its extensions, such as DFT+U and DFT+dynamical mean-field theory, are invaluable for studying magnetic properties in solids. However, rare-earth (R) materials remain challenging due to self-interaction errors and the lack of proper orbital polarization. We show how the orbital dependence of self-interaction error contradicts Hund’s rules and plagues magnetocrystalline anisotropy (MA) calculations, and how analyzing DFT states that respect Hund’s rules can mitigate this issue. We benchmark MA in RCo 5 , R 2 Fe 14 B, and RFe 12 , extending prior work on RMn 6 Sn 6 , achieving excellent agreement with experiments. Additionally, we illustrate a semi-analytical perturbation approach that treats crystal fields as a perturbation in the large spin-orbit coupling limit. Using Gd-4f crystal-field splitting, this method provides a microscopic understanding of MA and enables rapid screening of high-MA materials.
36 MATERIALS SCIENCE↗
Competition of magnetocrystalline anisotropy of uranium layers and zigzag chains in UNi 0.34 Ge 2 single crystals
Structural and thermodynamic properties of single-crystalline UNi 1-x Ge 2 with x = 0.66 have been investigated by measuring magnetization, specific heat, and thermal expansion over a wide range of temperatures and magnetic fields. The measurements revealed the emergence of a long-range antiferromagnetic ordering of uranium magnetic moments below the Néel temperature T N = 45.5 (1) K and the existence of two easy axes in the studied compound, namely b and c, which correspond to the planes of the uranium zig-zag chains. A magnetic field applied along these two crystallographic directions induces in the system a first-order metamagnetic phase transition (from antiferromagnetic to field-polarized paramagnetism), and the width of the magnetic hysteresis associated with that transition reaches as much as 40 kOe at the lowest temperatures. A magnetic phase diagram developed from the experimental data showed that the metastable region associated with that magnetic hysteresis forms a funnel that narrows toward the N´eel point in a zero magnetic field. The four-layer Ising model has successfully predicted the colinear antiferromagnetic structure in UNi 0.34 Ge 2 (known from earlier reports), its magnetic phase diagram, and temperature and field variations of its magnetization. Moreover, it suggests that the first-order phase transition extends down to zero magnetic field, although it is barely detectable in the experiments performed in low magnetic fields. According to this model, the second-order phase transition occurs in the compound only in zero field.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Searching for ternary magnetic Zr–Fe–B compounds through deep machine learning
We use deep machine learning (ML) combined with first-principles calculations to search for energetically favorable ternary magnetic zirconium–iron borides. We show that an iterative ML approach enables efficient screening of vast structural libraries, effectively selecting promising candidates for subsequent first-principles investigations. Twenty-two new Fe-rich ternary compounds with formation energies within 60 meV atom −1 above the known ternary convex hull and with magnetic polarization larger than 0.6 T are identified, among which ten structures exhibit significant uniaxial anisotropy with magnetocrystalline anisotropy constant K 1 ⩾ 0.8 MJ m −3 , including a Zr 2 Fe 14 B phase. Such an ML-guided approach dramatically accelerates the discovery of rare-earth-free permanent magnetic materials.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Revisiting Néel 60 years on: The magnetic anisotropy of L1 0 FeNi (tetrataenite)
The magnetocrystalline anisotropy energy of atomically ordered L1 0 FeNi (the meteoritic mineral tetrataenite) is studied within a first-principles electronic structure framework. Two compositions are examined: equiatomic Fe 0.5 Ni 0.5 and an Fe-rich composition, Fe 0.56 Ni 0.44 . It is confirmed that, for the single crystals modeled in this work, the leading-order anisotropy coefficient K 1 dominates the higher-order coefficients K 2 and K 3 . 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 K 1 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 K 2 and K 3 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.
