Anisotropy Axis Research Articles

Ferromagnetic resonance of a magnetic particle using the Landau–Lifshitz–Bloch equation

In this work, we employ the Landau–Lifshitz–Bloch equation to study the ferromagnetic resonance of a magnetic nanoparticle assumed in a mono-domain with uniaxial anisotropy. We consider a constant magnetic field applied perpendicularly to the easy axis of anisotropy. We investigated the temperature effect on the resonance spectrum through the complex magnetic susceptibility tensor. We found a decrease in the resonance frequency as the temperature is incremented and a decrement in the resonance field range when the driven frequency increases.

Scanning nitrogen-vacancy center magnetometry in large in-plane magnetic fields

Scanning magnetometry with nitrogen-vacancy (NV) centers in diamond has emerged as a powerful microscopy for studying weak stray field patterns with nanometer resolution. Due to the internal crystal anisotropy of the spin defect, however, external bias fields—critical for the study of magnetic materials—must be applied along specific spatial directions. In particular, the most common diamond probes made from {100}-cut diamond only support fields at an angle of θ=55° from the surface normal. In this paper, we report fabrication of scanning diamond probes from {110}-cut diamond where the spin anisotropy axis lies in the scan plane (θ=90°). We show that these probes retain their sensitivity in large in-plane fields and demonstrate scanning magnetometry of the domain pattern of Co–NiO films in applied fields up to 40 mT. Our work extends scanning NV magnetometry to the important class of materials that require large in-plane fields.

Crystal structures and magnetic properties of Fe1.93-xCoxP1-ySiy compounds

In view of the interest that (Fe,Co)2(P,Si) compounds have as potential permanent magnets, their structural and magnetic phase diagrams are explored focusing on establishing the range where the hexagonal Fe2P-type structure is observed. In Fe1.93-xCoxP1-ySiy, the highest Si content prior entering a mixed phase domain is y ≈ 0.5. At high Si content but low Co for Fe substitutions, a structural distortion leading to a body-centered orthorhombic structure occurs. At high Co contents, when the Fe2P unit cell reaches a critical volume of about 102.4 Å3, the samples crystallize in a Co2P-type orthorhombic structure. Within the Fe2P-type structural range, the evolution of the unit-cell volume appears to follow the Vegard’s law, but this hides strongly anisotropic changes. Simultaneous Co for Fe and Si for P substitutions increase the range where the hexagonal structure is observed in comparison to ternary Fe2(P,Si) and (Fe,Co)2P. The samples are ferromagnetic, but with Curie temperatures showing an unusual evolution, uncorrelated to the c/a ratio of the lattice parameters. At low Si content, TC increases with Co for Fe substitutions. For y = 0.2, the evolution is not significant, while at high Si content TC systematically decreases with the increase in Co. Large Si and Co substitutions lead to a swift weakening of the magnetocrystalline anisotropy until the easy axis anisotropy turns from the c axis toward the a-b plane. This study guides future investigations by restricting the range where desirable properties for permanent magnetic applications can be expected to 0.1 ≲x≲ 0.3 and 0.1 ≲y≲ 0.3.

The magnetic anisotropy of Tb-phthalocyanine films effected by molecular orientation

Tb-phthalocyanine (TbPc2) films have been grown on 25 °C and 150 °C glass substrates. The temperature dependence of magnetic hysteresis loops for the TbPc2 films was measured and analyzed. The out-of-plane and in-plane magnetic hysteresis loops are nearly overlapped for the TbPc2 film grown at 25 °C, indicating the film is basically magnetically isotropic. In contrast, the TbPc2 film grown at 150 °C shows a strong magnetic anisotropy, and its out-of-plane magnetic moment at 30 kOe is about 13% larger than that of in-plane value for the measurement at 2 K. To explore the inter-relation between the molecular stacking structure and magnetic properties of the TbPc2 films, the X-ray diffractometer and grazing-incidence wide-angle X-ray scattering were used to characterize the crystalline structures of TbPc2 films. The results demonstrate that TbPc2 film grown at 25 °C is nearly amorphous. While, TbPc2 film grown at 150 °C shows a clear crystalline texture. The relationship between molecular orientation and magnetic properties has been theoretically analyzed. Based on the consideration of magnetic anisotropy axis of TbPc2 molecules, the out-of-plane and in-plane magnetic loops of the present two films, it can be concluded that the TbPc2 molecules prefer to lie flat close to the substrate surface on 150 °C glass substrate. This work is significant to guide the design of electron devices based on single-molecule magnets.

