Triaxial Anisotropy Research Articles

Importance of magnetic shape anisotropy in determining triaxial magnetic anisotropy of ferromagnetic semiconductor CrSCl monolayer

Abstract Magnetic anisotropy (MA) is pivotal for stabilizing long-range magnetic order in two-dimensional (2D) systems against thermal fluctuations. Here, we conduct a comprehensive investigation of the electronic and magnetic properties of CrSCl monolayer using first-principles methods and Monte Carlo (MC) simulations. Our results reveal that CrSCl monolayer exhibit a direct band gap ferromagnetic semiconductor (FMS) with a high Curie temperature (TC, 143 K). Notably, we identify triaxial magnetic anisotropy in this monolayer, characterized by the easy magnetization axis along the y-axis, intermediate axis along the x-axis, and hard axis along the z-axis. This anisotropy arises from a combination of magnetocrystalline anisotropy and shape anisotropy, in which shape anisotropy dominating over weak magnetocrystalline anisotropy. Orbital projection analysis shows that the major contribution of magnetic anisotropy energy comes from the d orbital of Cr atom. These findings provide some insights into the strain response of MA and suggest that studies of other FM monolayers may uncover future contenders for strain-switchable and ultra-compact spintronics devices.

Tri-axial magnetic alignment and magnetic anisotropies in misfit-layered calcium-based cobaltites doped with rare-earth ions

In this study, we introduce an original method for quantifying tri-axial magnetic anisotropy in [Ca2CoO3-δ]0.62CoO2, and its rare earth (RE)-doped variants, [(Ca1-xREx)2CoO3-δ]0.62CoO2, utilizing a modulated rotating magnetic field of 10 T. Our findings reveal a significant correlation between the magnetic anisotropy and local structure of RE ions, particularly bond lengths and coordination numbers, which influence the magnetization axes of these magnetically aligned powders. We introduce an analytical methodology employing linear equations to calculate the magnetic susceptibilities along distinct crystallographic axes, enabling the prediction of tri-axial magnetic anisotropies at elevated concentrations of Er ions. This research not only advances our understanding of magnetic anisotropy control but also paves the way for the successful fabrication of triaxially-aligned ceramics using magneto-science techniques.

Ab initio calculation of magnetic anisotropy and thermal spin transition in the variable temperature crystal conformations of [Co(terpy)2]2.

The structure-property correlation of [Co(terpy)2]2+, which shows a spin crossover at 270 K, has been computationally investigated based on its variable temperature crystal structures. Among the employed DFT functionals, only the re-parametrized hybrid B3LYP* functional could describe the correct spin transition temperature. Explicit consideration of metal-ligand sigma bonding with dynamic electron correlation is found to be necessary for an accurate determination of the SCO temperature with multi-reference calculations. The metal-ligand axial bond distances are found to be the most significant internal coordinates in deciding SCO. A small structural change along the axial distance causes a change in the t2g orbital splitting pattern and a reorientation of the magnetization axes at the SCO temperature. The complex shows an unusual triaxial magnetic anisotropy, with an easy axis of magnetization developing at higher temperatures. The strong coupling of low-frequency wagging motion of the two terpyridine ligands with the spin states of the complex provides an effective pathway for the relaxation of magnetization, resulting in a small magnetic anisotropy barrier.

Dielectric tunability of magnetic properties in orthorhombic ferromagnetic monolayer CrSBr

Monolayer CrSBr is a recently discovered semiconducting spin-3/2 ferromagnet with a Curie temperature of around 146 K. In contrast to many other known 2D magnets, the orthorhombic lattice of CrSBr gives rise to spatial anisotropy of magnetic excitations within the 2D plane. Triaxial magnetic anisotropy and considerable magnetic dipolar interactions in CrSBr challenge its theoretical description in terms of spin Hamiltonians. Here, we employ a Green’s function formalism combined with first-principles calculations to study the magnetic properties of monolayer CrSBr in different regimes of surrounding dielectric screening. In the free-standing limit, the system is close to an easy-plane magnet, whose long-range ordering is partially suppressed. On the contrary, in the regime of large external screening, monolayer CrSBr behaves like an easy-axis ferromagnet with more stable magnetic ordering. Our findings suggest that anisotropic layered magnets form a potentially promising platform for studying the effects of substrate screening on magnetic ordering in 2D.

Spin-Lattice Coupled Metamagnetism in Frustrated van der Waals Magnet CrOCl.

