Magnetic Anisotropy Energy Research Articles

Evaluation of magnetic anisotropy in oriented plate-shaped strontium ferrite particles

Plate-shaped hexagonal SrFe12O19 particles, synthesized using potassium bromide as the molten salt flux, were dispersed in the resin using a planetary ball mill. Oriented sheets were prepared by coating the dispersion onto the films under a magnetic field. The coercive force and squareness ratio of the oriented sheets were 412 kA m−1 and 0.91, respectively. The magnetic anisotropy field was determined by measuring the rotational hysteresis losses of the oriented sheets with a magnetic torque meter. The anisotropy field was distributed in the range of approximately 200–1100 kA m−1, and particles with an anisotropy field of 478 kA m−1 comprised the majority. The magnetic anisotropy energy estimated from the magnetic anisotropy field was 104 KJ m−3. Assuming a reduction in the crystalline anisotropy field along the c-axis due to simply the shape anisotropy field resulting from the platelet shape of the particles, particles occupying the majority exhibited a maximum anisotropy field of 823 kA m−1.

Intrinsic multiferroicity and magnetoelectric coupling in VSI2 monolayer

Two dimensional (2D) multiferroic materials have great potential for miniaturized electronic and high-density multi-states data storage devices due to the coexistence of electric and spin polarization. Because the origins of magnetism and ferroelectricity are mutually exclusive and difficult to coexist, there are still rare to date 2D multiferroic semiconductors with good performance. Here, we propose a 2D multiferroic material, VSI2 monolayer, which has both ferromagnetic and ferroelectric properties by first principles calculation. It shows robust ferroelectricity with an appropriate switching barrier (∼140 meV), and the in-plane ferroelectric polarization is 1.44 × 10−10 C/m. At the same time, the VSI2 monolayer magnetic easy axis is along the b-axis direction and owns a large magnetic anisotropy energy (MAE) (512 μeV/V-ion). Based on Monte Carlo simulations of the Heisenberg model, the Curie temperature (TC) is calculated to be approximately 92 K. In addition, biaxial strain can significantly change the MAE, and the in-plane magnetic easy axis can be switched to the out-of-plane direction by 5% biaxial tensile strain. In particular, we can change the magnetic moment at the two ends of VSI2 nanoribbons by switching the direction of electric polarization, providing an opportunity for the application of magnetic-electric control and memory devices. Our theoretical prediction provides a good platform for studying the 2D multiferroic effects and spintronic properties.

Voltage-gated field-free spin–orbit torque switching in Pt/Co/Ir/MgO wedged structures

The ability to efficiently manipulate magnetization is of great significance for practical applications of spin–orbit torque (SOT) devices. In this study, we report the voltage-controlled, field-free SOT switching in perpendicular magnetized Pt/Co/Ir/MgO structures with wedge iridium interlayers. The insertion of a thin iridium interlayer at ferromagnet/oxide can significantly reduce the perpendicular magnetic anisotropy depending on the Ir thickness. The wedging of the iridium layer breaks lateral structural symmetry, resulting in deterministic switching without the assistance of in-plane magnetic fields. In such a structure, the SOT critical switching currents are remarkably decreased by 29% when a positive 6 V gate voltage is applied. Further quantitative analysis shows that multiple factors contribute to the decrease in switching currents, including a 23% reduction in magnetic anisotropy energy, a reduction in nucleation field, and a minor enhancement in damping-like torque under gate voltage. Moreover, the probabilistic hindrance that gate voltage poses to field-free switching is revealed by the decrease in current-induced perpendicular effective fields from symmetry-breaking. Our research shows that energy-efficient SOT switching can be controlled by gating and offers insight into the mechanism behind voltage-gated SOT switching.

