Orbital Magnetic Moments Research Articles

Orbital Hall effect in bilayer transition metal dichalcogenides: From the intra-atomic approximation to the Bloch states orbital magnetic moment approach

Using an effective Dirac model, we study the orbital Hall effect (OHE) in bilayers of transition metal dichalcogenides with 2H stacking (2H-TMD). We use first-order perturbation theory in the interlayer coupling of the bilayer system to obtain analytical expressions for the orbital Hall conductivity in the linear response regime. We use two distinct descriptions of the orbital angular momentum (OAM) operator. The first one is the intra-atomic approximation that considers only the intrasite contribution to the OAM [Cysne et al., Phys. Rev. Lett. 126, 056601 (2021)]. The second one uses the Berry phase formula of the orbital (valley) magnetic moment to describe the OAM operator [Bhowal and Vignale, Phys. Rev. B 103, 195309 (2021)]. This approach includes both intersite and intrasite contributions to the OAM. Our results suggest that the two approaches agree qualitatively in describing the OHE in bilayers of 2H-TMDs, although they present some quantitative differences. We also show that interlayer coupling plays an essential role in understanding the OHE in the unbiased bilayer of 2H-TMD. This coupling causes the Bloch states to become bonding (antibonding) combinations of states of individual layers, demanding the consideration of the non-Abelian structure of the orbital magnetic moment to the occurrence of OHE. As we discuss throughout the work, the emerging picture of transport of OAM in the unbiased bilayer of 2H-TMDs based on OHE is very different from the usual picture based on the valley Hall effect, shedding new light on previous experimental results. We also discuss the effect of the inclusion of a gate-voltage bias in the bilayer system. Our work gives support to recent theoretical predictions on OHE in two-dimensional materials.

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.

Structural, electronic and magnetic properties of La1.5Ca0.5(Co0.5Fe0.5)IrO6 double perovskite

In this work, we report the synthesis and investigation of structural, electronic, and magnetic properties of La1.5Ca0.5(Co0.5Fe0.5)IrO6. Our polycrystalline sample forms as a single-phase double perovskite in monoclinic P21/n space group. Co and Ir are most likely in bivalent and tetravalent oxidation states, respectively, while Mössbauer spectroscopy indicates that Fe is in a trivalent state. The ac and dc magnetization data suggest a ferrimagnetic behavior resulting from the presence of two antiferromagnetic sublattices at Co/Fe and Ir sites. The large coercive field HC≃ 32 kOe observed at 10 K, comparable to that of other double perovskites of interest for hard magnets, is discussed in terms of the structural distortion and the spin and orbital magnetic moments of the transition metal ions.

Suppression of magneto-optical transport in tilted Weyl semimetals by orbital magnetic moment

By incorporating the orbital magnetic moment, we investigate the magneto-optical transport of Weyl semimetals within a semiclassical approximation. In the linear or nonlinear response regime, an analytic expression for the magnetoconductivity is obtained, where a new term due to the orbital magnetic moment is added, and leads to a partial cancellation for the total magnetoconductivities. This suppressed feature is further manifested by analyzing the linear and quadratic contribution in the magnetic field to magnetoconductivities. This result may be used to explain the deviation between the recent theory and experiment.

Observing the orbital angular momentum of Fe and Co in chiral magnet Fe0.75Co0.25Si using soft x-ray magnetic circular dichroism

The intermetallic compound Fe1−xCoxSi has a helical magnetic order for 0.05<x<0.8, whereas its orbital angular momentum contributing to the occurrence of a Dzyaloshinskii–Moriya interaction has not yet been verified. We applied soft x-ray magnetic circular dichroism spectroscopy on the Fe L2,3 and Co L2,3 edges below Tc for Fe0.75Co0.25Si such that their orbital magnetic moments morb were evaluated independently. The dichroic signals provide direct experimental evidence that morb for both Fe and Co is coupled in a parallel manner with each spin counterpart mspin. The ratio of morb to mspin is independently estimated as morb/mspin∼3% for Fe and 9% for Co. By comparing the average of the two mspin values with the saturated magnetization using a commercial superconducting quantum interference device (SQUID) magnetometer, the hole number in the d bands for both Fe and Co is roughly estimated as approximately 1.5. This suggests that Fe and Co should be arranged closely for stabilizing the ferromagnetic moments.