The long-range magnetic ordering in frustrated magnetic systems is stabilized by coupling magnetic moments to various degrees of freedom, for example, by enhancing magnetic anisotropy via lattice distortion. Here, the unconventional spin-lattice coupled metamagnetic properties of atomically-thin CrOCl, a van der Waals antiferromagnet with inherent magnetic frustration rooted in the staggered square lattice, are reported. Using temperature- and angle-dependent tunneling magnetoconductance (TMC), in complementary with magnetic torque and first-principles calculations, the antiferromagnetic (AFM)-to-ferrimagnetic (FiM) metamagnetic transitions (MTs) of few-layer CrOCl are revealed to be triggered by collective magnetic moment flipping rather than the established spin-flop mechanism, when external magnetic field (H) enforces a lattice reconstruction interlocked with the five-fold periodicity of the FiM phase. The spin-lattice coupled MTs are manifested by drastic jumps in TMC, which show anomalous upshifts at the transition thresholds and persist much higher above the AFM Néel temperature. While the MTs exhibit distinctive triaxial anisotropy, reflecting divergent magnetocrystalline anisotropy of the c-axis AFM ground state, the resulting FiM phase has an a-c easy plane in which the magnetization axis is freely rotated by H. At the 2D limit, such a field-tunable FiM phase may provide unique opportunities to explore exotic emergent phenomena and novel spintronicsdevices.

Dynamics of a solitonic vortex in an anisotropically trapped superfluid

We analytically study the dynamics of a solitonic vortex (SV) in a superfluid confined in a non-axisymmetric harmonic trap. The study provides a framework for analyzing the role of the trap anisotropy in the oscillation of SVs observed in recent experiments on atomic Bose and Fermi superfluids. The emergence of common and statistics-dependent features is traced in a unified approach to both types of fluid. Our description, built in the hydrodynamic formalism, is based on a Lagragian approach which incorporates the vortex location as dynamical parameters of a variational ansatz. Previous operative Hamiltonian pictures are recovered through a canonically traced procedure. Our results improve the understanding of the experimental findings. Some of the observed features are shown to be specific to the tri-axial anisotropy of the trap. In particular, we characterize the nontrivial dependence of the oscillation frequency on the trapping transversal to the vortical line. The study reveals also the crucial role played by the nonlinear character of the dynamics in the observed oscillation: for the considered experimental conditions, the frequency, and, in turn, the effective inertial mass of the vortex, are found to significantly depend on the amplitude of the generated motion. It is also uncovered how the coupling with collective modes of the fluid induces a non-negligible shift in the oscillation frequency. The appearance of fine-structure features in the SV trajectory is predicted.

Origin and regulation of triaxial magnetic anisotropy in the ferromagnetic semiconductor CrSBr monolayer.

Magnetic anisotropy plays a vital role in stabilizing the long-range magnetic order of two-dimensional ferromagnetic systems. In this work, using the first-principles method, we systematically explored the triaxial magnetic anisotropic properties of a ferromagnetic semiconductor CrSBr monolayer, which is recently exfoliated from its bulk. Further analysis shows that the triaxial magnetic anisotropic properties originate from the coexistence of the magnetic dipole-dipole interaction (shape anisotropy) and the spin-orbit coupling interaction (magnetocrystalline anisotropy). Interestingly, the shape anisotropy, which has been neglected in most previous works, dominates over the magnetocrystalline anisotropy. Besides, the experimental Curie temperature of the CrSBr monolayer is well reproduced using Monte Carlo simulations. What is more, the easy magnetic axes and ferromagnetism in the CrSBr monolayer can be manipulated by strains and are relatively more susceptible to the uniaxial strain in the x direction. Our study not only explains the mechanism of triaxial magnetic anisotropy of the CrSBr monolayer, but also sheds light on how to tune the magnetic anisotropy and Curie temperature in ferromagnetic monolayers.

Magneto-structural properties of rhombohedral Ni and Ni–B nanotubes deposited by electroless-plating in track-etched mica templates

Rhombohedral Ni-based nanotubes embedded in mica templates display triaxial magnetic anisotropy. This provides an additional degree of freedom for tuning the particular magnetic behavior exhibited by these nanostructures.

Anisotropic Gigahertz Antiferromagnetic Resonances of the Easy-Axis van der Waals Antiferromagnet CrSBr.