36 MATERIALS SCIENCE↗
Tuning In-Plane Magnetic Anisotropy and Interfacial Exchange Coupling in Epitaxial La 2/3 Sr 1/3 CoO 3 /La 2/3 Sr 1/3 MnO 3 Heterostructures
Controlling the in-plane magnetocrystalline anisotropy and interfacial exchange coupling between ferromagnetic (FM) layers plays a key role in next-generation spintronic and magnetic memory devices. In this work, we explored the effect of tuning the magnetocrystalline anisotropy of La 2/3 Sr 1/3 CoO 3 (LSCO) and La 2/3 Sr 1/3 MnO 3 (LSMO) layers and the corresponding effect on interfacial exchange coupling by adjusting the thickness of the LSCO layer (t LSCO ). The epitaxial LSCO/LSMO bilayers were grown on (110) o -oriented NdGaO 3 (NGO) substrates with a fixed LSMO (top layer) thickness of 6 nm and LSCO (bottom layer) thicknesses varying from 1 to 10 nm. Despite the small difference (~0.2%) in lattice mismatch between the two in-plane directions, [001] o and [11̅0] o , a pronounced in-plane magnetic anisotropy was observed. Soft X-ray magnetic circular dichroism hysteresis loops revealed that for t LSCO ≤ 4 nm, the easy axes for both LSCO and LSMO layers were along the [001] o direction, and the LSCO layer was characterized by magnetically active Co 2+ ions that strongly coupled to the LSMO layer. No exchange bias effect was observed in the hysteresis loops. In contrast, along the [11̅0] o direction, the LSCO and LSMO layers displayed a small difference in their coercivity values, and a small exchange bias shift was observed. As t LSCO increased above 4 nm, the easy axis for the LSCO layer remained along the [100] o direction, but it gradually rotated to the [11̅0] o direction for the LSMO layer, resulting in a large negative exchange bias shift. Therefore, we provide a way to control the magnetocrystalline anisotropy and exchange bias by tuning the interfacial exchange coupling between the two FM layers.
36 MATERIALS SCIENCE↗
Large ordered moment with strong easy-plane anisotropy and vortex-domain pattern in the kagome ferromagnet Fe 3 Sn
We report the magnetic anisotropy of kagome bilayer ferromagnet Fe 3 Sn probed by the bulk magnetometry and magnetic force microscopy (MFM) on high-quality single crystals. The dependence of magnetization on the orientation of the external magnetic field reveals strong easyplane magnetocrystalline anisotropy and anisotropy of the saturation magnetization. The leading magnetocrystalline anisotropy constant shows a monotonous increase from $\mathrm{K_1$≈ –1.0 \times 10^6 J/m^3}$ at 300 K to $\mathrm{–1.3 \times 10^6 J/m^3}$ at 2 K. Our ab initio electronic structure calculations yield the value of total magnetic moment of 7.1$μ_Β$/$f.u.$ and a magnetocrystalline anisotropy energy density of –0.57 $\mathrm{meV/}$$f.u.$ $\mathrm{(–1.62 \times 10^6J/m^3)}$ both being in reasonable agreement with the experimental values. The MFM imaging reveals micrometer-scale magnetic vortices with weakly pinned cores that vanish at the saturation field of ~3T applied perpendicular to the kagome plane. The observed vortex-domain structure is well reproduced by the micromagnetic simulations, using the experimentally determined value of the anisotropy and exchange stiffness.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Synthesis and properties of bulk cobalt-carbide permanent magnets
Nanocrystalline bulk Co-C permanent magnets were produced by rapid hot consolidation of ball milled powder precursors. Bulk magnets with an average grain size of 20 nm and densities up to 94 percent of the theoretical density were successfully processed at pressures exceeding 1 GPa for the first time. Their microstructural and magnetic properties along with their magnetocrystalline anisotropy values are reported. Presence of iron contamination that results from the use steel milling media in milling was confirmed by elemental mapping of the bulk magnets. It is concluded that iron bonds in the form of hematite and does not adversely affect coercivity values. Here, this study shows that the Co 3 C compound does possess a sizable magnetocrystalline anisotropy, making it a suitable candidate as a rare earth free permanent magnet.
