Orbital Moment Anisotropy Research Articles

Investigating Magnetocrystalline Anisotropy in the System Au/Co-Staircase/Au(788) by Using XMCD

Here, we report the investigation of the influence of the magnetocrystalline anisotropy (MCA) in Cobalt ultrathin films grown on the vicinal surface Au(788), through the anisotropy of the orbital magnetic moment. The aim of this study was to apply the X-ray magnetic circular dichroism (XMCD) technique to probe the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">spin</i> magnetic moment and the orbital magnetic moment anisotropy within the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">spin</i> reorientation transition (SRT) range in the system Au/Co-Staircase/Au(788). The influence of increasing Co film thickness on SRT, from easy out-of-plane magnetization axis to in-plane magnetization was investigated by means of the magneto-optical <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Kerr</i> effect (MOKE). The preparation and surface quality of the Co films were characterized using LEED and STM. Analysis of XMCD measurements as a function of the film thickness for Au/Co-staircase/Au(788) reveals the anisotropic orbital magnetic moment during the SRT regime (8 to 12 ML range) indicating a decreasing influence of MCA with the increased thickness and nearly isotropic orbital magnetic moment above 12 ML, with a small MCA influence.

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.

Electric field effect on spectroscopic g-factor and magnetic anisotropy in a Pt/Co/MgO ultrathin film

We demonstrate that magnetic crystal anisotropy () and spectroscopic g-factor can be modulated simultaneously by gate voltage in a Pt/Co/MgO ultrathin film with our ferromagnetic resonance (FMR) measurement based on the rectification effect. The g-factor reflects on orbital magnetic moment, indicating that the electric field induced-modulations of magnetic anisotropy in cobalt originate from the change of the anisotropy of orbital moments (). The quantitative estimation reveals that to correlation when the electric field is applied significantly differs from the one inherent at the Pt/Co/MgO interfaces. This means that the correlation itself is also modulated by the electric field. Our results show that the FMR technique is very useful for probing the electric field effect on

Effect of chemical disorder on the magnetic anisotropy in L10 FeNi from first-principles calculations

We use first-principles calculations to investigate how deviations from perfect chemical order affect the magnetocrystalline anisotropy energy (MAE) in $L{1}_{0}$ FeNi. We first analyze the local chemical environment of the Fe atoms in various partially ordered configurations, using the orbital magnetic moment anisotropy (OMA) as proxy for a local contribution to the MAE. We are able to identify a specific nearest neighbor configuration and use this ``favorable environment'' to successfully design various structures with MAE higher than the perfectly ordered system. However, a systematic analysis of the correlation between local environment and OMA using smooth overlap of atomic positions indicates only a partial correlation, which exists only if the deviation from full chemical order is not too large, whereas in general no such correlation can be identified even using up to third nearest neighbors. Guided by the observation that the identified favorable environment implies an Fe-rich composition, we investigate the effect of randomly inserting additional Fe into the nominal Ni planes of the perfectly ordered structure. We find that the MAE increases with Fe content, at least up to 62.5% Fe. Thus, our paper shows that the perfectly ordered case is not the one with highest MAE and that an increased MAE can be obtained for slightly Fe-rich compositions.

Control of perpendicular magnetic anisotropy at the Fe/MgO interface by phthalocyanine insertion

Perpendicular magnetic anisotropy at an interface between Fe and MgO with Co-phthalocyanine (CoPc) adsorption has been investigated. We find that the CoPc adsorption at an Fe/MgO interface increases the perpendicular magnetic anisotropy energy (PMA) while maintaining the voltage-controlled magnetic anisotropy effect. By performing x-ray magnetic circular dichroism spectroscopy measurements, we reveal that the CoPc adsorption induces hole accumulation at the Fe surface. The origin of the PMA enhancement is attributed to the increased orbital magnetic moment anisotropy of the Fe atoms.

Interplay between chemical order and magnetic properties in L10 FeNi (tetrataenite): A first-principles study

We use first-principles-based calculations to investigate the interplay between chemical order and the magnetic properties of $L1_0$ FeNi. In particular, we investigate how deviations from perfect chemical order affect the energy difference between the paramagnetic and ferromagnetic states as well as the important magneto-crystalline anisotropy energy. Our calculations demonstrate a strong effect of the magnetic order on the chemical order-disorder transition temperature, and conversely, a strong enhancement of the magnetic transition temperature by the chemical order. Most interestingly, our results indicate that the magnetic anisotropy does not decrease significantly as long as the deviations from perfect order are not too large. Moreover, we find that in certain cases a slight disorder can result in a higher anisotropy than for the fully ordered structure. We further analyze the correlation between the magneto-crystalline anisotropy and the orbital magnetic moment anisotropy, which allows to study the effect of the local chemical environment on both quantities, potentially enabling further optimization of the magneto-crystalline anisotropy with respect to chemical order and stoichiometric composition.