Longitudinal remagnetization of uniaxial antiferromagnetic nanoparticles: the role of spontaneous magnetic moment.

A kinetic theory of magnetic response of uniaxial antiferromagnetic nanoparticles is presented. Within the developed framework, a particular case when an external field is applied strictly along the anisotropy axis is considered in detail. Analysis of the relaxation spectrum of an antiferromagnetic particle with a spontaneous magnetic moment is performed. It is shown that in a wide frequency range the magnetic response of such particle is determined entirely by the relaxation mode with the longest time. An analytical expression for this time that explicitly contains a value of the decompensation magnetic moment is derived. Also, simple formulae for both static and dynamic longitudinal magnetic susceptibility of an antiferromagnetic nanoparticle are obtained. According to them, longitudinal susceptibility grows quadratically with the value of the spontaneous magnetic moment. Besides, if the latter is not zero, the change of the static susceptibility with temperature turns out to be non-monotonic. The influence of the spontaneous magnetic moment of the particle on the magnetization curves in strong fields is analysed using both energy approach and kinetic theory. The calculated dependences of the dynamic coercivity on the amplitude and variation rate of the applied field are qualitatively compared with experimental data. This article is part of the theme issue 'Transport phenomena in complex systems (part 2)'.

Large easy-axis magnetic anisotropy in a series of trigonal prismatic mononuclear cobalt(ii) complexes with zero-field hidden single-molecule magnet behaviour: the important role of the distortion of the coordination sphere and intermolecular interactions in the slow relaxation

A N6-tripodal ligand allows the preparation of a family of prismatic mononuclear cationic CoIIcomplexes with SMM behavior. Their axial anisotropy, magnetic relaxation and hysteresis width are modulated by the anion effects on the crystal structure.

On the Origin of Seismic Anisotropy in the Shallow Crust of the Northern Volcanic Zone, Iceland

AbstractThe Icelandic crust is a product of its unique tectonic setting, where the interaction of an ascending mantle plume and the Mid‐Atlantic Ridge has caused elevated mantle melting, with the melt accreted and cooled in the crust to form an oceanic plateau. We investigate the strength and orientation of seismic anisotropy in the upper crust of the Northern Volcanic Zone using local earthquake shear‐wave splitting, with a view to understanding how the contemporary stress field may influence sub‐wavelength structure and processes. This is achieved using a data set comprising 50,000 earthquakes located in the top 10 km of the crust, recorded by up to 70 stations over a 9 year period. We find that anisotropy is largely confined to the top 3–4 km of the crust, with an average delay time of 0.10 ± 0.05 s, and an average orientation of the fast axis of anisotropy of N014°E ± 27°, which is perpendicular to the spreading direction of the Eurasian and North American plates (N106°E). These results are consistent with the presence of rift‐parallel cracks that gradually close with depth, the preferential opening of which is controlled by the regional stress field. Lateral variations in the strength of shear wave anisotropy (SWA) reveal that regions with the highest concentrations of earthquakes have the highest SWA values (∼10%), which reflects the presence of significant brittle deformation. Disruption of the orientation of the fast axis of anisotropy around Askja volcano can be related to local stress changes caused by underlying magmatic processes.

Retardance measurement by spatially probing the sample with optical vortices

Modern optical systems utilize various degrees of freedom, such as polarization, for shaping and controlling the light. Common representative of such a component is spatial light modulator (SLM), consisting of liquid crystal display, allowing for imposing predetermined retardation with given orientation of optical axis of anisotropy. Therefore, it is widely used for polarization coded phase shifting, polarization splitting of wavefront in digital holography etc. Narrowing tolerance in optical experiments puts higher demands on precise setting of the modulator and the parameters set. Consequently, measuring such devices and their parameters is essential for proper functionality. We present a single shot, common path method for measuring retardance map of the modulator, based on spatial probing the modulator with point images of spatially coherent light source and transforming them to optical vortices.

