Anisotropy Axis Research Articles

Haldane topological spin-1 chains in a planar metal-organic framework

Haldane topological materials contain unique antiferromagnetic chains with symmetry-protected energy gaps. Such materials have potential applications in spintronics and future quantum computers. Haldane topological solids typically consist of spin-1 chains embedded in extended three-dimensional (3D) crystal structures. Here, we demonstrate that [Ni(μ−4,4′-bipyridine)(μ-oxalate)]n (NiBO) instead adopts a two-dimensional (2D) metal-organic framework (MOF) structure of Ni2+ spin-1 chains weakly linked by 4,4′-bipyridine. NiBO exhibits Haldane topological properties with a gap between the singlet ground state and the triplet excited state. The latter is split by weak axial and rhombic anisotropies. Several experimental probes, including single-crystal X-ray diffraction, variable-temperature powder neutron diffraction (VT-PND), VT inelastic neutron scattering (VT-INS), DC susceptibility and specific heat measurements, high-field electron spin resonance, and unbiased quantum Monte Carlo simulations, provide a detailed, comprehensive characterization of NiBO. Vibrational (also known as phonon) properties of NiBO have been probed by INS and density-functional theory (DFT) calculations, indicating the absence of phonons near magnetic excitations in NiBO, suppressing spin-phonon coupling. The work here demonstrates that NiBO is indeed a rare 2D-MOF Haldane topological material.

Linear stability of shock waves in ultrarelativistic anisotropic hydrodynamics

Linear stability of a plane shock waves in ultrarelativistic anisotropic hydrodynamics is investigated. The properties of the amplitudes of perturbations of physical quantities are studied depending on the components of the wave vector of a small harmonic perturbation. Analytical calculations for the longitudinal and transverse propagation of shock wave normal with respect to the anisotropy axis (beam-axis) and numerical calculations for an arbitrary polar angle are carried out.

Trityl-Based Lanthanide-Supramolecular Assemblies Exhibiting Slow Magnetic Relaxation.

The triphenylmethane (trityl) group has been recognized as a supramolecular synthon in crystal engineering, molecular machine rotors and stereochemical chirality inductors in materials science. Herein we demonstrate for the first time how it can be utilized in the domain of molecular magnetic materials through shaping of single molecule magnet (SMM) properties within the lanthanide complexes in tandem with other non-covalent interactions. Trityl-appended mono- (HL1 ) and bis-compartmental (HL2 ) hydrazone ligands were synthesized and complexated with Dy(III) and Er(III) triflate and nitrate salts to generate four monometallic (1-4) and two bimetallic (5, 6) complexes. The static and dynamic magnetic properties of 1-6 were investigated, revealing that only ligand HL1 induces assemblies (1-4) capable of showing SMM behaviour, with Dy(III) congeners (1, 2) able to exhibit the phenomenon also under zero field conditions. Theoretical ab initio studies helped in determination of Dy(III) energetic levels, magnetic anisotropic axes and corroborated magnetic relaxation mechanisms to be a combination of Raman and quantum tunnelling in zero dc field, the latter being cancelled in the optimum non-zero dc field. Our work represents the first study of magneto-structural correlations within the trityl Ln-SMMs, leading to generation of slowly relaxing zero-field dysprosium complexes within the hydrogen-bonded assemblies.

Energetics of phase transitions in homogeneous antiferromagnets

Spatially uniform static phases in an antiferromagnet (AFM) at 0 K accessible by varying an external magnetic field along the anisotropy axis are investigated. Using the macrospin model, the energy contributions are comprised of the external field, effective anisotropy, and spatially homogeneous AFM exchange. The critical energy configurations are fully cataloged, and local energy concavity is used to identify stable states. Relative energy levels are taken into account to classify phase transitions. Phase diagrams for energetic stability and phase transitions are provided in terms of the strength of the applied field and the ratio between anisotropy and the AFM exchange. Two nonstandard critical energy states are identified as energy saddle points so are not stable but function as energy barriers between multiple stable states. The results determine thermal switching rates and suggest interesting AFM textures and solitons.