Perpendicular orbital and quadrupole anisotropies at Fe/MgO interfaces detected by x-ray magnetic circular and linear dichroisms

We investigated interfacial perpendicular magnetic anisotropy (PMA) in ultrathin Fe/MgO(001) using both x-ray magnetic circular dichroism and magnetic linear dichroism (XMLD). We developed the XMLD technique for detecting the signals from the PMA samples. The PMA energy and quadrupole moments at an Fe/MgO interface were deduced from the XMLD sum rules, whose values explain the microscopic origin of PMA. We found that orbital moment anisotropy is dominant at the Fe/MgO interfacial PMA and the contribution of quadrupole moments is small but finite at the lattice distorted interfaces.

Spin-orbit coupling and crystal-field distortions for a low-spin 3d5 state in BaCoO3

We have studied the electronic structure of BaCoO$_3$ using soft x-ray absorption spectroscopy at the Co-$L_{2,3}$ and O-$K$ edges, magnetic circular dichroism at the Co-$L_{2,3}$ edges, as well as valence band hard x-ray photoelectron spectroscopy. The quantitative analysis of the spectra established that the Co ions are in the formal low-spin tetravalent 3$d^5$ state and that the system is a negative charge transfer Mott insulator. The spin-orbit coupling plays also an important role for the magnetism of the system. At the same time, a trigonal crystal field is present with sufficient strength to bring the 3$d^5$ ion away from the $J_{eff} = 1/2$ state. The sign of this crystal field is such that the $a_{1g}$ orbital is doubly occupied, explaining the absence of a Peierl's transition in this system which consists of chains of face-sharing CoO$_6$ octahedra. Moreover, with one hole residing in the $e_g^{\pi}$, the presence of an orbital moment and strong magneto-crystalline anisotropy can be understood. Yet, we also infer that crystal fields with lower symmetry must be present to reproduce the measured orbital moment quantitatively, thereby suggesting the possibility for orbital ordering to occur in BaCoO$_3$.

Impact of single atomic defects and vacancies on the magnetic anisotropy energy of CoPt thin films

The impact of surface vacancies and single adatoms on the magnetic properties of tetragonal L10 CoPt thin films is investigated from first principles. We consider Co and Fe single adatoms deposited on a Pt-terminated thin film while a Pt adatom is assumed to be supported by a Co-terminated film. The vacancy is injected in the top-surface layer of the films with both types of termination. After finding the most stable location of the defects, we discuss their magnetic properties tied to those of the substrate and investigate the magnetocrystalline anisotropy energy (MAE). Previous simulations (Brahimi et al 2016 J. Phys.: Condens. Matter 28 496002) predicted a large out-of-plane surface MAE for the Pt-terminated CoPt films (4 meV per f.u.) in contrast to in-plane surface MAE for Co-terminated films (−1 meV per f.u.). Here, we find that the surface MAE is significantly modified upon the presence of the atomic defects. All investigated defects induce an in-plane MAE, which is large enough for Fe adatom and Pt vacancy to switch the surface MAE from out-of-plane to in-plane for the Pt-terminated films. Interestingly, among the investigated defects Pt vacancy has the largest effect on the MAE in contrast to Co vacancy, which induced the smallest but still significant effect. This behavior is explained in terms of the orbital moment anisotropy of the thin films.

Strain-induced reversible manipulation of orbital magnetic moments in Ni/Cu multilayers on ferroelectric BaTiO3

Controlling magnetic anisotropy by orbital magnetic moments related to interfacial strains has considerable potential for the development of future devices using spins and orbitals. For the fundamental physics, the relationship between strain and orbital magnetic moment is still unknown, because there are few tools to probe changes of orbital magnetic moment. In this study, we developed an electric field (E)-induced X-ray magnetic circular dichroism (EXMCD) technique to apply E to a ferroelectric BaTiO3 substrate. We reversibly tuned the interfacial lattice constants of Ni/Cu multilayers on BaTiO3 using this technique. As the domain structures in BaTiO3 are modulated by E, EXMCD measurements reveal that the changes in the magnetic anisotropy of Ni/Cu films are induced through the modulation of orbital magnetic moments in Ni with magneto-elastic contributions. The strained Ni layer that induces the perpendicular magnetic anisotropy without E is released at E = 8 kV/cm, and in-plane magnetization also occurs. We observed that EXMCD measurements clarified the origin of the reversible changes in perpendicular magnetic anisotropy and established the relationship between macroscopic inverse magnetostriction effects and microscopic orbital moment anisotropy.