Janus monolayer ScXY (X≠Y = Cl, Br and I) for piezoelectric and valleytronic application: a first-principle prediction

Coexistence of ferromagnetism, piezoelectricity and valley in two-dimensional (2D) materials is crucial to advance multifunctional electronic technologies. Here, Janus ScXY (X≠Y = Cl, Br and I) monolayers are predicted to be piezoelectric ferromagnetic semiconductors with dynamical, mechanical and thermal stabilities. They all show an in-plane easy axis of magnetization by calculating magnetic anisotropy energy (MAE) including magnetocrystalline anisotropy energy and magnetic shape anisotropy energy. The MAE results show that they intrinsically have no spontaneous valley polarization. The predicted piezoelectric strain coefficients d 11 and d 31 (absolute values) are higher than ones of most 2D materials. Moreover, the d 31 (absolute value) of ScClI reaches up to 1.14 pm V−1, which is highly desirable for ultrathin piezoelectric device application. To obtain spontaneous valley polarization, charge doping are explored to tune the direction of magnetization of ScXY. By appropriate hole doping, their easy magnetization axis can change from in-plane to out-of-plane, resulting in spontaneous valley polarization. Taking ScBrI with 0.20 holes per f.u. as an example, under the action of an in-plane electric field, the hole carriers of K valley turn towards one edge of the sample, which will produce anomalous valley Hall effect, and the hole carriers of Γ valley move in a straight line. These findings could pave the way for designing piezoelectric and valleytronic devices.

Two-dimensional 4f magnetic EuSn2X2 (X = P, As) monolayers: A first-principles study

Two-dimensional (2D) ferromagnetic semiconductors (FMSs) hold exciting and promising potential for application in spintronic devices at the nanoscale. Currently, most 2D FMSs are based on 3d electrons; 4f electrons can provide nontrivial magnetism but have been much less studied to date. This paper presents a theoretical study, via first-principles calculations, of EuSn2X2 (X = P, As) monolayers based on rare-earth cations with f-electrons. The results show that EuSn2X2 monolayers possess a large magnetization (7 μB/Eu), a controllable magnetic anisotropy energy, and a unique d-electron-mediated f–f exchange mechanism. Both types of EuSn2X2 (X = P, As) monolayers are FMSs with indirect bandgaps of 1.00 and 0.99 eV, respectively, based on the Heyd–Scuseria–Ernzerhof (HSE06) method, which can be transform to direct bandgap semiconductors under biaxial strain. Interestingly, under the latter, spin–orbit coupling interaction gradually replaces the dipole–dipole interaction in the dominant position of magnetic anisotropy, resulting in the magnetic easy axis changing from in-plane to the more desirable out-of-plane. Considering their excellent dynamic, thermal, and mechanical stabilities and small cleavage energy, these EuSn2X2 monolayers can be exfoliated from their synthesized bulk. Our study not only helps to understand the properties of 2D 4f rare-earth magnets but also signposts a route toward improving the performance of EuSn2X2 monolayers in nano-electronic devices.

Strain-controllable high Curie temperature and magnetic anisotropy energy in two-dimensional Fe2Si and Fe2Ge

Strain-controllable high Curie temperature and magnetic anisotropy energy in two-dimensional Fe2Si and Fe2Ge

Tuning Crystal Packing and Magnetic Properties in a Series of [Dy12] Metallocubanes Based on Azobenzene Derivatives of Salicylic Acid.

A series of four new Dy12 dodecanuclear clusters based on azobenzene derivative ligands of salicylic acid (L1-L4) has been synthesized and characterized in the crystalline phase using X-ray diffraction on single crystal and powder, IR spectroscopy, elemental analysis, and DSC-TGA methods. It was revealed that all obtained clusters exhibit the formation of the similar metallic cluster nodes, as vertex-sharing heterocubanes, obtained from four Dy3+ cations, three bridging hydroxyl groups, and O atoms from the salicylic ligands. The coordination geometry around the Dy(III) centers has been carefully analyzed. Whereas Dy12-L1 and Dy12-L2 with L1 and L2 containing Me and OMe groups in para positions of the phenyl rings, respectively, form similar porous 3D diamond-like molecular networks due to CH-π interactions, for Dy12-L3 with L3 bearing NO2-electron-withdrawing group, the generation of 2D molecular grids assembled by π-π staking is observed, and for Dy12-L4 with L4 bearing phenyl substituent, 3D hexagonal channels have been generated. The complexes Dy12-L1, Dy12-L2, and Dy12-L3 exhibit a zero-field slow magnetic relaxation effect. After UV irradiation of Dy12-L1, a decrease of the magnetic anisotropy energy barrier displaying the possibility of control over magnetic properties by the external stimulus has been observed.