Mn(III)–Salen Complexes with Metallophilic Interactions

We synthesized a series of five novel Mn–salen-based compounds (1a–1c, 2a, 2b) through the reaction between precursor chloride complexes and potassium silver/gold dicyanide. The prepared compounds were structurally and magnetically characterized. Our findings revealed that all the Mn(III) central atoms exhibited an axially elongated coordination polyhedron, leading to the observation of axial magnetic anisotropy as indicated by the negative axial magnetic parameter D, which was determined through fitting the experimental magnetic data and supported by theoretical CASSCF/NEVPT2 calculations. Furthermore, we observed magnetic-exchange interactions only in compounds with a special supramolecular topology involving O–H···O hydrogen-bonded dimers. In these cases, the weak magnetic exchange (J/cm−1 = −0.58(2) in 1b and −0.73(7) in 2b) was mediated by the O–H···O hydrogen bonds. These findings were further supported by BS–DFT calculations, which predicted weak antiferromagnetic exchanges in these complexes and ruled out exchange interactions mediated by diamagnetic cyanido metallo–complex bridges. Additionally, we investigated the observed Ag···π (1b) and Au···Au (2b) interactions using QT–AIM calculations, confirming their non-covalent nature. We compared these results with previously reported Mn–salen-based compounds with metallophilic interactions arising from the presence of the [Ag/Au(CN)2]− bridging units.

Magneto-impedance tomography of CoFeTaSiB amorphous wires

The paper presents the results of a study of the radial distribution of the magnetic permeability of an Co66Fe4Ta2.5Si12.5B15 amorphous wire with a radius of 55 μm. The study was performed using magneto-impedance tomography in the frequency range of alternating current from 0.01 to 100 MHz. It was found that the magnetic permeability significantly depends on the radial coordinate. Wherein the inner regions of the wire have predominantly axial anisotropy, while the outer layer about 2.5 µm thick has circular anisotropy. It is shown that the magnetoelastic mechanism is not the main one in the formation of magnetic anisotropy in the surface layer of the wire.

A Paramagnetic Compass Based on Lanthanide Metal-Organic Framework.

Macroscopic compass-like magnetic alignment at low magnetic fields is natural for ferromagnetic materials but is seldomly observed in paramagnetic materials. Herein, we report a "paramagnetic compass" that magnetically aligns under ∼mT fields based on the single-crystalline framework constructed by lanthanide ions and organic ligands (Ln-MOF). The magnetic alignment is attributed to the Ln-MOF's strong macroscopic anisotropy, where the highly-ordered structure allows the Ln-ions' molecular anisotropy to be summed according to the crystal symmetry. In tetragonal Ln-MOFs, the alignment is either parallel or perpendicular to the field depending on the easiest axis of the molecular anisotropy. Reversible switching between the two alignments is realized upon the removal and re-adsorption of solvent molecules filled in the framework. When the crystal symmetry is lowered in monoclinic Ln-MOFs, the alignments become even inclined (47°-66°) to the field. These fascinating properties of Ln-MOFs would encourage further explorations of framework materials containing paramagnetic centers.

A Paramagnetic Compass Based on Lanthanide Metal‐Organic Framework

AbstractMacroscopic compass‐like magnetic alignment at low magnetic fields is natural for ferromagnetic materials but is seldomly observed in paramagnetic materials. Herein, we report a “paramagnetic compass” that magnetically aligns under ~mT fields based on the single‐crystalline framework constructed by lanthanide ions and organic ligands (Ln‐MOF). The magnetic alignment is attributed to the Ln‐MOF's strong macroscopic anisotropy, where the highly‐ordered structure allows the Ln‐ions’ molecular anisotropy to be summed according to the crystal symmetry. In tetragonal Ln‐MOFs, the alignment is either parallel or perpendicular to the field depending on the easiest axis of the molecular anisotropy. Reversible switching between the two alignments is realized upon the removal and re‐adsorption of solvent molecules filled in the framework. When the crystal symmetry is lowered in monoclinic Ln‐MOFs, the alignments become even inclined (47°‐66°) to the field. These fascinating properties of Ln‐MOFs would encourage further explorations of framework materials containing paramagnetic centers.