Origin of perpendicular magnetic anisotropy in CoxFe3−xO4+δ thin films studied by x-ray magnetic circular and linear dichroisms

We investigate the element-specific spin and orbital states and their roles on magnetic anisotropy in the Co-ferrite (Co$_x$Fe$_{3-x}$O$_{4+\delta}$ (001)) thin films which exhibit perpendicular magnetic anisotropy (PMA). The origin of PMA in the low $x$ region ($x$ $<$ 1) can be mainly explained by the large perpendicular orbital magnetic moments in the Co$^{2+}$ (3$d^7$) states detected by X-ray magnetic circular and linear dichroisms (XMCD/XMLD). The XMLD for a PMA film ($x=0.2$) with square hysteresis curve shows the oblate charge distribution in the Co$^{2+}$ site, which is consistent with the change in local nearest neighbor distance in Co detected by extended X-ray absorption fine structure analysis. Our finding reveals that the microscopic origin of PMA in Co-ferrite comes from the enhanced orbital magnetic moments along out-of-plane [001] direction through in-plane charge distribution by tensile strain, which adds the material functionalities in spinel ferrite thin films from the viewpoint of strain and orbital magnetic moments.

Light-Induced Magnetization at the Nanoscale.

Triggering and switching magnetic moments is of key importance for applications ranging from spintronics to quantum information. A noninvasive ultrafast control at the nanoscale is, however, an open challenge. Here, we propose a novel laser-based scheme for generating atomic-scale charge current loops within femtoseconds. The associated orbital magnetic moments remain ferromagnetically aligned after the laser pulses have ceased and are localized within an area that is tunable via laser parameters and can be chosen to be well below the diffraction limit of the driving laser field. The scheme relies on tuning the phase, polarization, and intensities of two copropagating Gaussian and vortex laser pulses, allowing us to control the spatial extent, direction, and strength of the atomic-scale charge current loops induced in the irradiated sample upon photon absorption. In the experiment we used He atoms driven by an ultraviolet and infrared vortex-beam laser pulses to generate current-carrying Rydberg states and test for the generated magnetic moments via dichroic effects in photoemission. Abinitio quantum dynamic simulations and analysis confirm the proposed scenario and provide a quantitative estimate of the generated local moments.

Critical behavior and phase diagram of layered ferromagnetic FeTa3S6 single crystals

The magnetization of the highly air-stable two-dimensional (2D) intrinsic ferromagnet ${\mathrm{FeTa}}_{3}{\mathrm{S}}_{6}$ single crystal has been systematically investigated. Magnetization measurement revealed paramagnetic to ferromagnetic (PM-FM) phase transition at around 35 K and a strong magnetic anisotropy along the crystallographic c axis ($H\ensuremath{\parallel}c$). The critical exponents $\ensuremath{\beta}$ = 0.189(2), $\ensuremath{\gamma}$ = 1.423(1), and $\ensuremath{\delta}=8.531(7)$ with ${T}_{c}$ = 35 K suggest that the spin interaction of a two-dimensional (2D) Ising type in ${\mathrm{FeTa}}_{3}{\mathrm{S}}_{6}$ coupled with long-range ($\ensuremath{\sigma}=1.581$) interaction. A comprehensive magnetic phase diagram based on detailed magnetization measurements and universality scaling of ${\mathrm{FeTa}}_{3}{\mathrm{S}}_{6}$ is constructed over three magnetic field regions. The magnetic phase diagram of ${\mathrm{FeTa}}_{3}{\mathrm{S}}_{6}$ is analogous to that of ${\mathrm{CrNb}}_{3}{\mathrm{S}}_{6}$, which exhibits a chiral magnetic soliton lattice. DFT simulation reveals that the large magnetic anisotropy energy in ${\mathrm{FeTa}}_{3}{\mathrm{S}}_{6}$ originates from the combined effects such as considerable orbital magnetic moment, host lattice spin-orbit coupling, and hybridization between host lattice $2\mathrm{H}\ensuremath{-}{\mathrm{TaS}}_{2}$ and the intercalated Fe component. Furthermore, the magnetic anisotropy ($\ensuremath{\parallel}$ c) in ${\mathrm{FeTa}}_{3}{\mathrm{S}}_{6}$ is due to the dominant contribution of the spin conserving process $\mathrm{\ensuremath{\Delta}}{S}_{z}$ = 0 in magnetic anisotropy energy, which differs from that of ${\mathrm{CrNb}}_{3}{\mathrm{S}}_{6}$, or ${\mathrm{MnNb}}_{3}{\mathrm{S}}_{6}$, where the spin flipping process $\mathrm{\ensuremath{\Delta}}{S}_{z}$ = 1 dominates, causing in-plane ($\ensuremath{\perp}$ c) magnetic anisotropy.