Classification of Yu-Shiba-Rusinov states of magnetic impurities on superconducting surfaces: A fully relativistic first-principles study

Magnetic adatoms at surfaces of superconductors may induce localized bound states within the superconducting energy gap referred to as Yu-Shiba-Rusinov (YSR) states. We solve the Kohn-Sham-Dirac Bogoliubov--de Gennes equations within the fully relativistic multiple scattering Green's function method to study the nature of the YSR states for $3d$ magnetic impurities (Cr, Mn, Fe, and Co) placed on a pristine Nb(110) surface, as well as capped by a monolayer of Bi, Re, or Ir. First, we perform self-consistent relativistic calculations in the normal state and determine the direction of the easy axis and the magnetic anisotropy energy. Then we study the relation between the electronic structure in the normal state and the YSR states. We show that the YSR states can be categorized according to the energy-resolved singlet and triplet order parameters as normal, superconducting singlet, or induced triplet states. Finally, we demonstrate that the rotation of the adatom magnetic moment shifts the energy of the YSR states as a consequence of the spin orbit coupling. During this rotation, some branches of the YSR states might cross the Fermi energy, implying that at certain paths in the configuration space a peak can be found at zero energy.

Hinge-like Co2S3and Co2Te3Nanosheets: Promising Two-Dimensional Optical, Thermoelectric, and Spintronic Materials

In this study, the structural and physical properties of hinge-like Co2S3 and Co2Te3 nanosheets are predicted using spin-polarized density functional theory. Our calculations show that Co2S3 and Co2Te3 nanosheets are ferromagnetic semiconductors and antiferromagnetic metals in the ground state, respectively, and these nanosheets are dynamically and thermodynamically stable. According to the mean-field theory, Co2S3 and Co2Te3 nanosheets have the Néel temperature of 933 K and the Curie temperature of 285 K. Also, Co2Te3 nanosheets have unique properties such as significant total magnetic momentum (5.07 μB) and high magnetic anisotropy energy (2.62 meV). The examination of optical properties shows that Co2S3 and Co2Te3 nanosheets can be used in optoelectronic devices such as strong far- ultraviolet and ultraviolet absorbers, respectively. Calculating thermoelectric properties using Boltzmann’s theory shows that the Co2S3 nanosheet not only has ZT = 1 at 100 K but has significant thermoelectric efficiency at temperatures higher than room temperature (ZT = 0.97 at 700 K). Based on spin-dependent transport calculations, the current passing through Co2S3 (37.55 μA) and Co2Te3 (75 μA) nanosheets is higher than many 2D nanostructures, and the transport properties of these nanosheets are anisotropic. Therefore, Co2S3 and Co2Te3 nanosheets can be promising candidates for the development of nanoscale thermoelectric and spintronic devices.

Na3VAs2 monolayer: A two-dimensional intrinsic room-temperature ferromagnetic half-metal with large desired perpendicular magnetic anisotropy

Recent experiments have proved that the intrinsic two-dimensional (2D) magnetism has aroused strong interest in the application of advanced spintronics. However, low Curie temperature and low magnetic anisotropy energy (MAE) greatly limit their application range. By density functional theory calculation, we predict a stable 2D Na3VAs2 monolayer, which shows intrinsic ferromagnetic (FM) order and a large MAE (570 μeV per V atom). The Na3VAs2 monolayer has a local magnetic moment about 2 μB/V. Monte Carlo simulation shows that the Curie temperature (TC) of Na3VAs2 monolayer is up to 305 K based on anisotropic Heisenberg mode. More interestingly, the 2D Na3VAs2 monolayer shows an ideal half-metallic abundance, and it still maintains half-metallic characteristics under various strains. In addition, this monolayer has good dynamic, thermal, and mechanical stability. The excellent properties of the Na3VAs2 monolayer makes it great potential to be used in spintronic devices.