Monte Carlo simulation of a magnetic nanoparticles system under an external rotating magnetic field

The magnetic response of an identical magnetic nanoparticles (MNP) system to a rotating external field (RMF) is studied via Monte Carlo simulations. The field of amplitude H0 and frequency ω, was applied in the y−z plane rotating clockwise. The energy was modeled by the Stoner–Wohlfarth scheme for fixed or random orientations of the anisotropy, and is in contact with a thermal bath at a temperature T. Interparticle dipolar interactions were also considered.In the non-interacting system and for low temperature, hysteresis is observed in the z magnetization component Mz for both orientations of the anisotropy axis and only in the y component (My) for the random case. Furthermore, the loop areas were estimated, and increased with ω for all orientations and (My,Mz) components. At higher temperatures the superparamagnetic state is observed, so both the blocking temperatures TB and loop areas were estimated. The values of TB were close from the room temperature TR=300K for all components, and the areas decreased with T but they are practically not zero at TB.When dipolar interactions are included a new scenario is revealed. In the low temperature regime, the blocked state is present for both My and Mz for all anisotropy orientations, and extends beyond the interval of amplitudes H0 estimated theoretically for the model without interactions and fixed anisotropy. The loops are displaced with respect to the origin of the magnetization-external field plane. When the temperature is raised, the blocked state extends for a larger range than the model without interactions, and the loop displacement decreases with T. These behaviors could be explained by observing that the average dipolar field per particle produces an effective field – the sum of both dipolar and external field – that is asymmetric with respect to the zero field line at low temperatures, becomes half-wave symmetric at higher temperatures, so the the centered character of the loops is restored . In addition, the loop areas show a peak for all orientations of the anisotropy axes in an intermediate range of temperatures. This result can be associated with a dominance of the anisotropy induced by the dipolar field.Finally, by comparing the areas of the loops of the models with and without interactions, it was found that the non-interacting model have larger areas at low temperatures that vanish near the room temperature, unlike the areas of the model with interactions due to the extension of the blocked state.

Micro-mechanical numerical analysis on ductile damage in multiaxially loaded anisotropic metals

The paper deals with numerical analysis of the effect of stress state and loading direction with respect to the rolling direction on damage and fracture behavior of anisotropic metals. The continuum damage model has been enhanced to take into account the influence of production-induced anisotropies and loading direction on damage criteria and on evolution equations of damage strains. Constitutive parameters are determined using experimental results taken from tests with uni- and biaxially loaded specimens. The focus of the paper is on three-dimensional micro-mechanical numerical analyses of micro-defect-containing representative volume elements covering a wide range of stress states. These calculations lead to more insight in the different damage and failure processes on the micro-scale and their influence on the macroscopic damage laws. With the obtained numerical results it is possible to detect general trends, to propose governing equations for the damage criteria, to develop evolution equations for the damage strains, and to identify constitutive parameters of the anisotropic material model. It is shown that the anisotropic behavior and the loading direction with respect to the principal axes of anisotropy affect the evolution of damage mechanisms on the micro-level as well as the corresponding damage strains.

Variable scintillation arcs of millisecond pulsars observed with the Large European Array for Pulsars

