The origin of perpendicular magneto-crystalline anisotropy in L1(0)-FeNi under tetragonal distortion

Understanding magnetocrystalline anisotropy based on orbital and quadrupole moments

Understanding magnetocrystalline anisotropy (MCA) is fundamentally important for developing novel magnetic materials. Therefore, clarifying the relationship between MCA and local physical quantities observed by spectroscopic measurements, such as the orbital and quadrupole moments, is necessary. In this review, we discuss MCA and the distortion effects in magnetic materials with transition metals (TMs) based on the orbital and quadrupole moments, which are related to the spin-conserving and spin-flip terms in the second-order perturbation calculations, respectively. We revealed that orbital moment stabilized the spin moment in the direction of the larger orbital moment, while the quadrupole moment stabilized the spin moment along the longitudinal direction of the spin-density distribution. The MCA of the magnetic materials with TMs and their interfaces can be determined from the competition between these two contributions. We showed that the perpendicular MCA of the face-centered cubic Ni with tensile tetragonal distortion arose from the orbital moment anisotropy, whereas that of Mn-Ga alloys originated from the quadrupole moment of spin density. In contrast, in the Co/Pd(111) multilayer and Fe/MgO(001), both the orbital moment anisotropy and quadrupole moment of spin density at the interfaces contributed to the perpendicular MCA. Understanding the MCA of magnetic materials and interfaces based on orbital and quadrupole moments is essential to design MCA of novel magnetic applications.

Large magnetic anisotropy in Co-Fe-Ni-N ordered structures: a first-principles study

Material design of promising rare-earth free permanent magnet requires tailoring and controlling the intrinsic magnetic properties namely large saturation magnetizationμ₀M_s, giant uniaxial magnetic anisotropyK_u, and high Curie temperatureT_C. Based on first-principles electronic structure calculations, we present a detailed analysis for the intrinsic magnetic properties of Co_xFe_1-xNi and Co_xFe_1-xNiN_0.25ordered structures. We predict an enhanced structural stability with improvedK_uranging from 1.53-2.29 MJ m^-3for Co_xFe_1-xNiN_0.25ordered structures, with the exception of CoNiN_0.25having planar anisotropy. Detailed analysis of the predicted largeK_u, based on perturbation theory and electronic structure calculations, is attributed to the cumulative effect of contribution from the increased tetragonal distortion and induced orbital distortion from the simultaneous Co substitution and interstitial N-doping. By tailoring theK_u, we may create efficient and affordable PMs, bridging the gap between commonly used ferrite and high-performance Nd-Fe-B magnets.

First-principles study of electronic structure and magnetic properties of L10-ordered FeNi, FePd, and FePt alloys

The structural, electronic, and magnetic properties of three spin configurations of L1₀-ordered FeM alloys (M = Ni, Pd, or Pt) were studied using the first-principles method. The calculations were carried out using Quantum ESPRESSO package within the framework of Density Functional Theory (DFT). The exchange-correlation functional potentials were studied using local density approximation (LDA) of Perdew-Zunger (PZ), the generalized gradient approximation (GGA) of Perdew–Burke–Ernzerhof (PBE), Perdew and Wang 91 (PW91), and Perdew-Burke-Ernzerhof revised for solids (PBEsol). We found that the PBE approximation has the most accurate results for lattice parameters compared to the experimental values. Furthermore, our results reveal that the most stable spin configuration for the considered alloys is the ferromagnetic configuration, where all spins are aligned perpendicular to the (001) plane. However, in FePd and FePt alloys, a small variation in the tetragonality ratio c/a (from 0.98 to 0.92) can transform them from ferromagnetic to antiferromagnetic state. In an antiferromagnetic state, a pseudogap is observed just below fermi energy for each alloy. Moreover, our calculations reveal large magnetocrystalline anisotropies for FePt alloy in the order of 3 meV/f.u. On the other hand, FePd and FeNi show relatively lower values in the range of 0.18–0.42 meV/f.u. Finally, Heisenberg exchange interactions are calculated from first-principles and Green's functions formalism.