We report measurements of antiferromagnetic resonances in the van der Waals easy-axis antiferromagnet CrSBr. The interlayer exchange field and magnetocrystalline anisotropy fields are comparable to laboratory magnetic fields, allowing a rich variety of gigahertz-frequency dynamical modes to be accessed. By mapping the resonance frequencies as a function of the magnitude and angle of applied magnetic field, we identify the different regimes of antiferromagnetic dynamics. The spectra show good agreement with a Landau-Lifshitz model for two antiferromagnetically coupled sublattices, accounting for interlayer exchange and triaxial magnetic anisotropy. Fits allow us to quantify the parameters governing the magnetic dynamics: At 5 K, the interlayer exchange field is μ0HE = 0.395(2) T, and the hard and intermediate-axis anisotropy parameters are μ0Hc = 1.30(2) T and μ0Ha = 0.383(7) T. The existence of within-plane anisotropy makes it possible to control the degree of hybridization between the antiferromagnetic resonances using an in-plane magnetic field.

Triaxial magnetic anisotropy and Morin transition in α-Fe2O3 epitaxial films characterized by spin Hall magnetoresistance

We grew epitaxial thin films of hematite (α-Fe2O3) on (0 0 0 1) Al2O3 substrates by pulsed laser deposition and investigated their magnetic properties. α-Fe2O3 films grown at lower temperatures are found to undergo the Morin transition at higher temperatures, implying that lowering the growth temperature and managing lattice defects associated with strain relaxation are key to realizing Morin transition. We also characterized films' magnetic properties by spin Hall magnetoresistance (SMR). We show that tri-axial magnetic anisotropy can be detected as SMR features having a 60° period with respect to in-plane magnetic field rotations. Furthermore, a large change in SMR ratio associated with Néel vector re-orientation due to Morin transition is seen. Details of SMR properties for α-Fe2O3 films and their analysis results, including the influence of the fabrication process on SMR behaviors, are discussed.

Intrinsic ferromagnetism and the quantum anomalous Hall effect in two-dimensional MnOCl2 monolayers.

Due to their potential application in spintronic devices, two-dimensional (2D) ferromagnetic materials are highly desired. We used first-principles calculations and Monte Carlo simulations to investigate the electronic structure and magnetic characteristics of the MnOCl2 monolayers. We discovered two stable monolayer structures, Pmna-MnOCl2 and Pmmn-MnOCl2. Our findings show that the Pmna-MnOCl2 monolayer is an intrinsic ferromagnetic semiconductor with an indirect band gap of 0.152 eV and a Curie temperature (TC) of 202 K, while the Pmmn-MnOCl2 monolayer is an intrinsic ferromagnetic Dirac semimetal with a high TC (910 K) and triaxial magnetic anisotropy. We also show that a Pmmn-MnOCl2 monolayer with a nontrivial band gap of 6.2 meV can achieve the quantum anomalous Hall effect (QAHE) with Chern number C = 1. Additionally, the existence of a gapless edge state can be flexibly regulated by choosing the terminal edges. Our studies reveal that the Pmmn-MnOCl2 monolayer can serve as a candidate material to achieve high-temperature QAHE.

Magnetic Domain State and Anisotropy in Hematite (α‐Fe2O3) From First‐Order Reversal Curve Diagrams

AbstractHematite carries magnetic signals of interest in tectonic, paleoclimatic, paleomagnetic, and planetary studies. First‐order reversal curve (FORC) diagrams have become an important tool for assessing the domain state of, and magnetostatic interactions among, magnetic particles in such studies. We present here FORC diagrams for diverse hematite samples, which provide a catalog for comparison with other studies and explain key features observed for hematite. Ridge‐type signatures typical of uniaxial single‐domain particle assemblages and “kidney‐shaped” FORC signatures, and combinations of these responses, occur commonly in natural and synthetic hematite. Asymmetric features that arise from the triaxial basal plane anisotropy of hematite contribute to vertical spreading in kidney‐shaped FORC distributions and are intrinsic responses even for magnetostatically noninteracting particles. The dominant FORC distribution type in a sample (ridge, kidney‐shaped, or mixture) depends on the balance between uniaxial/triaxial switching. The identified signals explain magnetization switching and anisotropy features that are intrinsic to the magnetic properties of hematite and other materials with multiaxial magnetic anisotropy.