ABSTRACT We present the first large sample of scintillation arcs in millisecond pulsars (MSPs), analysing 12 sources observed with the Large European Array for Pulsars (LEAP), and the Effelsberg 100-m telescope. We estimate the delays from multipath propagation, measuring significant correlated changes in scattering time-scales over a 10 yr time span. Many sources show compact concentrations of power in the secondary spectrum, which in PSRs J0613−0200 and J1600−3053 can be tracked between observations, and are consistent with compact scattering at fixed angular positions. Other sources such as PSRs J1643−1224 and J0621+1002 show diffuse, asymmetric arcs which are likely related to phase-gradients across the scattering screen. PSR B1937+21 shows at least three distinct screens which dominate at different times and evidence of varying screen axes or multiscreen interactions. We model annual and orbital arc curvature variations in PSR J0613−0200, providing a measurement of the longitude of ascending node, resolving the sense of the orbital inclination, where our best-fit model is of a screen with variable axis of anisotropy over time, corresponding to changes in the scattering of the source. Unmodelled variations of the screen’s axis of anisotropy are likely to be a limiting factor in determining orbital parameters with scintillation, requiring careful consideration of variable screen properties, or independent very long baseline interferometry (VLBI) measurements. Long-term scintillation studies such as this serve as a complementary tool to pulsar timing, to measure a source of correlated noise for pulsar timing arrays, solve pulsar orbits, and to understand the astrophysical origin of scattering screens.

Particle-matrix debonding with Strength-Differential effects

In this work the onset of failure caused by particle-matrix debonding in aluminum alloy 2090-T3 and magnesium alloy AZ31 under either overall uniaxial plane strain tension or compression load is studied numerically using a unit cell model. Especially for magnesium AZ31, experiments show a significant difference in the tensile-compressive yield stresses, the so-called Strength-Differential-effect (SD-effect). This SD-effect cannot be captured by any isotropic yield function and only by recent anisotropic yield functions. To accurately model AA 2090-T3 and magnesium AZ31 the general yield function by Yoon et al. (2014) is adopted in addition to the isotropic von Mises plasticity yield function and the anisotropic yield function of Hill (1948). The numerically predicted strain at which void nucleation initiates is generally found to be larger for magnesium AZ31 than for AA 2090-T3. However, depending on the orientation of the principal axes of plastic anisotropy this void nucleation strain varies significantly. This holds true for both materials, but the void nucleation strain of AA 2090-T3 in compression is numerically predicted to be practically identical whether or not isotropic or anisotropic plasticity is considered. In tension the void nucleation strain of AA 2090-T3 based on anisotropic plasticity is found to be more than double the strain obtained by von Mises plasticity. The numerically predicted void nucleation strain of magnesium AZ31 is significantly affected by the yield function adopted. For the von Mises yield function the value of the void nucleation strain is in between the predictions based on the anisotropic yield functions. For both tension and compression, the yield function of Yoon et al. (2014) results in the largest void nucleation strain, whereas the yield function of Hill results in the smallest strain value. This holds true for all five orientations of the principal axes of plastic anisotropy investigated.

Are Actinyl Cations Good Probes for Structure Determination in Solution by NMR?

We report on NMR spectroscopy, CAS-based method calculations, and X-ray diffraction of AnV and AnVI complexes with a neutral and slightly flexible TEDGA ligand. After checking that pNMR shifts mainly arise from pseudocontact interactions, we analyze pNMR shifts considering the axial and rhombic anisotropy of the actinyl magnetic susceptibilities. The results are compared to those of a previous study performed on [AnVIO2]2+ complexes with dipicolinic acid. It is shown that 5f2 cations (PuVI and NpV) make very good candidates for determining the structure of actinyl complexes in solution by 1H NMR spectroscopy as shown by the invariance of the magnetic properties to the equatorial ligands, as opposed to the NpVI complexes with a 5f1 configuration.

Surface Deposition Induced Reduction of the Ground State Spin in Cr10 Wheel

AbstractWe report the deposition of monolayers and multilayers of {Cr10(OMe)20(O2CCMe3)10} wheels, hereafter {Cr10}, onto Au(111) and Cu(111) single‐crystal substrates, and their characterization combining scanning tunneling microscopy, X‐ray photoelectron spectroscopy, X‐ray absorption spectroscopy, X‐ray natural linear dichroism, and X‐ray magnetic circular dichroism (XMCD). {Cr10} in bulk shows axial magnetic anisotropy and a cluster total spin S = 9 ground state, stemming from an interaction scheme of two semi‐crowns containing four Cr3+ ions interacting ferromagnetically, separated by two Cr3+ antiferromagnetically coupled. The one‐monolayer (1ML) samples of {Cr10} sublimated on Ag(111) and Cu(111) show slightly different applied magnetic field dependence of XMCD signal. The field‐dependence of the magnetization evolves from a lower curve for the 1ML {Cr10} samples to a curve resembling the bulk one as the number of layers is increased, as shown in a 14ML sample. Monte Carlo simulations allow rationalizing the magnetization curves of the 1ML samples in terms of a reduction of the cluster ground‐state total spin, S = 3 or S = 6, as a consequence of variations in the intra‐wheel coupling interactions induced by the on‐surface deposition. The sensitivity of the magnetic configuration of {Cr10} to minor distortions of the intramolecular conformation might be exploited to control magnetism by external stimuli for applications.