Crystal structure prediction of magnetic materials

We present a methodology to predict magnetic systems using ab initio methods. By employing crystal structure method and spin-polarized calculations, we explore the relation between crystalline structures and their magnetic properties. In this work, testbed cases of transition metal alloys (FeCr, FeMn, FeCo and FeNi) are study in the ferromagnetic case. We find soft-magnetic properties for FeCr, FeMn while for FeCo and FeNi hard-magnetic are predicted. In particular, for the family of FeNi, a candidate structure with energy lower than the tetrataenite was found. The structure has a saturation magnetization (M _s) of 1.2 MA m^-1, magnetic anisotropy energy (MAE) above 1200 kJ m^-3 and hardness value close to 1. Theoretically, this system made of abundant elements could be the right candidate for permanent magnet applications. Comparing with the state-of-the-art (Nd₂Fe₁₄B) hard-magnet, (M _s of 1.28 MA m^-1 and MAE of 4900 kJ m^-3) is appealing to explore this low energy polymorph of FeNi further. Considering the relatively limited number of magnets, predicting a new system may open routes for free rare-earth magnets. Furthermore, the use of the computational algorithm as the one presented in this work, hold promises in this field for which in near future improvements will allow to study numerous complex systems, larger simulations cells and tackled long-range antiferromagnetic cases.

Electronic correlation effects and local magnetic moments in L10phase of FeNi

We study the electronic and magnetic properties of L10phase of FeNi, a perspective rare-earth-free permanent magnet, by using a combination of density functional and dynamical mean-field theory. Although L10FeNi has a slightly tetragonally distorted fcc lattice, we find that magnetic properties of its constituent Fe atoms resemble those in pure bcc Fe. In particular, our results indicate the presence of well-localized magnetic moments on Fe sites, which are formed due to Hund's exchange. At the same time, magnetism of Ni sites is much more itinerant. Similarly to pure bcc Fe, the self-energy of Fe 3d states is found to show the non-Fermi-liquid behavior. This can be explained by peculiarities of density of Fe 3d states, which has pronounced peaks near the Fermi level. Our study of local spin correlation function and momentum dependence of particle-hole bubble suggests that the magnetic exchange in this substance is expected to be of RKKY-type, with iron states providing local-moment contribution, and the states corresponding to nickel sites (including virtual hopping to iron sites) providing itinerant contribution.

Detecting quadrupole: a hidden source of magnetic anisotropy for Manganese alloys

Mn-based alloys exhibit unique properties in the spintronics materials possessing perpendicular magnetic anisotropy (PMA) beyond the Fe and Co-based alloys. It is desired to figure out the quantum physics of PMA inherent to Mn-based alloys, which have never been reported. Here, the origin of PMA in ferrimagnetic Mn_{3− δ} Ga ordered alloys is investigated to resolve antiparallel-coupled Mn sites using x-ray magnetic circular and linear dichroism (XMCD/XMLD) and a first-principles calculation. We found that the contribution of orbital magnetic moments in PMA is small from XMCD and that the finite quadrupole-like orbital distortion through spin-flipped electron hopping is dominant from XMLD and theoretical calculations. These findings suggest that the spin-flipped orbital quadrupole formations originate from the PMA in Mn_{3− δ} Ga and bring the paradigm shift in the researches of PMA materials using x-ray magnetic spectroscopies.

Magnetic properties of Fe16-x (Ta/W) x N2 ternary alloy: first principles and atomistic simulations

Using the first principles method, we explored the magnetic properties of Fe_16-x (Ta/W) _x N₂ alloy. We calculated the alloy formation energy, dynamical and thermal stabilities and proved the possibility of materialization of Fe_16-x (Ta/W) _x N₂ alloy. The Fe₁₄Ta₂N₂ had a Curie temperature of 1020 K while it was 950 K in Fe₁₄W₂N₂. We found greatly enhanced uniaxial anisotropy in ternary alloy systems. Particularly, the Fe₁₄W₂N₂ alloy has a uniaxial anisotropy constant of 2.68 MJ m^-3 which is almost a five times enhancement of the value of 0.57 MJ m^-3 in the Fe₁₆N₂. The increase in the uniaxial anisotropy resulted in an enhancement of the coercive field (H _C). The Fe₁₄W₂N₂ had a coercive field of 27 kOe at 300 K and this is comparable to that of 25.6 kOe in Dy-doped Nd based magnet. Besides, the (BH)_max of 54.5 MGOe in Fe₁₄W₂N₂ alloy was even larger than the value of 40 MGOe in Dy-doped Nd-based magnet. Overall, we propose that the Fe_16-x (Ta/W) _x N₂ can be a potential rare-earth-free permanent magnet.