Magnetoelastic anisotropy in Heusler-type Mn2−δCoGa1+δ films

Perpendicular magnetization is essential for high-density memory application using magnetic materials. High-spin polarization of conduction electrons is also required for realizing large electric signals from spin-dependent transport phenomena. Heusler alloy is a well-known material class showing the half-metallic electronic structure. However, its cubic lattice nature favors in-plane magnetization and thus minimizes the perpendicular magnetic anisotropy (PMA), in general. This study focuses on an inverse-type Heusler alloy, Mn$_{2-\delta}$CoGa$_{1+\delta}$ (MCG) with a small off-stoichiometry ($\delta$) , which is expected to be a half-metallic material. We observed relatively large uniaxial magnetocrystalline anisotropy constant ($K_\mathrm{u}$) of the order of 10$^5$ J/m$^3$ at room temperature in MCG films with a small tetragonal distortion of a few percent. A positive correlation was confirmed between the $c/a$ ratio of lattice constants and $K_\mathrm{u}$. Imaging of magnetic domains using Kerr microscopy clearly demonstrated a change in the domain patterns along with $K_\mathrm{u}$. X-ray magnetic circular dichroism (XMCD) was employed using synchrotron radiation soft x-ray beam to get insight into the origin for PMA. Negligible angular variation of orbital magnetic moment ($\Delta m_\mathrm{orb}$) evaluated using the XMCD spectra suggested a minor role of the so-called Bruno's term to $K_\mathrm{u}$. Our first principles calculation reasonably explained the small $\Delta m_\mathrm{orb}$ and the positive correlation between the $c/a$ ratio and $K_\mathrm{u}$. The origin of the magnetocrystalline anisotropy was discussed based on the second-order perturbation theory in terms of the spin--orbit coupling, claiming that the mixing of the occupied $\uparrow$- and the unoccupied $\downarrow$-spin states is responsible for the PMA of the MCG films.

Origin of magnetic field-induced magnetic anisotropy in amorphous CoFeB thin films

Magnetic anisotropy (MA) is an important property of magnetic materials, which not only determines the orientation of the magnetic moment in the magnetic material but also influences the working frequency of magnetoelectric devices. Unrevealing the origin of MA has become an important topic and attracts lasting interest. Here, we report a quite significant magnetic field-induced uniaxial MA in amorphous CoFeB thin films containing double ferromagnetic atoms. The thickness independence of MA was obtained by observing a series of hysteresis loops and magnetic domains. The MA is proved subtly to be related to the variation of orbital magnetic moment acquired by ferromagnetic resonance. Furthermore, we found that atoms combine into clusters and incline to an order in amorphous CoFeB thin films with field-induced MA. Based on these experimental results, we proposed a direction-like order model to interpret the origin of magnetic field-induced MA in amorphous CoFeB thin films well.