Comparison of Two Approaches for Microstructural Modeling of the Ferromagnetic Alloys Behavior

In this letter, two approaches to describe the behavior of a ferromagnetic alloy in an external magnetic field within the framework of the micromagnetism theory are compared. The first one is based on the minimization of total magnetic energy. Another approach is based on describing the dynamics of the process using the Landau–Lifshitz–Gilbert equation. We have considered the problems of magnetization of a single martensite variant of the Ni <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> MnGa alloy within the framework of the theory of magnetism, in which one of the structural elements is a domain wall of a certain thickness, using bothapproaches. The solutions to these boundary value problems were obtained numerically by the finite-element method using the FeniCS package. The evolution of the magnetic structure was investigated. Magnetization curves were obtained in the external magnetic field directed at different angles to the anisotropy axis.

Исследование неравновесного критического поведения сильно неупорядоченной трехмерной анизотропной модели Гейзенберга

The results of a Monte Carlo study of strongly structural disorder influence on nonequilibrium critical behavior of three-dimensional anisotropic Heisenberg models with spin concentration p = 0.5 are presented with its evolution from high and low temperature initial state. It is shown that presence of strongly disorder changes characteristics of nonequilibrium critical behavior of anisotropic model with easy axis anisotropy type in comparison with both pure anisotropic and isotropic Heisenberg models.

Неравновесное критическое поведение слабо неупорядоченной трехмерной анизотропной модели Гейзенберга

The results of a Monte Carlo study of weakly structural disorder influence onnonequilibrium critical behavior of three-dimensional anisotropic Heisenberg models with spin concentration p = 0.9 are presented with its evolution from high temperature initial state. It is shown that presence of even weakly disorder changes characteristics of nonequilibrium critical behavior of anisotropic model with easy axis anisotropy type in comparison with both pure anisotropic and isotropic Heisenberg models.

Paramagnetic 7Li NMR Shifts and Magnetic Properties of Divalent Transition Metal Silylamide Ate Complexes [LiM{N(SiMe3)2}3] (M2+ = Mn, Fe, Co).

7Li NMR shifts and magnetic properties have been determined for three so-called ate complexes [LiM{N(SiMe3)2}3] (M2+ = Mn, Fe, Co; e.g., named lithium-tris(bis(trimethylsilylamide))-manganate(II) in accordance with a formally negative charge assigned to the complex fragment [M{N(SiMe3)2}3]-, which comprises the transition metal). They are formed by addition reactions of LiN(SiMe3)2 and [M{N(SiMe3)2}2] and stabilized by Lewis base/Lewis acid interactions. The results are compared to those of the related "ion-separated" complexes [Li(15-crown-5)][M{N(SiMe3)2}3]. The ate complexes with the lithium atoms connected to the 3d metal atoms manganese, iron, or cobalt via μ2 nitrogen bridges reveal strong 7Li NMR paramagnetic shifts of about -75, 125, and 171 ppm, respectively, whereas the shifts for the lithium ions coordinated by the 15-crown-5 ether are close to zero. The observed trends of the 7Li NMR shifts are confirmed by density-functional theory calculations. The magnetic dc and ac properties display distinct differences for the six compounds under investigation. Both manganese compounds, [LiMn{N(SiMe3)2}3] and [Li(15-crown-5)][Mn{N(SiMe3)2}3], display almost pure and ideal spin-only paramagnetic behavior of a 3d5 high-spin complex. In this respect slightly unexpected, both complexes show slow relaxation behavior at low temperatures under applied dc fields, which is especially pronounced for the ate complex [LiMn{N(SiMe3)2}3]. Dc magnetic properties of the iron complexes reveal moderate g-factor anisotropies with small values of the axial magnetic anisotropy parameter D and a larger E (transversal anisotropy). Both complexes display at low temperatures and, under external dc fields of up to 5000 Oe, only weak ac signals with no maxima in the frequency range from 1 to 1500 s-1. In contrast, the two cobalt complexes display strong g-factor anisotropies with large values of D and E. In addition, in both cases, the ac measurements at low temperatures and applied dc fields reveal two, in terms of their frequency range, well separated relaxation processes with maxima lying for the most part outside of the measurement range between 1 and 1500 s-1.