L10-FeNi films on Au-Cu-Ni buffer-layer: a high-throughput combinatorial study

The fct L10-FeNi alloy is a promising candidate for the development of high performance critical-elements-free magnetic materials. Among the different materials, the Au-Cu-Ni alloy has resulted very promising; however, a detailed investigation of the effect of the buffer-layer composition on the formation of the hard FeNi phase is still missing. To accelerate the search of the best Au-Cu-Ni composition, a combinatorial approach based on High-Throughput (HT) experimental methods has been exploited in this paper. HT magnetic characterization methods revealed the presence of a hard magnetic phase with an out-of-plane easy-axis, whose coercivity increases from 0.49 kOe up to 1.30 kOe as the Au content of the Cu-Au-Ni buffer-layer decreases. Similarly, the out-of-plane magneto-crystalline anisotropy energy density increases from 0.12 to 0.35 MJ/m3. This anisotropy is attributed to the partial formation of the L10 FeNi phase induced by the buffer-layer. In the range of compositions we investigated, the buffer-layer structure does not change significantly and the modulation of the magnetic properties with the Au content in the combinatorial layer is mainly related to the different nature and extent of interlayer diffusion processes, which have a great impact on the formation and order degree of the L10 FeNi phase.

Anatomy of interfacial spin-orbit coupling in Co/Pd multilayers using X-ray magnetic circular dichroism and first-principles calculations

Element-specific orbital magnetic moments and their anisotropies in perpendicularly magnetised Co/Pd multilayers are investigated using Co L-edge and Pd M-edge angle-dependent x-ray magnetic circular dichroism. We show that the orbital magnetic moments in Co are anisotropic, whereas those in Pd are isotropic. The first-principles density-functional-theory calculations also suggest that the Co/Pd interfacial orbital magnetic moments in Co are anisotropic and contribute to the perpendicular magnetic anisotropy (PMA), and that the isotropic ones in Pd manipulates the Co orbitals at the interface through proximity effects. Orbital-resolved anatomy of Co/Pd interfaces reveals that the orbital moment anisotropy in Co and spin-flipped transition related to the magnetic dipoles in Pd are essential for the appearance of PMA.

Voltage controlled interfacial magnetism through platinum orbits

Electric fields at interfaces exhibit useful phenomena, such as switching functions in transistors, through electron accumulations and/or electric dipole inductions. We find one potentially unique situation in a metal–dielectric interface in which the electric field is atomically inhomogeneous because of the strong electrostatic screening effect in metals. Such electric fields enable us to access electric quadrupoles of the electron shell. Here we show, by synchrotron X-ray absorption spectroscopy, electric field induction of magnetic dipole moments in a platinum monatomic layer placed on ferromagnetic iron. Our theoretical analysis indicates that electric quadrupole induction produces magnetic dipole moments and provides a large magnetic anisotropy change. In contrast with the inability of current designs to offer ultrahigh-density memory devices using electric-field-induced spin control, our findings enable a material design showing more than ten times larger anisotropy energy change for such a use and highlight a path in electric-field control of condensed matter.

Electric field control of magnetization is usually weak and this hampers its application for the ultralow-power-consumption spintronic devices. Here, the authors demonstrate a mechanism to enhance the control of magnetic anisotropy by voltage-induced electric quadrupole in a metal–dielectric interface.

Resonant x-ray diffraction revealing chemical disorder in sputtered L10 FeNi on Si(0 0 1)

In the search for new rare earth free permanent magnetic materials, FeNi with a L10 structure is a possible candidate. We have synthesized the phase in the thin film form by sputtering onto HF-etched Si(0 0 1) substrates. Monatomic layers of Fe and Ni were alternately deposited on a Cu buffer layer, all of which grew epitaxially on the Si substrates. A good crystal structure and epitaxial relationship was confirmed by in-house x-ray diffraction (XRD). The chemical order, which to some part is the origin of an uniaxial magnetic anisotropy, was measured by resonant XRD. The 0 0 1 superlattice reflection was split in two symmetrically spaced peaks due to a composition modulation of the Fe and Ni layers. Furthermore the influence of roughness induced chemical anti-phase domains on the RXRD pattern is exemplified. A smaller than expected magnetic uniaxial anisotropy energy was obtained, which is partly due to the composition modulations, but the major reason is concluded to be the Cu buffer surface roughness.