Electron Correlation Enhances Orbital Polarization at a Ferromagnetic Metal/Insulator Interface: Depth-Resolved X-ray Magnetic Circular Dichroism and First-Principles Study

The Fe(CoB)/MgO interface is vital to spintronics as it exhibits the tunneling magnetoresistance (TMR) effect and interfacial perpendicular magnetic anisotropy (PMA) simultaneously. To further enhance TMR and PMA for the development of high-density magnetoresistive random access memory, it is essential to clarify the behavior of Fe atoms interfaced with MgO. This study reveals that the spin and orbital magnetic moments of Fe are enhanced at the Fe/MgO interface. The enhancement in the orbital magnetic moment is much more significant than that predicted by the standard density functional theory. Theoretical calculations based on the orbital polarization correction reproduce this enhancement, the origin of which is attributed to the electron–electron correlation resulting from electron localization at the Fe/MgO interface. The present findings highlight the importance of electron–electron correlation at ferromagnet/oxide interfaces, which has often been disregarded in spintronics.

Elucidate interfacial disorder effects on the perpendicular magnetic anisotropy at Fe/MgO heterostructure from first-principles calculations

The interfacial perpendicular magnetic anisotropy (PMA) plays a key role in spintronic applications such as memory recording and computational devices. Despite robust PMA being reported at the Fe/MgO interface, there are still inconsistencies in the disorder effects on the interfacial magnetic anisotropy. Here we reported a comprehensive study of the influence of the interfacial disorder, including the underoxidization, overoxidization, and oxygen migration, on the PMA of the Fe/MgO interface using first-principles calculations. Compared to the pristine Fe/MgO interface, the underoxidation at the Fe/MgO interface keeps the interfacial PMA but reduces the interfacial anisotropy constant (K i ). The overoxidization and oxygen migration at the interface both reduce the K i and even switch the easy magnetization axis from the out-of-plane to in-plane direction at high oxygen percentage. In all the cases, the K i was found strongly correlated to the difference of the orbital magnetic moment along the in-plane and out-of-plane direction. Calculated layer-resolved and orbital-resolved K i revealed that the orbital coupling between the d xy and states of the interfacial Fe layer plays a key role in determining the interfacial magnetic anisotropy. This work provides deep insights into the oxidation effects on the interfacial magnetic anisotropy of Fe/MgO system and a possible avenue to tune the K i via interfacial engineering.

Emergence of room-temperature perpendicular magnetic anisotropy in metallic NiCo2O4 thin film

Room-temperature perpendicular magnetic anisotropy (PMA) is an essential property for devices based on spintronic technology, and is still a great challenge in transition-metal oxide conductors. In this work, we demonstrated the development of the high-quality NiCo2O4 (NCO) films onto MgAl2O4 (MAO) substrate by precise control over the growth parameters in the pulsed laser deposition process. The characteristics of strong out-of-plane magnetic easy axis, robust anomalous Hall effect, and smaller angle dependence of magnetoresistance in perpendicular direction are observed in metallic NCO films above 300 K. Thus, the obvious room-temperature PMA behavior is supported by these electric transport and magnetic results. This work is further expanded to investigate the valence state, spin and orbital magnetic moment of the NCO film. The Ni2+, Ni3+, Co2+, and Co3+ cations are existed in NCO film, and the orbital magnetic moment of Ni and Co are antiparallel with each other. As a result, the cation concentration ratio exhibits significant influence upon the magnetism and electric transport. The remarkable coexistence of room-temperature PMA and metallic transport is promising to the multi-function application in spintronics devices.

XAS and XMCD Reveal a Cobalt(II) Imide Undergoes High-Pressure-Induced Spin Crossover