Triaxial magnetic anisotropy in the two-dimensional ferromagnetic semiconductor CrSBr

Two-dimensional ferromagnets have recently drawn extensive attention, and here we study the electronic structure and magnetic properties of the bulk and monolayer of CrSBr using first-principles calculations and Monte Carlo simulations. Our results show that bulk CrSBr is a magnetic semiconductor and has the easy magnetization $b$ axis, hard $c$ axis, and intermediate $a$ axis. Thus the experimental triaxial magnetic anisotropy (MA) is well reproduced here, and it is identified to be the joint effects of spin-orbit coupling and magnetic dipole-dipole interaction. We find that bulk CrSBr has a strong ferromagnetic (FM) intralayer coupling but a marginal interlayer one. We also study the CrSBr monolayer in detail and find that the intralayer FM exchange persists and the shape anisotropy has a more pronounced contribution to the MA. Using the parameters of the FM exchange and the triaxial MA, our Monte Carlo simulations show that the CrSBr monolayer has Curie temperature ${T}_{\mathrm{C}}=175$ K. Moreover, we find that a uniaxial tensile (compressive) strain along the $a$ $(b)$ axis would further increase the ${T}_{\mathrm{C}}$.

Investigating Complex Magnetic Anisotropy in a Co(II) Molecular Compound: A Charge Density and Correlated Ab Initio Electronic Structure Study.

Understanding magnetic anisotropy and specifically how to tailor it is crucial in the search for high-temperature single-ion magnets. Herein, we investigate the magnetic anisotropy in a six-coordinated cobalt(II) compound that has a complex geometry and distinct triaxial magnetic anisotropy from the perspective of the electronic structure, using electronic spectra, ab initio calculations, and an experimental charge density, of which the latter two provides insight into the d-orbital splitting. The analysis showed that the d-orbital splitting satisfactorily predicted the complex triaxial magnetic anisotropy exhibited by the compound. Furthermore, a novel method to directly compare the ab initio results and the d-orbital populations obtained from the experimental charge density was developed, while a topological analysis of the density provided insights into the metal-ligand bonding. This work thus further establishes the validity of using d-orbitals for predicting magnetic anisotropy in transition metal compounds while also pointing out the need for a more frequent usage of the term triaxial anisotropy in the field of single-molecule magnetism.

Harmonic Fine Tuning and Triaxial Spatial Anisotropy of Dressed Atomic Spins

The addition of a weak oscillating field modifying strongly dressed spins enhances and enriches the system quantum dynamics. Through low-order harmonic mixing, the bichromatic driving generates additional rectified static field acting on the spin system. The secondary field allows for a fine tuning of the atomic response and produces effects not accessible with a single dressing field, such as a spatial triaxial anisotropy of the spin coupling constants and acceleration of the spin dynamics. This tuning-dressed configuration introduces an extra handle for the system full engineering in quantum control applications. Tuning amplitude, harmonic content, spatial orientation, and phase relation are control parameters. A theoretical analysis, based on perturbative approach, is experimentally tested by applying a bichromatic radiofrequency field to an optically pumped Cs atomic vapour. The theoretical predictions are precisely confirmed by measurements performed with tuning frequencies up to the third harmonic.

Stabilization of exponential number of discrete remanent states with localized spin–orbit torques

Using bilayer films of β-Ta/Ni0.8Fe0.2, we fabricate structures consisting of two, three, and four crossing ellipses, which exhibit shape-induced bi-axial, tri-axial, and quadro-axial magnetic anisotropy in the crossing area, respectively. Structures consisting of N crossing ellipses can be stabilized in 2N remanent states by applying (and removing) an external magnetic field. However, we show that with field-free spin–orbit torques induced by flowing currents in individual ellipses, the number of remanent states grows to 2N. Furthermore, when the current flows between the edges of different ellipses, the number of remanent states jumps to 22N, including states that exhibit a π-Néel domain wall in the overlap area. The very large number of accessible remanent magnetic states that are exhibited by the relatively simple magnetic structures paves the way for intriguing spintronics applications including memory devices.

Field-induced SIM behaviour of a Co(II) complex with a 1,1'-diacetylferrocene-derived ligand.