Electronic structure of CeAuAl$_3$ using density functional theory

We studied the magnetic properties and electronic structure of CeAuAl_3CeAuAl3 using density functional theory. This compound shows a large Sommerfeld coefficient, a Kondo temperature, {T_K=4\,K}TK=4K and antiferromagnetic order below {T_N=1.1\,K}TN=1.1K. We calculated the magnetic groundstate of {CeAuAl_3}CeAuAl3 and the magnetic anisotropy energies. Treating the 4f-electrons as localized with DFT+U we obtain a good match with the magnetic properties observed experimentally. We also report salient features of the electronic structure of {CeAuAl_3}CeAuAl3, including features of the Fermi surface and associated quantum oscillatory spectra, when the 4f-electrons are treated either as localized or itinerant.

Two-dimensional GdI2/GeC van der Waals heterostructure: Bipolar magnetic semiconductor, high critical temperature and large magnetic anisotropy

The band alignment, intrinsic ferromagnetism, Dzyaloshinskii-Moriya interaction, magnetic anisotropy and critical temperature (TC) of a GdI2/GeC van der Waals (vdW) heterostructure were systematically investigated by first-principles calculations and Monte Carlo simulations. The proposed GdI2/GeC vdW heterostructure is a bipolar magnetic semiconductor with Type-I band alignment, large in-plane magnetic anisotropy energy (MAE) of − 0.912 mJ/m2 and high critical temperature of 466 K. In addition, under biaxial strains, the heterostructure transformed from semiconductor into metal, while the easy magnetization axis maintained in-plane and TC increased. The results indicated that the GdI2/GeC vdW heterostructure presented large MAE and high TC, having potential applications in spintronic devices.

Huge perpendicular magnetic anisotropy in a 12-fold planar hypercoordinate W@B12(NCCN)3 monolayer

Two-dimensional (2D) materials with planar hypercoordinate motifs are attractive in terms of both fundamental science and technological applications. Herein, we construct a stable hexagonal 2D W@B12(NCCN)3 monolayer using W@B12 cluster as a building block and –NCCN– as a bridge linker. Multi-center bonding analysis reveals that the abundant 3c–1e B–W–Β σ bonds are responsible for the stability of a 12-fold coordinated W@B12 wheel, which has the highest coordination number reported for a planar system. Moreover, 3c–1e Β−Ν−Β, 4c − 1e N–C–C–N, and 13c − 1e W–B12 π bonds together form big delocalized π bonds, endowing 2D W@B12(NCCN)3 with unusual stability. Remarkably, 2D W@B12(NCCN)3 is a robust ferromagnetic half-metal with a large orbital moment anisotropy of 1.3 μB, a high out-of-plane magnetic anisotropy energy of 199 meV/atom, and a high Curie temperature of 150 K, which provides a potential candidate for high-density memory devices. These findings provide vital guidance for the design of 2D magnets with planar hypercoordination and unusual functionality.

Perpendicular Magnetic Anisotropy of an Ultrathin Fe Layer Grown on NiO(001)

The magnetic anisotropy and magnetic interactions at the interface between $\mathrm{Fe}$ and $\mathrm{Ni}\mathrm{O}$(001) were investigated. Depending on the growth conditions of the $\mathrm{Ni}\mathrm{O}$(001) layers and the postannealing temperature, the preferential magnetization direction of the ultrathin $\mathrm{Fe}$ layer grown on a $\mathrm{Ni}\mathrm{O}$(001) layer changed from the in-plane direction to a direction perpendicular to the film plane. The lattice constant of the $\mathrm{Ni}\mathrm{O}$(001) layers parallel to the growth direction increased with ${\mathrm{O}}_{2}$ flow rate, while that parallel to the in-plane direction were locked onto the MgO(001) substrate regardless of the growth conditions of the NiO layers. Moreover, perpendicular magnetization was observed only when the NiO layer was grown with ${\mathrm{O}}_{2}$ flow rates higher than 2.0 sccm corresponding to oxygen-rich NiO. X-ray magnetic circular dichroism measurements revealed an enhancement in anisotropic orbital magnetic moments similar to the origin of perpendicular magnetic anisotropy at the $\mathrm{Fe}$/MgO(001) interface. The interfacial magnetic anisotropy energies were 0.93 and $1.02\phantom{\rule{0.2em}{0ex}}{\mathrm{mJ}/\mathrm{m}}^{2}$ at room temperature and at 100 K, respectively, indicating less temperature dependence. In contrast, the coercivity ${H}_{c}$ exhibited a significant temperature dependence. Although no signature of exchange bias or unidirectional loop shift was observed, ${H}_{c}$ was strongly dependent on the NiO layer thickness, indicating that the exchange interaction at the interface between the ferromagnetic and antiferromagnetic layers was not negligible, despite the NiO(001) being a spin-compensated surface.