The spin crossover (SCO) transition is investigated in two molecular Co2+ bis-imide compounds, Co(dpzca)2 and Co(pypzca)2 (where Hdpzca = N-(2-pyrazylcarbonyl)-2-pyrazinecarboxamide and Hpypzca = N-(2-pyrazylcarbonyl)-2-pyridinecarboxamide). They crystallize solvent-free with similar crystal structures but have been reported to exhibit different temperature-dependent magnetic behaviors. Using temperature- and pressure-dependent element selective X-ray absorption spectroscopy (XAS and XMCD) measurements, it is revealed herein that although Co(pypzca)2 does not afford a temperature-induced SCO, it undergoes a reversible pressure-induced SCO transition that is less abrupt, and is complete at a higher pressure (3.5 GPa), than for Co(dpzca)2 (0.5 GPa). Wave function-based calculations performed on isolated complexes confirm the LS state nature of Co(dpzca)2 at low temperatures, and the values of spin and orbital magnetic moments are determined. Calculations show the similarity of ground-state properties for HS Co(dpzca)2 and HS Co(pypzca)2 and the existence of a double-well HS-LS in the potential energy surface for both compounds. It is concluded that the observed, significant differences in pressure- and temperature-induced SCO transitions of Co(dpzca)2 versus Co(pypzca)2 are probably due to different intermolecular interactions between Co(dpzca)2 and Co(pypzca)2, which would hamper the temperature-induced SCO in Co(pypzca)2.

Magnetic anisotropy and orbital magnetic moment in Co films and Co/X bilayers ( X=Pd and Pt)

Magnetocrystalline anisotropy (MCA) energy and the anisotropy of the orbital magnetic moment (AOM), relations between them, and methods of their calculation are investigated for the (001) fcc Co film and $\mathrm{Co}/X$ bilayers ($X=\mathrm{Pd}$ and Pt), using a realistic tight-binding model. The relations derived by Bruno [Phys. Rev. B 39, 865 (1989)] and van der Laan [J. Phys.: Condens. Matter 10, 3239 (1998)], including the AOM of Co only, are found to give largely incorrect mean values of the MCA energy but reproduce its oscillatory variation versus the Co thickness, with scaling factors needed for the bilayers. The presently proposed extension of the Bruno relation, with the AOM of both Co and Pd or Pt included, predicts the correct sign of the MCA energy for both bilayers and reproduces its magnitude and oscillation pattern very well, without extra scaling, for the Co/Pd bilayer, though this relation is not satisfied locally, by the MCA and AOM layer terms. A similarly extended van der Laan relation fails to reproduce the MCA energy, its sign, and the oscillation pattern, and largely overestimates its magnitude. For all investigated systems, the Co orbital moment oscillates versus the Co thickness with the 2 monolayer (ML) period for the out-of-plane direction of magnetization and the 5 ML period for the in-plane direction while the oscillations of the Pd and Pt orbital moments are more complex and similar for both magnetization directions. The exact and approximate MCA energies obtained with the force theorem and the perturbation theory (PT), respectively, are close to each other for the Co film and the Co/Pd bilayer. For the Co/Pt bilayer, only the mean value of the MCA energy is well approximated by the PT while its oscillation amplitude is overestimated a few times due to the large SOC in Pt. It is also shown that the MCA energy includes the intraband term, usually neglected, but, in fact, finite and vital for systems without the inversion symmetry as its magnitude is comparable to that of the interband term for the Co/Pd bilayer.

MARMOT: magnetism, anisotropy, and more, using the relativistic disordered local moment picture at finite temperature

We present MARMOT, a hybrid Python/FORTRAN implementation of the disordered local moment picture within multiple scattering density-functional theory. MARMOT takes atom-centred, scalar-relativistic potentials and constructs an effective medium (within the coherent potential approximation) to describe the disordered magnetic moment orientations at finite temperature. By solving the single-site scattering problem fully relativistically, spin–orbit effects are included, allowing the magnetocrystalline anisotropy to be calculated. Magnetic transition temperatures, spin and orbital moments, the density-of-states, and analytical parameterizations of the magnetic potential energy surface can also be calculated. Here, we describe the theory and practical implementation of MARMOT, and demonstrate its use by calculating Curie temperatures, magnetizations and anisotropies of bcc Fe, GdFe2 and YCo5.

Unveiling a Chemisorbed Crystallographically Heterogeneous Graphene/L10-FePd Interface with a Robust and Perpendicular Orbital Moment.