Magnetic properties of chains of spherical nanoparticles with cubic magnetic anisotropy: A Monte Carlo study

Monte Carlo techniques are used to simulate magnetic properties of chains of identical, spherical, single-domain, ferromagnetic nanoparticles with cubic magnetocrystalline anisotropy. Nanoparticles are placed along a straight line with their positions and directions of anisotropy axes fixed in changing external magnetic field. Hysteresis curves as well as zero field cooled (ZFC) and field cooled (FC) experiments are simulated for chains of different lengths, i.e. differing in both: the number of particles and inter-particle distances. Strongly anisotropic dipole–dipole inter-particle interactions lead to significant differences in system’s response to the external magnetic fields oriented parallel and perpendicular to the chain, and further, to the occurrence of wasp-waisted hysteresis loops. We compare results for chains that differ in the size of particles they are built of. To get the idea about the quantitative scale of the discussed phenomena we assume values of magnetocrystalline anisotropy constants for fcc-Co.

Analysis of a Strip Antenna Located at a Plane Interface of Uniaxial Metamaterials

A rigorous solution is found to the problem of determining the current distribution and input impedance of a straight strip antenna located at a plane interface of two uniaxial metamaterials. The anisotropy axes of the metamaterials are parallel to each other and to the medium interface. The antenna is oriented perpendicular to these axes and excited by a given time-harmonic voltage. Using the Fourier transform technique, singular integral equations for the antenna current are derived and solved for all possible combinations of the metamaterial parameters. Closed-form representations for the current distribution and input impedance of an infinitely long strip are obtained and their generalization to the case of a finite-length antenna is discussed.

H-T magnetic phase diagram of CuCrO2: A Monte Carlo study based on a realistic 3D classical Heisenberg model

In the multiferroic geometrically frustrated triangular antiferromagnet CuCrO2, we investigate the magnetic phases as function of temperature under a magnetic field 70 T ≤ B ≤ 120 T along the [001] axis using the importance sampling Monte Carlo method. We consider a realistic three-dimensional classical Heisenberg model, which takes into consideration the distortion and exchange interactions up to the third-nearest neighbors in the ab planes and an interplane interaction, in addition to hard and easy anisotropy axes along the [110] and the [001] directions, respectively. For 70 T ≤ B < 106 T, our calculations show that two phase transitions occur when decreasing the temperature. The first one, which takes place around 30 K, is a “paramagnetic ↔ up-up-down (UUD)” transition and the second one, at lower temperatures, is an “UUD ↔ commensurate Y (CY)” transition. Thus, the colinear UUD phase is stable in an intermediate temperature range. For B = 90 T, our estimates of the critical exponents indicate that the two transitions belong to the universality class of the two-dimensional Ising model. For 106 T ≤ B < 110 T, since the CY phase is identical to the UUD one, only a “paramagnetic ↔ up-up-down (UUD)” transition occurs. For 110 T ≤ B ≤ 120 T, only a “paramagnetic ↔ V” transition is observed at ∼27 K. Our results are in good agreement with the existing experimental data on the stable phases in this magnetic field range. Moreover, we have determined the temperature range where the CY and UUD phases are stable which was not done previously.