Spin-polarized two-dimensional electron/hole gas at the interface of nonmagnetic semiconducting half-Heusler compounds: Modified Slater-Pauling rule for half-metallicity at the interface

Half-Heusler compounds with 18 valence electrons per unit cell are well-known nonmagnetic semiconductors. Employing first-principles electronic band-structure calculations, we study the interface properties of the half-Heusler heterojunctions based on FeVSb, CoTiSb, CoVSn, and NiTiSn compounds, which belong to this category of materials. Our results show that several of these heterojunction interfaces become not only metallic but also magnetic. The emergence of spin-polarization is accompanied by the formation of two-dimensional electron gas or hole gas at the interface. A qualitative analysis of the origin of the spin polarization at the interfaces suggests that strong correlations are responsible. For the cases of magnetic interfaces where half-metallicity is also present, we propose a modified Slater-Pauling rule similar to the one for bulk half-metallic half-Heusler compounds. Additionally, we calculate exchange parameters, Curie temperatures, and magnetic anisotropy energies for magnetic interfaces. Our study, along with recent experimental evidence confirming the presence of two-dimensional electron gas at CoTiSb/NiTiSn heterojunctions, may motivate future efforts to explore and realize device applications using these heterojunctions.

Two-Dimensional Robust Ferromagnetic Semiconductors via Assembly of Magnetic Superatoms [Fe6S8(CN)6]5.

Cluster-assembled materials are of considerable interest owing to their unique properties and extensive application prospects. Nevertheless, the majority of cluster-assembled materials developed to date are nonmagnetic, limiting their applications in spintronics. Thus, two-dimensional (2D) cluster-assembled sheets with intrinsic ferromagnetism are very desirable. Here, via first-principles calculations, utilizing the recently synthesized magnetic superatomic cluster [Fe6S8(CN)6]5- as a building block, we design a series of thermodynamically stable 2D nanosheets [NH4]3[Fe6S8(CN)6]TM (TM = Cr, Mn, Fe, Co) with robust ferromagnetic ordering (Curie temperatures (Tc) up to 130 K), medium band gaps (from 1.96 to 2.01 eV), and sizable magnetic anisotropy energy (up to 0.58 meV per unit cell). Among these nanosheets, the [NH4]3[Fe6S8(CN)6]Cr is a bipolar magnetic semiconductor, whereas the other three ([NH4]3[Fe6S8(CN)6]TM (TM = Mn, Fe, Co) are half semiconductors. Additionally, the electronic and magnetic properties of [NH4]3[Fe6S8(CN)6]TM (TM = Cr, Mn, Fe, Co) nanosheets can be easily modulated by electron and hole doping via simply controlling the number of ammonium counterions. Furthermore, the Curie temperatures of the 2D nanosheets can be improved to 225 and 327 K by choosing 4d/5d transition metals TM = Ru and Os, respectively.

First-principles study on the effects of atomic configuration on the magnetic anisotropy energy of (Fe,Co)16(N,C)2 alloys

Herein, the first-principles technique combined with a coherent potential approximation is utilized to investigate the magnetic anisotropy energy (MAE) of (Fe1-xCox)16(N,C)2 alloys. The alloys contain an ordered α″-phase and partially ordered α′-phase, where α-Fe is distorted to form a bct structure with c/a = 1.1 owing to the random intrusion of (N, C) atoms. For the α″-phase, the MAE is sensitive to Co substitution sites and reaches approximately 3 MJ/m3 at an x of 0.25 when Co atoms occupy the 4d sites. For the α′-phase, the lattice distortion c/a = 1.1 alone cannot provide a positive MAE when x = 0 (FeN0.125 and FeC0.125). Evidently, both Co substitution and further increasing the c/a over 1.1 must be performed to realize a positive MAE in the α'-phase. Finally, the importance of local distortion of the (Fe, Co) lattice in further increasing the c/a beyond 1.1 is discussed as it increases the effective c/a even when the global c/a is fixed at 1.1.