A crystallographically heterogeneous interface was fabricated by growing hexagonal graphene (Gr) using chemical vapor deposition (CVD) on a tetragonal FePd epitaxial film grown by magnetron sputtering. FePd was alternately arranged with Fe and Pd in the vertical direction, and the outermost surface atom was identified primarily as Fe rather than Pd. This means that FePd has a high degree of L10-ordering, and the outermost Fe bonds to the carbon of Gr at the interface. When Gr is grown by CVD, the crystal orientation of hexagonal Gr toward tetragonal L10-FePd selects an energetically stable structure based on the van der Waals (vdW) force. The atomic relationship of Gr/L10-FePd, which is an energetically stable interface, was unveiled theoretically and experimentally. The Gr armchair axis was parallel to FePd [100]L10, where Gr was under a small strain by chemical bonding. Focusing on the interatomic distance between the Gr and FePd layers, the distance was theoretically and experimentally determined to be approximately 0.2 nm. This shorter distance (≈0.2 nm) can be explained by the chemisorption-type vdW force of strong orbital hybridization, rather than the longer distance (≈0.38 nm) of the physisorption-type vdW force. Notably, depth-resolved X-ray magnetic circular dichroism analyses revealed that the orbital magnetic moment (Ml) of Fe in FePd emerged at the Gr/FePd interface (@inner FePd: Ml = 0.16 μB → @Gr/FePd interface: Ml = 0.32 μB). This interfacially enhanced Ml showed obvious anisotropy in the perpendicular direction, which contributed to interfacial perpendicular magnetic anisotropy (IPMA). Moreover, the interfacially enhanced Ml and interfacially enhanced electron density exhibited robustness. It is considered that the shortening of the interatomic distance produces a robust high electron density at the interface, resulting in a chemisorption-type vdW force and orbital hybridization. Eventually, the robust interfacial anisotropic Ml emerged at the crystallographically heterogeneous Gr/L10-FePd interface. From a practical viewpoint, IPMA is useful because it can be incorporated into the large bulk perpendicular magnetic anisotropy (PMA) of L10-FePd. A micromagnetic simulation assuming both PMA and IPMA predicted that perpendicularly magnetized magnetic tunnel junctions (p-MTJs) using Gr/L10-FePd could realize 10-year data retention in a small recording layer with a circular diameter and thickness of 10 and 2 nm, respectively. We unveiled the energetically stable atomic structure in the crystallographically heterogeneous interface, discovered the emergence of the robust IPMA, and predicted that the Gr/L10-FePd p-MTJ is significant for high-density X nm generation magnetic random-access memory (MRAM) applications.

High pressure induced secondary and tertiary gaps in relaxed graphene on hexagonal boron nitride

We study the electronic phase diagram of fully relaxed moir\'e superlattices in the monolayer graphene on hexagonal boron nitrogen (MLG/BN) with varying twist angle ($\ensuremath{\theta}$) and high pressure. In systems with small $\ensuremath{\theta}$, the secondary gap (${\mathrm{\ensuremath{\Delta}}}_{S}^{(e)}$) on the electron side and the tertiary gap (${\mathrm{\ensuremath{\Delta}}}_{T}^{(h)}$) on the hole side are opened by the high pressure up to 8 GPa, and the pressure also greatly enhances the primary band gap (${\mathrm{\ensuremath{\Delta}}}_{0}$) at the charge neutrality point and the secondary gap (${\mathrm{\ensuremath{\Delta}}}_{S}^{(h)}$) on the hole side. Under a given high pressure, the gaps ${\mathrm{\ensuremath{\Delta}}}_{T}^{(h)}, {\mathrm{\ensuremath{\Delta}}}_{S}^{(e)}$, and ${\mathrm{\ensuremath{\Delta}}}_{S}^{(h)}$ become closed in succession with varying $\ensuremath{\theta}$ from ${0}^{\ensuremath{\circ}}$ to ${2}^{\ensuremath{\circ}}$. In contrast to the direct ${\mathrm{\ensuremath{\Delta}}}_{0}$ and ${\mathrm{\ensuremath{\Delta}}}_{S}^{(h)}$ at small $\ensuremath{\theta}, {\mathrm{\ensuremath{\Delta}}}_{S}^{(e)}$ only becomes direct for a range of medium pressure, and ${\mathrm{\ensuremath{\Delta}}}_{T}^{(h)}$ remains indirect. Compared with the local continuum Hamiltonian (${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{H}}_{c}$), the effects of nonlocal terms and those beyond the first harmonics in the full Hamiltonian become important for the quantitative values of the gaps under high pressure, while the qualitative behavior of the gaps with increasing pressure can still be understood by the variations of parameters in ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{H}}_{c}$. The band isolation due to the pressure induced gaps leads to emergence or evolution of the van Hove singularities, the ballistic resistance peaks, and the peaks of the density of orbital magnetic moments, which may be observed experimentally.