First-principles study of magnetism of TM@Cu&lt;sub&gt;12&lt;/sub&gt;N&lt;sub&gt;12&lt;/sub&gt; nanoclusters

The stability of structure, spin, orbital magnetic moment and magnetic anisotropy energy of TM@Cu&lt;sub&gt;12&lt;/sub&gt;N&lt;sub&gt;12&lt;/sub&gt; (TM = Mn, Fe, Co, Ni, Cu, Ru, Rh, Pd, Ir, Pt) are systematically investigated within the framework of the generalized gradient approximation with on-site coulomb repulsion density-functional theory (DFT-GGA+&lt;i&gt;U&lt;/i&gt;). In the orbital moment and magnetic anisotropy energy (MAE) computation procedure, the spin-orbit coupling is considered and implemented. In this article, we mainly focus on the structure stability and tunable magnetism of the TM atom (Mn, Fe, Co, Ni, Cu, Ru, Rh, Pd, Ir, Pt) substituting the centre atom of icosahedron (ICO) Cu&lt;sub&gt;13&lt;/sub&gt;N&lt;sub&gt;12&lt;/sub&gt; cluster, finally disclose the physics origin of the structure stability, change magnetism and larger MAE. The results show that the different TM atom doping makes the ICO structure of Cu&lt;sub&gt;13&lt;/sub&gt;N&lt;sub&gt;12&lt;/sub&gt; cluster appears a tiny deformation. The stabilities of the clusters are evidently enhanced due to the formation of Cu—N and Cu—TM bond. In addition, the N-capped clusters more prefer to present a larger magnetic moment than the pure Cu&lt;sub&gt;13&lt;/sub&gt; one. The magnetic environment of clusters is improved to varying degrees by doping different TM (TM = Mn, Fe, Co, Ni, Cu, Ru, Rh, Pd, Ir, Pt) atoms, which endows TM@Cu&lt;sub&gt;12&lt;/sub&gt;N&lt;sub&gt;12&lt;/sub&gt; clusters with various magnetic properties. For instance, the doping of 3d atoms further enhances the spin magnetic moment of the clusters, the Mn, Fe and Co atoms replacing the centre atom of the ICO Cu&lt;sub&gt;13&lt;/sub&gt;N&lt;sub&gt;12&lt;/sub&gt; generate 35, 32 and 33 giant moments, respectively. In light of the doping of 4d, 5d transition metal atoms, the orbital moments of the TM@Cu&lt;sub&gt;12&lt;/sub&gt;N&lt;sub&gt;12&lt;/sub&gt; clusters do not increase evidently, but the MAE remarkably strengthens for the doping of Rh and Pt atoms, the MAE values reach to 15.34 meV/atom and 6.76 meV/atom for Rh@Cu&lt;sub&gt;12&lt;/sub&gt;N&lt;sub&gt;12&lt;/sub&gt; and Pt@Cu&lt;sub&gt;12&lt;/sub&gt;N&lt;sub&gt;12&lt;/sub&gt;, respectively. The tunable magnetism of TM@Cu&lt;sub&gt;12&lt;/sub&gt;N&lt;sub&gt;12&lt;/sub&gt; cluster provides promising applications in spintronics.

Machine Learning Approach for Data Analysis of Magnetic Orbital Moments and Magnetocrystalline Anisotropy in Transition-Metal Thin Films on MgO(001)

Using the Least Absolute Shrinkage and Selection Operator (LASSO) technique, we analyze a long-standing issue in the field of magnetism: the relationship between orbital magnetic moments and magnetocrystalline anisotropy (MCA) energy in transition-metal thin films. Our LASSO regression utilizes the data obtained from first principles calculations for single slabs with six atomic-layers of binary Au-Fe, Au-Co, and Fe-Co films on MgO(001). In the case of Fe-Co thin films, we have successfully regressed the MCA energy against the anisotropy of orbital moments along the in-plane and the perpendicular plane directions, giving a linear behavior. For the Au-Fe and Au-Co thin films, however, our data-driven analysis shows no relation between the MCA energy and the anisotropy of orbital moments.