New Mn(III) complexes with tetradentate cis-N2O2, acacen-type ligands. Synthesis and characterization, single-crystal X-ray diffraction and DFT studies

One of the challenges of manganese(III) magnetochemistry is the design and synthesis of new building block systems to study and develop molecular magnets. In this context, two new Mn(III) complexes were synthesized using new tetradentate cis-N2O2 acacen ligands from the condensation of 1-anisyl-1,3-butanedione and 1,2-diaminoethane (2:1 ratio). All compounds were fully characterized by conventional spectroscopic techniques, such as FT-IR, HRMS, and UV–Vis, and rationalized with DFT and TD-DFT studies. The resulting cationic complexes were composed of N4O2 coordination spheres using a tetradentate ligand (N2O22−) in the equatorial plane and two axial pyridines with general formulae as [MnIII(L)(Py)2](X) (X = BF4−; ClO4−). Single-crystal X-ray diffraction revealed that both complexes are isostructural with typical axial anisotropy due to the Jahn-Teller effect by tetragonal distortion. A complete analysis of the crystalline structures revealed a nonclassical intermolecular interaction of CH···F and CH···O. Supported by Hirshfeld surfaces and 2D- fingerprint plots, it was possible to isolate and calculate the contribution of intermolecular interactions in the supramolecular arrangement. For both complexes, the magnetic susceptibility confirmed a high spin state (HS) with 4.8 µB and 4.9 µB related to the spin-only contribution to the magnetic moment.

Model of a 3D Magnetic Permeability Tensor Considering Rotation and Saturation States in Materials with Axial Anisotropy.

The paper proposes a 3D extension of the linear tensor model of magnetic permeability for axially anisotropic materials. In the proposed model, all phases of a magnetization process are considered: linear magnetization, magnetization rotation, and magnetic saturation. The model of the magnetization rotation process is based on the analyses of both anisotropic energy and magnetostatic energy, which directly connect the proposed description with physical phenomena occurring during a magnetization process. The proposed model was validated on the base of previously presented experimental characteristics. The presented extension of the tensor description of magnetic permeability enables the modelling of inductive devices with cores made of anisotropic magnetic materials and the modelling of magnetic cores subjected to mechanical stresses. It is especially suitable for finite element modelling of the devices working in a magnetic saturation state, such as fluxgate sensors.

ELASTIC TRANSVERSAL-ISOTROPIC SPACE WITH TWO UNIAXIAL PARALLEL CIRCULAR CRACKS AND ASSOCIATED PROBLEMS OF BASICITY

In the paper a problem of the stress state in a transversely isotropic space with two parallel circular cracks, the centers of which are located on the axis of anisotropy of the space, is investigated. A constant normal load acts on the crack planes. The problem is solved by the generalized Fourier method. For this purpose, systems of compressed spheroidal coordinates are introduced, the origins of which are connected to the centers of cracks. The general solution of the problem is constructed in the form of series based on axisymmetric variants of the general vector solutions of the system of equations of equilibrium of a transversely isotropic body in spheroidal coordinates, which were previously constructed by one of the authors of the paper. To implement the method, it is further generalized to compressed spheroidal coordinate systems with origins shifted along the axis. For this purpose, new addition theorems for basic vector displacements of transversally isotropic bodies in the above-mentioned coordinate systems are obtained. After applying the generalized Fourier method, the problem is reduced to an infinite system of linear algebraic equations. It is proved that under certain geometrical and mechanical conditions the operator of the system is a Fredholm operator. The reduction method is used for the numerical solution of the system. Graphs of normal stresses in the plane of one of the cracks outside its boundaries, as well as values of stress intensity factor at the top of the crack for different geometric parameters of the cracks, are obtained. The obtained results agree with the known value of the stress intensity factor in the problem with one crack. The practical convergence of the reduction method is studied.&#x0D; As an important related problem, the problem of proving the basicity of a general axisymmetric set of external solutions of the system of equilibrium equations of a transversally isotropic body whose boundary is described in compressed spheroidal coordinates is considered. The key problem here is obtaining subtle estimates from below of the modulus of the determinant of the first boundary value problem. As a corollary of the obtained result, several important estimates from the theory of special functions are derived, in which Legendre functions of the second kind from a purely imaginary argument appear.