Co3 C↗
On the origin of magnetic anisotropy in 4f-free ferromagnets based on the CaCu 5 structure *
Using first-principles calculations, we investigate the origin of magnetocrystalline anisotropy in a series of 4f-electron-free intermetallics with CaCu 5 -based structures: YCo 5 , YCo 4 B, and Y 3 Co 13 B 2 . The electronic structure of these compounds is characterized by a set of narrow 3d bands near the Fermi level. In YCo 5 the easy-axis anisotropy originates primarily in the spin–orbit coupling-induced mixing of the electronic states with Co d x 2 -y 2 and d xy character. The analysis of k-resolved anisotropy shows that positive contributions accumulate from the entire Brillouin zone but are particularly large near the k z = 0 plane. The analysis of the single-site and two-site terms reveals a large positive single-site contribution to the magnetocrystalline anisotropy from the Co atoms on the honeycomb sublattice, along with two-site contributions from both honeycomb and kagome sublattices.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Accurate machine-learning predictions of coercivity in high-performance permanent magnets
Increased demand for high-performance permanent magnets in the electric vehicle and wind-turbine industries has prompted the search for cost-effective alternatives. Discovering magnetic materials with the desired intrinsic and extrinsic permanent magnet properties presents a significant challenge to researchers because of issues with the global supply of rare-earth elements, material stability, and a low maximum magnetic energy product BH max . While first-principles density functional theory (DFT) predicts materials’ magnetic moments, magnetocrystalline anisotropy constants, and exchange interactions, it cannot compute extrinsic properties such as coercivity (H c ). Although it is possible to calculate H c theoretically with micromagnetic simulations, the predicted value is larger than the experiment by almost an order of magnitude due to the Brown paradox. To circumvent these issues, we employ machine-learning (ML) methods on an extensive database obtained from experiments, DFT calculations, and micromagnetic modeling. The use of a large experimental dataset enables realistic H c predictions for materials such as Ce-doped Nd 2 Fe 14 B, comparing favorably against micromagnetically simulated coercivities. Remarkably, our ML model accurately identifies uniaxial magneto-crystalline anisotropy as the primary contributor to H c . With DFT calculations, we predict the Nd-site-dependent magnetic anisotropy behavior in Nd 2 Fe 14 B, confirming that Nd 4g sites mainly contribute to uniaxial magnetocrystalline anisotropy, and also calculate the Curie temperature (T c ). Finally, both calculated results are in good agreement with the experiments. The coupled experimental dataset and ML modeling with DFT input predict H c with far greater accuracy and speed than was previously possible using micromagnetic modeling. Further, we reverse engineer the grain-boundary and intergrain exchange coupling with micromagnetic simulations by employing the ML predictions.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Inhomogeneous Magnetic Anisotropy in an Fe 5– x GeTe 2 Nanoflake Observed by Imaging
Few-layer flakes of ferromagnetic Fe 5–x GeTe 2 with x = 0.3 (F5GT) possess a c-axis magnetocrystalline anisotropy that is large enough below ∼200 K to outcompete the easy-plane shape anisotropy, yielding distinctive magnetic microstructures with out-of-plane (OOP) magnetizations. Using photoemission electron microscopy (PEEM) with magnetic contrast from X-ray magnetic circular dichroism (XMCD) to study a thermally demagnetized h-BN-protected nanoflake of F5GT at 110 K, we observe a micron-scale coexistence between domains with OOP magnetizations (∼70% areal fraction) and hitherto unknown domains in which in-plane (IP) magnetization components dominate (∼30% areal fraction). The regions with dominant IP magnetization components do not correlate with small variations of flake thickness (6–10 nm) and instead arise from local changes of magnetocrystalline anisotropy due to a hitherto unidentified chemical inhomogeneity that we suggest to be a higher concentration of Fe vacancies. Our observation of micron-scale inhomogeneity would likely be missed if imaging a single flake orientation and should affect the viability and performance of van der Waals (vdW) spintronic devices with F5GT electrodes.
2D materials↗
Accelerating Nature: Induced Atomic Order in Equiatomic FeNi
Abstract 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.