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.

Magnetocrystalline anisotropy in cobalt based magnets: a choice of correlation parameters and the relativistic effects

The dependence of the magnetocrystalline anisotropy energy (MAE) in MCo5 (M = Y, La, Ce, Gd) and CoPt on the Coulomb correlations and strength of spin orbit (SO) interaction within the GGA + U scheme is investigated. A range of parameters suitable for the satisfactory description of key magnetic properties is determined. We show that for a large variation of SO interaction the MAE in these materials can be well described by the traditional second order perturbation theory. We also show that in these materials the MAE can be both proportional and negatively proportional to the orbital moment anisotropy (OMA) of Co atoms. Dependence of relativistic effects on Coulomb correlations, applicability of the second order perturbation theory for the description of MAE, and effective screening of the SO interaction in these systems are discussed using a generalized virial theorem. Such determined sets of parameters of Coulomb correlations can be used in much needed large scale atomistic simulations.

Magnetism of a Co monolayer on Pt(111) capped by overlayers of 5d elements: A spin-model study

Using first-principles calculations, we study the magnetic properties of a Co monolayer on a Pt(111) surface with a capping monolayer of selected $5d$ elements (Re, Os, Ir, Pt and Au). First we determine the tensorial exchange interactions and magnetic anisotropies characterizing the Co monolayer for all considered systems. We find a close relationship between the magnetic moment of the Co atoms and the nearest-neighbor isotropic exchange interaction, which is attributed to the electronic hybridization between the Co and the capping layers, in spirit of the Stoner picture of ferromagnetism. The Dzyaloshinskii-Moriya interaction is decreased for all overlayers compared to the uncapped Co/Pt(111) system, while even the sign of the Dzyaloshinskii-Moriya interaction changes in case of the Ir overlayer. We conclude that the variation of the Dzyaloshinskii-Moriya interaction is well correlated with the change of the magnetic anisotropy energy and of the orbital moment anisotropy. The unique influence of the Ir overlayer on the Dzyaloshinskii-Moriya interaction is traced by scaling the strength of the spin--orbit coupling of the Ir atoms in Ir/Co/Pt(111) and by changing the Ir concentration in the Au$_{1-x}$Ir$_{x}$/Co/Pt(111) system. Our spin dynamics simulations indicate that the magnetic ground state of Re/Co/Pt(111) thin film is a spin spiral with a tilted normal vector, while the other systems are ferromagnetic.

Effect of Pt substitution on the magnetocrystalline anisotropy of Ni2MnGa : A competition between chemistry and elasticity

The magnetocrystalline anisotropy (MAE) of ${\mathrm{Ni}}_{2\ensuremath{-}x}{\mathrm{Pt}}_{x}\mathrm{MnGa}(0\ensuremath{\le}x\ensuremath{\le}0.25)$ alloys are investigated using the singular point detection technique and density functional theory. A slight reduction in MAE as compared to that of ${\mathrm{Ni}}_{2}\mathrm{MnGa}$ is observed due to Pt substitution. The calculated MAE varies almost linearly with the orbital moment anisotropy. A competition between the elastic and the chemical contributions explains the observed trend of the MAE with increasing Pt content. The large MAE in combination with the previously reported increase of the martensitic transition temperature makes these alloys promising candidates for ferromagnetic shape memory applications near room temperature.

Deposition Morphology and Magnetism of Co, Pt Adatoms and Small CoPt Adclusters on Ni(100) Substrate

Theoretical calculations of Co\(_{n-x}\)Pt\(_x\) (n = 1–3; \(x \le n\)) clusters on Ni(100) surface for their spin and orbital magnetic moments, as well as the magnetic anisotropy energy (MAE), are performed by using the density-functional theory (DFT) method including a self-consistent treatment of spin–orbit coupling (SOC). The results reveal that the ferromagnetic Co atoms in intra Co\(_{n-x}\)Pt\(_x\) adclusters couple ferromagnetically to their underlayer Ni atoms. The predominant inter-interactions between Co adatoms and Ni surface with the partly filled 3d band, together with the secondary intra-interactions between Co adatoms and Pt adatoms with fully filled 5d band, lead to a strongly quenched orbital moment (\(\mu _{\mathrm{{orb}}}^{\mathrm{{Co}}}\) = 0.18–0.14 \(\mu _B\); \(\mu _{\mathrm{{orb}}}^{\mathrm{{Pt}}} \approx \) 0.24–0.19 \(\mu _B\)) but a less quenched spin moment (\(\mu _{\mathrm{{spin}}}^{\mathrm{{Co}}} \approx \) 2.0 \(\mu _B\); \(\mu _{\mathrm{{spin}}}^{\mathrm{{Pt}}} \approx \) 0.35 \( \mu _B\)). The MAEs of CoPt adclusters exhibit a strong dependence on alloying effect rather than size effect, which is direly proportional to SOC strength and orbital moment anisotropy. The oxidations of CoPt clusters always reduce orbital magnetic moments and consequently decrease the corresponding MAEs.