Phase transition of Mg3(PO4)2 polymorphs at high-temperature: In-situ synchrotron X-ray diffraction and Raman spectroscopic study

In-situ synchrotron X-ray diffraction and Raman spectroscopy were used to study the stabilities, thermal expansion and vibrational modes of synthetic Mg3(PO4)2. The polymorphs (Mg3(PO4)2-I, II, III) were investigated in the temperature range of 299 ∼ 1173 K at ambient pressure. An irreversible phase transition was observed for both Mg3(PO4)2-II and Mg3(PO4)2-III, whereas Mg3(PO4)2-I is stable in the present study. Based on the in-situ synchrotron X-ray diffraction and Raman spectroscopic measurements, Mg3(PO4)2-II and Mg3(PO4)2-III transform to Mg3(PO4)2-I at 1073 K and 1023 K, respectively. The volumetric thermal expansion coefficients of Mg3(PO4)2-I, II and III were determined as 3.31(4) × 10-5 K−1, 3.91(4) × 10-5 K−1, and 3.25(5) × 10-5 K−1, respectively. All three Mg3(PO4)2 polymorphs show axial thermal expansive anisotropy since the thermal expansion coefficients along different axes are inconsistent. The effect of temperature on the Raman vibrations of the three Mg3(PO4)2 polymorphs was quantitatively analyzed. And the isobaric mode Grüneisen parameters of three Mg3(PO4)2 polymorphs are calculated, which are in the range of 0.07 ∼ 3.54.

Magnetic properties of chiral EuIr2P2

We present a minimal model that provides a description of the magnetic and thermodynamic properties of \Eu. The model contains two exchange coupling parameters, which are calculated using Density Functional Theory, and a local easy axis magnetic anisotropy term. The classical ground state of the system is a generalization of the well known 120$^\circ$ structure observed in triangular antiferromagnets. Monte Carlo simulations show two phase transitions as a function of the temperature. With increasing temperature, the system transitions from the ground state into a high-entropy collinear antiferromagnet, which in turn at higher temperatures presents a second order transition to a paramagnetic state. A high enough external magnetic field parallel to the anisotropy axis produces a spin-flop transition at low temperatures. The field also reduces the temperature range of stability of the collinear antiferromagnet phase and leads to a single phase transition as a function of the temperature. The reported behavior of the specific heat, the magnetization, and the magnetic susceptibility is in agreement with the available experimental data. Finally, we present the magnetic phase diagrams for magnetic fields parallel and perpendicular to the easy axis.

Polarized Neutron Diffraction: An Excellent Tool to Evidence the Magnetic Anisotropy—Structural Relationships in Molecules

This publication reviews recent advances in polarized neutron diffraction (PND) studies of magnetic anisotropy in coordination compounds comprising d or f elements and having different nuclearities. All these studies illustrate the extent to which PND can provide precise and direct information on the relationship between molecular structure and the shape and axes of magnetic anisotropy of the individual metal sites. It makes this experimental technique (PND) an excellent tool to help in the design of molecular-based magnets and especially single-molecule magnets for which strong uniaxial magnetic anisotropy is required.

Nanostructuring at oblique incidence deposition of cobalt

Nanocolumnar Co thin films growth by oblique angle deposition on Si substrate is experimentally studied. Formation of regular arrays of tilted Co nanocolumns has been observed at incidence angles more than 70°. It was found that the optimal conditions for nanostructuring are realized at the inclination angle 85°. As obtained films have magnetic anisotropy axis inclined to the substrate surface and oriented along nanocolumns. Such films might be perspective material for applications as a magnetic recording media for next generations of hard disks.

Precise measurement of angles between two magnetic moments and their configurational stability in single-molecule magnets

A key parameter for the low-temperature magnetic coupling of in dinuclear lanthanide single-molecule magnets (SMMs) is the barrier $U_{FA}$ resulting from the exchange and dipole interactions between the two $4f$ moments. Here we extend the pseudospin model previously used to describe the ground state of dinuclear endofullerenes to account for variations in the orientation of the single-ion anisotropy axes and apply it to the two SMMs Dy$_2$ScN@C$_{80}$ and Dy$_2$TiC@C$_{80}$. While x-ray magnetic circular dichroism (XMCD) indicates the same $J_z=15/2$ Dy groundstate in both molecules, the Dy-Dy coupling strength and the stability of magnetization is distinct. We demonstrate that both the magnitude of the barrier $U_{FA}$ and the angle between the two $4f$ moments are determined directly from precise temperature-dependent magnetization data to an accuracy better than $1^{\circ}$. The experimentally found angles between the $4f$ moments are in excellent agreement with calculated angles between the quantisation axes of the two Dy ions. Theory indicates a larger deviation of the orientation of the Dy magnetic moments from the Dy bond axes to the central ion in Dy$_2$TiC@C$_{80}$. This may explain the lower stability of the magnetisation in Dy$_2$TiC@C$_{80}$, although it exhibits a $\sim 49\%$ stronger exchange coupling than in Dy$_2$ScN@C$_{80}$.