36 MATERIALS SCIENCE↗
Strain and Defect-Tailored Magnetotransport in NiCo 2 O 4 Thin Films and Freestanding Membranes
Magnetic spinel NiCo 2 O 4 is promising for developing spintronic applications due to its high magnetic Curie temperature, high spin polarization, fast spin dynamics, and strain-tunable magnetic anisotropy, while its electronic and magnetic properties depend sensitively on epitaxial strain and disorder. Here, in this study, we use epitaxial NiCo 2 O 4 thin films and freestanding NiCo 2 O 4 membranes as model systems to reveal the complex interplay of strain and defects in determining the metallicity and magnetotransport properties of the ferrimagnetic spinel. NiCo 2 O 4 on perovskite substrates and NiCo 2 O 4 membranes exhibit insulating behaviors and spin canting, in sharp contrast to the metallic NiCo 2 O 4 films on spinel substrates that possess strong perpendicular magnetic anisotropy. Anisotropic magnetoresistance studies provide critical information about disorder-induced spin scattering and strain-induced tetragonal magnetocrystalline anisotropy, which is corroborated by comprehensive electron microscopy characterizations. Our study presents a promising venue for designing flexible magnetic memory, sensor, and spintronic applications.
36 MATERIALS SCIENCE↗
Sensitivity of the MnTe valence band to the orientation of magnetic moments
An effective model of the hexagonal (NiAs-structure) manganese telluride valence band in the vicinity of the A point of the Brillouin zone is derived. It is shown that whereas for the usual antiferromagnetic order (magnetic moments on the basal plane) band splitting at A is small, their out-of-plane rotation enhances the splitting dramatically (to about 0.5 eV). Here we propose extensions of recent experiments where such inversion of magnetocrystalline anisotropy has been observed in Li-doped MnTe to confirm this unusual sensitivity of a semiconductor band structure to magnetic order.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Hard and semi-hard Fe-based magnetic materials
Iron (Fe) is the most important ferromagnetic element, not only for its high magnetic moment and high Curie temperature but for its abundance as well. Fe-based magnetic materials are therefore widely applied in technologies and industries, with most of the applications for soft magnetic materials, because of the low magnetocrystalline anisotropy (MCA) of Fe. However, it is possible to realize magnetic hardening in Fe-based materials as we have learned from the early carbon steel permanent magnets although their coercivity was modest. Recent efforts to search for rare-earth-free hard magnetic materials have shown more promising evidences for achieving high MCA in Fe-based materials. In this paper, we review the history and the recent developments of Fe-based hard and semi-hard magnetic materials with a focus on mechanisms of high MCA in Fe-based phases and the related crystal and electronic structures. Here, we have tabulated and discussed the structures and the magnetic properties of the Fe-based binary or ternary systems containing p-block and d-block elements, with many of them showing considerable MCA. Furthermore, it is important to know and to understand that the MCA in Fe-based magnetic materials can be tailored/enhanced through chemical and/or structural modifications that will lead to “artificially engineered” hard and semi-hard magnetic materials for advanced permanent magnets in the future.
36 MATERIALS SCIENCE↗
Design guidance for ferrites: Insights from density functional theory on magnetic properties
A grand challenge in materials research is identifying the relationship between composition and performance. Herein, we explore this relationship for magnetic properties, specifically magnetic saturation (M s ) and magnetocrystalline anisotropy energy (K) of ferrites. Ferrites are materials derived from magnetite (chemical formula = Fe 3 O 4 ) that comprise metallic elements such as Fe, Mn, Ni, Co, Cu and Zn. Experimentally, synthesizing and characterizing ferrites is time consuming. Further, selection of compositions to achieve particular magnetic properties currently relies on intuition. To address this, in this work, density functional theory (DFT) is used to predict M s and K for 571 ferrite structures. These structures are primarily double-substituted non-stoichiometric ferrites with formulae M1 x M2 y Fe 3–x–y O 4 , where M1 and M2 can be Mn, Ni, Co, Cu and/or Zn and 0 ≤ x ≤ 1 and y = 1–x. Calculated magnetic properties for the structures in this study vary from 0.04 × 10 5 to 9.6 × 10 5 A m −1 for M s and from 0.02 × 10 5 to 14.08 × 10 5 J m −3 for K. All structures are made publicly available in a FAIR database.
36 MATERIALS SCIENCE↗