Correlated oscillations of the magnetic anisotropy energy and orbital moment anisotropy in thin films: The role of quantum well states

We report the first-principles study of the correlated behavior of the magnetic anisotropy energy (MAE) and orbital moment anisotropy (OMA) as the functions of the thickness $N$ of the Fe film. The work is motivated by recent experimental studies combining photoemission, x-ray magnetic circular dichroism, and magnetic anisotropy measurements. In agreement with experiment, the correlated oscillations of $\mathrm{MAE}(N)$ and $\mathrm{OMA}(N)$ are obtained that have their origin in the formation of the 3d quantum well states (QWS) confined in the films. The main contribution to the oscillation amplitude comes from the surface layer. This is an interesting feature of the phenomenon consisting in the peculiar dependence of the physical quantities on the thickness of the film. We demonstrate that the band structure of the bulk Fe does not reflect adequately the properties of the 3d QWS in thin films and, therefore, does not provide the basis for understanding the oscillations of $\mathrm{MAE}(N)$ and $\mathrm{OMA}(N)$. A detailed point-by-point analysis in the two-dimensional (2D) Brillouin zone (BZ) of the film shows that the contribution of the $\mathrm{\ensuremath{\Gamma}}$ point, contrary to a rather common expectation, does not play an important role in the formation of the oscillations. Instead, the most important contributions come from a broad region of the 2D BZ distant from the center of the BZ. Combining symmetry arguments and direct calculations we show that orbital moments of the electronic states possess nonzero transverse components orthogonal to the direction of the spin magnetization. The account for this feature is crucial in the point-by-point analysis of the OMA. On the basis of the calculations for noncollinear spin configurations we suggest interpretations of two interesting experimental findings: fast temperature decay of the oscillation amplitude in $\mathrm{MAE}(N)$ and unexpectedly strong spin mixing of the initial states of the photoemission process.

Electronic, magnetic, and transport properties of Fe-intercalated2H−TaS2studied by means of the KKR-CPA method

The electronic, magnetic and transport properties of Fe intercalated 2H-TaS$_2$ have been investigated by means of the Korringa-Kohn-Rostoker (KKR) method. The non-stoichiometry and disorder in the system has been accounted for using the Coherent Potential Approximation (CPA) alloy theory. A pronounced influence of disorder on the spin magnetic moment has been found for the ferro-magnetically ordered material. The same applies for the spin-orbit induced orbital magnetic moment and magneto-crystalline anisotropy energy. The temperature-dependence of the resistivity of disordered 2H-Fe$_{0.28}$TaS$_2$ investigated on the basis of the Kubo-St\v{r}eda formalism in combination with the alloy analogy model has been found in very satisfying agreement with experimental data. This also holds for the temperature dependent anomalous Hall resistivity $ \rho_{\rm xy}(T) $. The role of thermally induced lattice vibrations and spin fluctuations for the transport properties is discussed in detail.

Orbital moment anisotropy in ultrathin FePt layers

The anisotropy of the Fe orbital moment is investigated in epitaxial ultrathin ($l2\phantom{\rule{0.28em}{0ex}}\mathrm{nm}$) FePt layers by angular dependent x-ray magnetic circular dichroism (XMCD) for two distinct epitaxial systems, CoO/FePt/Pt(001) and Pt/FePt/MnPt/Pt(001). Element selective hysteresis loops obtained from the XMCD signal at the Fe ${L}_{3}$ edge are used to quantify the anisotropy constants, which are consistent with the corresponding chemical order parameter. A careful procedure for XMCD sum rules data analysis is set up to avoid experimental overestimation of the orbital moment. The measured orbital moment of Fe is found comparable to theoretical values and shows a significant anisotropy. This orbital moment anisotropy is discussed in the light of the current theoretical understanding of magnetocrystalline anisotropy in ordered alloys.