Optical signatures of the coupled spin-mechanics of a levitated magnetic microparticle

We propose a platform that combines the fields of cavity optomagnonics and levitated optomechanics to control and probe the coupled spin-mechanics of magnetic dielectric particles. We theoretically study the dynamics of a levitated Faraday-active dielectric microsphere serving as an optomagnonic cavity, placed in an external magnetic field and driven by an external laser. We find that the optically driven magnetization dynamics induces angular oscillations of the particle with low associated damping. Further, we show that the magnetization and angular motion dynamics can be probed via the power spectrum of the outgoing light. Namely, the characteristic frequencies attributed to the angular oscillations and the spin dynamics are imprinted in the light spectrum by two main resonance peaks. Additionally, we demonstrate that a ferromagnetic resonance setup with an oscillatory perpendicular magnetic field can enhance the resonance peak corresponding to the spin oscillations and induce fast rotations of the particle around its anisotropy axis.

Determination of anisotropic elastic parameters from morphological parameters of cancellous bone for osteoporotic lumbar spine

In biomechanics, large finite element models with macroscopic representation of several bones or joints are necessary to analyze implant failure mechanisms. In order to handle large simulation models of human bone, it is crucial to homogenize the trabecular structure regarding the mechanical behavior without losing information about the realistic material properties. Accordingly, morphology and fabric measurements of 60 vertebral cancellous bone samples from three osteoporotic lumbar spines were performed on the basis of X-ray microtomography (μCT) images to determine anisotropic elastic parameters as a function of bone density in the area of pedicle screw anchorage. The fabric tensor was mapped in cubic bone volumes by a 3D mean-intercept-length method. Fabric measurements resulted in a high degree of anisotropy (DA = 0.554). For the Young’s and shear moduli as a function of bone volume fraction (BV/TV, bone volume/total volume), an individually fit function was determined and high correlations were found (97.3 ≤ R2 ≤ 99.1,p < 0.005). The results suggest that the mathematical formulation for the relationship between anisotropic elastic constants and BV/TV is applicable to current μCT data of cancellous bone in the osteoporotic lumbar spine. In combination with the obtained results and findings, the developed routine allows determination of elastic constants of osteoporotic lumbar spine. Based on this, the elastic constants determined using homogenization theory can enable efficient investigation of human bone using finite element analysis (FEA).Graphical Cancellous Bone with Fabric Tensor Ellipsoid representing anisotropy and principal axis (colored coordinate system) of given trabecular structure

A Dicobalt(II) Single-Molecule Magnet via a Well-Designed Dual-Capping Tetrazine Radical Ligand

The recent years have witnessed the glory development for the construction of high-performance mononuclear single molecule magnets (SMMs) within a specific coordination geometry, which, however, is not well applied in cluster-based SMMs due to the synthetic challenges. Given that the monocobalt(II) complexes within a trigonal-prismatic (TPR) coordination geometry have been classified as excellent SMMs with huge axial anisotropy (D ≈ -100 cm-1), here we designed and synthesized a new dual-capping tetrazine ligand, 3,6-bis(6-(di(1H-pyrazol-1-yl)methyl)pyridin-2-yl)-1,2,4,5-tetrazine (bpptz), and prepared a novel dicobalt(II) complex, [Cp2CoIII][{(hfac)CoII}2(bpptz•-)][hfac]2·2Et2O (1, hfac = hexafluoroacetylacetonate). In the structure of 1, the bpptz•- radical ligand enwraps two Co(II) centers within quasi-TPR geometries, which are further bridged by the tetrazine radical in the trans mode. The magnetic study revealed that the interaction between the Co centers and the tetrazine radical is strongly antiferromagnetic with a coupling constant (J) of -65.8 cm-1 (in the -2J formalism). Remarkably, 1 exhibited the typical SMM behavior with an effective energy barrier of 69 cm-1 under a 1.5 kOe dc field, among the largest for polynuclear transition metal SMMs. In addition, DFT and ab initio calculations suggested that the presence of a strong Co(II)-radical magnetic interaction effectively quenches the QTM effect and enhances the barrier height for the magnetization reversal.