Herein, we report the synthesis and magnetic properties of the Co(ii) coordination compound with the 1,1'-bis(1-((pyrid-2-ylmethylene)hydrazono)ethyl)ferrocene (L) ligand, having the general formula [CoLCl2]. The static magnetic data analysis supported by the CASSCF/NEVPT2 calculations revealed the presence of the triaxial magnetic anisotropy with Dexp = +35.2 cm-1 and large rhombicity (E/D = 0.31) in this complex (Dcalc = +34.5 cm-1, E/Dcalc = 0.30). The dynamic magnetic data confirm that the complex shows a slow field-induced (HDC = 1000 Oe) magnetic relaxation behaviour.

Switching of multi-state magnetic structures via domain wall propagation triggered by spin-orbit torques

Spin-orbit torques emerge as a promising method for manipulating magnetic configurations of spintronic devices. Here, we show that these torques can induce a magnetization reversal via domain wall propagation which may open new ways in developing novel spintronic devices and in particular in realizing high-density multi-level magnetic memory. Our devices are bi-layer heterostructures of Ni0.8Fe0.2 on top of β-Ta patterned in the form of two or three crossing ellipses which exhibit in the crossing area shape-induced biaxial and triaxial magnetic anisotropy, respectively. We demonstrate field-free switching between discrete remanent magnetic states of the structures by spin-orbit torques induced by flowing electrical current through one of the ellipses. We note switchings induced by the coupling between the ellipses where current flowing in one ellipse triggers a reversal in a neighboring ellipse which propagates from the center outwards. Numerical tools successfully simulate the observed coupling-induced switching using experimentally extracted parameters.

Influence of nanoholes array geometrical parameters on magnetic properties of Dy–Fe antidot thin films

Nanoscale artificially engineered spintronic materials could be used to enlarge the storage density of magnetic recording media. For this purpose, magnetic nanostructures such as antidot arrays exhibiting high uniaxial magnetic anisotropy are new contestants in the field of ultrahigh density magnetic data storage devices. In this context, we focus on the synthesis of nanostructured magnetic materials consisting of Dy–Fe alloyed antidot thin films, deposited onto the surface of nanoporous alumina membranes served as patterned templates. Noticeable variations of in the in-plane magnetic anisotropy have been observed by modifying the layer thickness at both microscopic and macroscopic scales. The microscopic magnetic properties have been locally studied by Nano-MOKE magnetometry. For thinner antidot samples with 15, 20 and 25 nm in thickness, a tri-axial in-plane magnetic anisotropy has been detected. Meanwhile, for thicker antidot samples (40–60 nm of layer thickness), an in-plane uniaxial magnetic anisotropy has been noted. We attribute these changes in the magnetic anisotropy to the strong correlation between the edge-to-edge distance among adjacent nanoholes, W, and the local magnetic anisotropy of antidot samples. The effective magnetic anisotropy exhibits an unexpected crossover from the in-plane to out-of-plane direction due to the increasing of the effective perpendicular magnetic anisotropy with varying the layer thickness of antidot thin films. Therefore, we detected a critical layer thickness, t = 25 nm for the Dy–Fe alloy antidot arrays, at which the appearance of the perpendicular magnetization is observed. Furthermore, an enhancement in the Curie temperature of the antidot arrays compared to the continuous thin films has been obtained. We attribute these effects to the complex magnetization reversal processes and the high thermal stability of the hexagonal structure of antidot arrays. These findings can be of high interest for the development of novel magnetic sensors and for thermo-magnetic recording patterned media based on template-assisted deposition techniques.

Relationship between biaxial orientation degrees and grain in magnetically aligned (Y1−xErx)Ba2Cu3Oy powders with twin microstructures

We report the degrees of biaxial orientation for (Y1−xErx)Ba2Cu3Oy [(Y1−xErx)123] powder samples aligned in epoxy resin under a modulated rotating magnetic field of 10 T at room temperature. Although the triaxial magnetic anisotropy of ErBa2Cu3Oy was found to be approximately 20 times higher than that of YBa2Cu3Oy, the orientation degrees for (Y1−xErx)123 powder samples decreased with x. In the fabrication of (Y1−xErx)123 powders, sintering temperature is one of the parameters that predominantly affect orientation degree, and the sintering at temperatures close to the peritectic temperature leads to improvement of the orientation degree. In the case of the biaxial magnetic alignment of REBa2Cu3Oy (RE123: RE, rare-earth element) powders, the reduction of in-plane magnetic anisotropy induced by twin microstructures at the RE123 grain level should be taken into account. Therefore, in this study, we clarified that the fabrication processes of RE123 powders are important in addition to the control of the chemical composition using RE ions with high magnetic anisotropy.