Magnetic anisotropy of the van der Waals ferromagnet Cr2Ge2Te6 studied by angular-dependent x-ray magnetic circular dichroism

The van der Waals ferromagnet ${\mathrm{Cr}}_{2}{\mathrm{Ge}}_{2}{\mathrm{Te}}_{6}$ (CGT) has a two-dimensional crystal structure where each layer is stacked through van der Waals force. We have investigated the nature of the ferromagnetism and the weak perpendicular magnetic anisotropy (PMA) of CGT by means of x-ray absorption spectroscopy and x-ray magnetic circular dichroism (XMCD) studies of CGT single crystals. The XMCD spectra at the Cr ${L}_{2,3}$ edge for different magnetic field directions were analyzed on the basis of the cluster-model multiplet calculation. The Cr valence is confirmed to be $3+$ and the orbital magnetic moment is found to be nearly quenched, as expected for the high-spin ${t}_{2g}^{3}$ configuration of the ${\mathrm{Cr}}^{3+}$ ion. A large ($\ensuremath{\sim}0.2$ eV) trigonal crystal-field splitting of the ${t}_{2g}$ level caused by the distortion of the $\mathrm{Cr}{\mathrm{Te}}_{6}$ octahedron has been revealed, while the single-ion anisotropy (SIA) of the Cr atom is found to have a sign opposite to the observed PMA and too weak compared to the reported anisotropy energy. The present result suggests that anisotropic exchange coupling between the Cr atoms through the ligand Te $5p$ orbitals having strong spin-orbit coupling has to be invoked to explain the weak PMA of CGT, as in the case of the strong PMA of ${\mathrm{CrI}}_{3}$.

Quenching of spin-orbit coupling and signature of Griffiths Phase in nanocrystalline La0.6Ba0.4MnO3 perovskite manganite

The size-dependent structural and magnetic properties of nano and bulk samples of 40 ​mol% Ba2+-doped LaMnO3 (i.e., La0.6Ba0.4MnO3) manganite have been investigated in detail. The Rietveld refinement of X-ray diffraction data confirms that nano and bulk La0.6Ba0.4MnO3 manganites crystallize into ideal cubic perovskite structure with Pm3¯m space group. The refined unit cell parameters decrease with increasing calcinations temperature or particle size. The temperature dependent magnetization measurements reveal that both the bulk and nano samples exhibit paramagnetic (PM) to ferromagnetic (FM) phase transition at Curie temperature (TC). A distinct bifurcation between magnetization curves under zero-field cooled (MZFC) and field-cooled (MFC) measurements reveals the possible existence of frustrated magnetic ordering or spin glass clusters. For nano sample, a sharp downward deviation in inverse susceptibility from Curie-Weiss law is observed, which indicates the existence of Griffiths Phase. The analysis of the field dependent magnetization M(H) curves measured at 10 ​K, in terms of saturation moments, reveals that there is a coupling between spin and orbital magnetic moments, in bulk sample of La0.6Ba0.4MnO3 manganite, which can be quenched by reducing particle size of the manganite. According to the Banerjee's criterion, nano sample exhibits first-order magnetic transition and bulk sample shows second-order magnetic transition in the low magnetic field region.