First-principles calculations of perpendicular magnetic anisotropy in Fe1-x Co x /MgO(001) thin films

The perpendicular magnetic anisotropy (PMA) of Fe1-x Co x thin films on MgO(001) was investigated via first-principles density-functional calculations. Four different configurations were considered based on their ground states: Fe/MgO, Fe12Co4/MgO, Fe10Co6/MgO, and Fe8Co8/MgO. As the Co composition increases, the amplitude of PMA increases first from Fe/MgO to Fe12Co4/MgO, and then decreases in Fe10Co6/MgO; finally, the magnetic anisotropy becomes horizontal in Fe8Co8/MgO. Analysis based on the second-order perturbation of the spin-orbit interaction was carried out to illustrate the contributions from Fe and Co atoms to PMA, and the differential charge density was calculated to give an intuitive comparison of 3d orbital occupancy. The enhanced PMA in Fe12Co4/MgO is ascribed to the optimized combination of occupied and unoccupied 3d states around the Fermi energy from both interface Fe and Co atoms, while the weaker PMA in Fe10Co6/MgO is mainly attributed to the modulation of the interface Co-d xy orbital around the Fermi energy. By adjusting the Co composition in Fe1-x Co x , the density of states of transitional metal atoms will be modulated to optimize PMA for future high-density memory application.

Enhancement of perpendicular magnetic anisotropy by compressive strain in alternately layered FeNi thin films

The effect of the lattice strain on magnetic anisotropy of alternately layered FeNi ultrathin films grown on a substrate, Cu(tCu = 0-70 ML)/Ni(48)Cu(52)(124 ML)/Cu(0 0 1) single crystal, is systematically studied by means of in situ x-ray magnetic circular dichroism (XMCD) and reflection high-energy electron diffraction (RHEED) analyses. To investigate the magnetic anisotropy of the FeNi layer itself, a non-magnetic substrate is adopted. From the RHEED analysis, the in-plane lattice constant, ain, of the substrate is found to shrink by 0.8% and 0.5% at tCu = 0 and 10 ML as compared to that of bulk Cu, respectively. Fe L-edge XMCD analysis is performed for n ML FeNi films grown on various ain, and perpendicular magnetic anisotropy (PMA) is observed at n = 3 and 5, whereas the film with n = 7 shows in-plane magnetic anisotropy. Moreover, it is found that PMA is enhanced with decreasing ain, in the case where a Cu spacer layer is inserted. We suppose that magnetic anisotropy in the FeNi films is mainly carried by Fe, and the delocalization of the in-plane orbitals near the Fermi level increases the perpendicular orbital magnetic moment, which leads to the enhancement of PMA.

Structural, magnetic and electronic state characterization of L1 0-type ordered FeNi alloy extracted from a natural meteorite

To understand the hard magnetism of L10-type ordered FeNi alloy, we extracted the L10-FeNi phase from a natural meteorite, and evaluated its fundamental solid-state properties: sample composition, magnetic hysteresis, crystal structure and electronic structure. We executed multidirectional analyses using scanning electron microscopy with an electron probe micro-analyzer (SEM-EPMA), a superconducting quantum interference device (SQUID), x-ray diffraction (XRD) and magnetic circular dichroism (MCD). As a result, we found that the composition was Fe: 50.47 ± 1.98 at.%, Ni: 49.60 ± 1.49 at.%, and an obvious superlattice peak is confirmed. The estimated degree of order was 0.608, with lattice constants a = b = 3.582 Å and c = 3.607 Å. The obtained coercivity was more than 500 Oe. MCD analysis using the K absorption edge suggests that the magnetic anisotropy could originate from the orbital magnetic moment of 3d electrons in Fe; this result is consistent with that in a previous report obtained with synthetic L10-FeNi.

Fe-Ni composition dependence of magnetic anisotropy in artificially fabricated L1 0-ordered FeNi films

We prepared L10-ordered FeNi alloy films by alternate deposition of Fe and Ni monatomic layers, and investigated their magnetic anisotropy. We employed a non-ferromagnetic Au-Cu-Ni buffer layer with a flat surface and good lattice matching to L10-FeNi. An L10-FeNi film grown on Au6Cu51Ni43 showed a large uniaxial magnetic anisotropy energy (Ku = 7.0 × 10(6) erg cm(-)3). Ku monotonically increased with the long-range order parameter (S) of the L10 phase. We investigated the Fe-Ni composition dependence by alternating the deposition of Fe 1 − x and Ni 1 + x monatomic layers (− 0.4 < x < 0.4). Saturation magnetization (Ms) and Ku showed maxima (Ms = 1470 emu cm(-3), Ku = 9.3 × 10(6) erg cm(-3)) for Fe60Ni40 (x = -0.2) while S showed a maximum at the stoichiometric composition (x = 0). The change in the ratio of lattice parameters (c/a) was small for all compositions. We found that enrichment of Fe is very effective to enhance Ku. The large Ms and Ku of Fe60Ni40 indicate that Fe-rich L10-FeNi is promising as a rare-earth-free permanent magnet.