Room-temperature ferromagnetic half metal in (C, Mn) co-doped orthorhombic ZnO with large magneto-crystalline anisotropy energy

Room-temperature ferromagnetic (FM) half-metallic materials are essential for spintronics applications. Here, we find that (C, Mn) co-doped orthorhombic ZnO (termed (C, Mn) @Orth-ZnO) is a room-temperature FM half-metal with a magnetic moment of 3μ B per Mn atom. A detailed investigation of the electronic structure of the (C, Mn) @Orth-ZnO system demonstrates that the FM interaction originates mainly from the p–d exchange hybridization between the C2p and Mn3d states. Moreover, the induced extended spin-polarized states of nonmetallic C can mediate the long-range FM exchange interactions beyond the nearest-neighbor situation. The Curie temperature T C of the (C, Mn) @Orth-ZnO system is 371 K based on the mean-field approximation. The (C, Mn) @Orth-ZnO system also has a large magnetic anisotropy energy of 0.63 meV, which is mainly attributed to (dyz, dz 2) orbitals of the Mn atom. Finally, we discuss the influence of carrier concentration and external strain on the stability of the ferromagnetism of the (C, Mn) @Orth-ZnO system. We highlight the application prospects of (C, Mn) @Orth-ZnO in practical spintronic nano-devices.

Stacking and layer dependence of magnetic properties in Ti2C and Fe2C

Magnetic MXenes are becoming an important family of materials for exploring 2D magnetism. However, investigations into the interdependence of layer thickness, stacking patterns and magnetism in these materials, from a microscopic point of view, are still lacking. In this work, we have used density functional theory based calculations to understand the effects of layer thickness and stacking on the magnetic properties in two magnetic MXenes, Ti2C and Fe2C, in their monolayer and bilayer forms. The ground-state magnetic structures, magnetic moments, magnetic exchange interactions, magnetic transition temperatures and magnetic anisotropy energies are calculated and analysed using their electronic structures and standardised models. We find that in both systems an increase in layer thickness (monolayer to bilayer) affects the ground-state magnetic configuration, which is driven by the changes in the magnetic exchange interactions. While the effects of the stacking pattern are rather weak in Ti2C, they are substantial, both qualitatively and quantitatively, in Fe2C. The computed results are analysed from their electronic structures. The results suggest that fascinating physical effects can be obtained in Fe2C by tuning the layer thickness and stacking patterns, making it more suitable for device applications.

Tailing the Magnetoelectric Properties of Cr2Ge2Te6 by Engineering Covalently Bonded Cr Self-Intercalation: Ferromagnetic Half-Metal

Two-dimensional intrinsic ferromagnetic half-metals (HMs) are important for spintronics. Based on a systematic research of CrGeTe3 (CGT) bilayers and multilayers with the self-intercalated (SI) Cr (CrSI) atom, we find that self-intercalation can enhance interlayer magnetic coupling, which results in a super-exchange interaction between interlayers. The CGT bilayer keeps half-metallicity with the interlayer ferromagnetic (FM) order after Cr’s self-intercalation, independent of CrSI atoms’ concentration and stacking orders. Moreover, SI-CGT multilayers with interlayer FM order transform from HMs into normal spin-polarized metals, as the states at the Fermi level increase. Moreover, the magnetic anisotropy energies (MAEs) of SI-CGT-AA and SI-CGT-AB are −0.160 and −0.42 meV/f.u., respectively, which are modulated by the CrSI atoms. The MAEs of SI-CGT-AA and SI-CGT-AB are different, as the hybridization interactions between Cr’s d orbitals are different from each other. SI-CGT bilayers’ magnetic easy axis (EA) switches from the original [001] of CGT to the [100] direction, independent of the stacking orders. It is inferred that the MAE is mainly contributed by the hybridization between Te’s px and py, py and pz orbitals, and that this hybridization interaction is obviously weakened as CrSI atom is inserted. The SI-CGT bilayers and multilayers show good dynamic and thermal stability at 300 and 500 K. These findings offer a promising way to manipulate the interlayer exchange interaction and magnetoelectric properties of CGT multilayers and other vdW magnets.