Order Anisotropy Research Articles

Liquid-Crystalline Polymer Particles Prepared by Classical Polymerization Techniques.

Liquid‐crystalline polymer particles prepared by classical polymerization techniques are receiving increased attention as promising candidates for use in a variety of applications including micro‐actuators, structurally colored objects, and absorbents. These particles have anisotropic molecular order and liquid‐crystalline phases that distinguish them from conventional polymer particles. In this minireview, the preparation of liquid‐crystalline polymer particles from classical suspension, (mini‐)emulsion, dispersion, and precipitation polymerization reactions are discussed. The particle sizes, molecular orientations, and liquid‐crystalline phases produced by each technique are summarized and compared. We conclude with a discussion of the challenges and prospects of the preparation of liquid‐crystalline polymer particles by classical polymerization techniques.

Anisotropic magnetocaloric effect and magnetoresistance in antiferromagnetic HoNiGe3 single crystal

We report anisotropic magnetocaloric effect and magnetoresistance in antiferromagnetic HoNiGe3 single crystal grown by Ge flux method. HoNiGe3 single crystal exhibits antiferromagnetic order and large magnetocrystalline anisotropy below the Néel temperature TN = 10.5 K. Meanwhile, with increasing the magnetic field, HoNiGe3 undergoes the spin-flip transition induced by the magnetic field along the a axis, while the spin-flop transition occurs for the field along the other orientations, which gives rise to anisotropic magnetoresistance behavior along three axes. With the magnetic field change of 0–50 kOe, the maximum magnetic entropy changes obtained along the a, b, and c axes are −13.9, 2.5 and −7.7 J kg−1K−1, respectively. The maximum rotating magnetic entropy change is −12.3 J kg−1K−1 under 50 kOe by rotating the magnetic field from the b axis to the a axis, and the corresponding refrigeration capacity is 193 J/kg, which demonstrates HoNiGe3 to be an attractive candidate for novel rotating magnetic refrigeration at low temperature region.

Enhanced annealing stability of ferrimagnetic Tb/FeCo multilayers

In this study, we have investigated amorphous 20-nm-thick Tb/Fe80Co20 multilayer samples with different individual layer thicknesses and their corresponding alloy counterpart. In particular, the structural and magnetic properties were analyzed upon post-annealing. Up to a certain critical thickness of the individual layers in the multilayer, no significant difference between the multilayers and the alloy is observed in their as-deposited states, which indicates the importance of interfacial intermixing. With a further increase in thicknesses of the individual layers, regions with significant larger Tb content emerge, resulting in a reduced effective Tb moment. The loss in perpendicular magnetic anisotropy upon annealing seems to be delayed for multilayers with thin individual layers compared to the alloy sample. We contribute this behavior to the underlying anisotropic short-range order enforced by the multilayer structure, which hinders the structural relaxation process. At higher temperatures, the multilayers strongly intermix and Fe and Co diffuse through the capping layer. This process leads to a strong enhancement of the saturation magnetization at a certain annealing temperature, due to the formation of separated FeCo and Tb-rich TbFeCo alloy layers, until the sample gets oxidized.

Tunable topological states hosted by unconventional superconductors with adatoms

Chains of magnetic atoms, placed on the surface of s-wave superconductors, have been established as a laboratory for the study of Majorana bound states. In such systems, the breaking of time reversal due to magnetic moments gives rise to the formation of in-gap states, which hybridize to form one-dimensional topological superconductors. However, in unconventional superconductors even non-magnetic impurities induce in-gap states since scattering of Cooper pairs changes their momentum but not their phase. Here, we propose a path for creating topological superconductivity, which is based on an unconventional superconductor with a chain of non-magnetic adatoms on its surface. The topological phase can be reached by tuning the magnitude and direction of a Zeeman field, such that Majorana zero modes at its boundary can be generated, moved and fused. To demonstrate the feasibility of this platform, we develop a general mapping of films with adatom chains to one-dimensional lattice Hamiltonians. This allows us to study unconventional superconductors such as Sr$_2$RuO$_4$ exhibiting multiple bands and an anisotropic order parameter.

Finite transverse conductance and anisotropic magnetoconductance under an applied in-plane magnetic field in two-dimensional electron gases with strong spin–orbit coupling

The current in response to a bias in certain two-dimensional electron gas (2DEG), can have a nonzero transverse component under a finite magnetic field applied in the plane where electrons are confined. This phenomenon known as planar Hall effect (PHE) is accompanied by dependencies of both the longitudinal and the transverse components of the current on the angle ϕ between the bias direction and the magnetic field. This effect can be observed in a variety of systems, for example in topological insulators where spin-momentum locking of the topologically protected surface states is the root cause for the effect and in magnetic systems where anisotropic magnetic ordering induces it. In 2DEG with spin orbit coupling (SOC) such as oxide interfaces, this effect has been experimentally witnessed. Further, a fourfold oscillation in longitudinal resistance as a function of ϕ has also been observed. Motivated by these, we perform scattering theory calculations on a 2DEG with SOC in presence of an in-plane magnetic field connected to two-dimensional leads on either sides to obtain longitudinal and transverse conductances. We find that the longitudinal conductance is π-periodic and the transverse conductance is 2π-periodic in ϕ. The magnitude of oscillation in transverse conductance with ϕ is enhanced in certain patches in (α, b)-plane where α is the strength of SOC and b is Zeeman energy due to magnetic field. The oscillation in transverse conductance with ϕ can be highly multi-fold for large values of α and b. The highly multi-fold oscillations of transverse conductance are due to Fabry–Pérot type interference between the modes in the central region as backed by its length dependent features. Our study establishes that SOC in a material is sufficient to observe PHE without the need for anisotropic magnetic ordering or nontrivial topology of the bandstructure.

Yb delafossites: Unique exchange frustration of4fspin-12moments on a perfect triangular lattice

While the Heisenberg model for magnetic Mott insulators on planar lattice structures is comparatively well understood in the case of transition metal ions, the intrinsic spin-orbit entanglement of $4f$ magnetic ions on such lattices shows fascinating new physics largely due to corresponding strong anisotropies both in their single-ion and their exchange properties. We show here that the Yb delafossites, containing perfect magnetic ${\mathrm{Yb}}^{3+}$ triangular lattice planes with pseudospin $s=\frac{1}{2}$ at low temperatures, are an ideal platform to study these phenomena. Competing frustrated interactions may lead to an absence of magnetic order associated to a gapless spin liquid ground state with a huge linear specific heat exceeding that of many heavy fermions, whereas the application of a magnetic field induces anisotropic magnetic order with successive transitions into different long-range ordered structures. In this comparative study, we discuss our experimental findings in terms of a unified crystal-field and exchange model. We combine electron paramagnetic resonance (EPR) experiments and results from neutron scattering with measurements of the magnetic susceptibility, isothermal magnetization up to full polarization, and specific heat to determine the relevant model parameters. The impact of the crystal field is discussed as well as the symmetry-compatible form of the exchange tensor, and we give explicit expressions for the anisotropic $g$ factor, the temperature dependence of the susceptibility, the exchange-narrowed EPR linewidth, and the saturation field.

Bright correlated twin-beam generation and radiation shaping in high-gain parametric down-conversion with anisotropy.

Uniaxial anisotropy in nonlinear birefringent crystals limits the efficiency of nonlinear optical interactions and breaks the spatial symmetry of light generated in the parametric down-conversion (PDC) process. Therefore, this effect is usually undesirable and must be compensated for. However, high gain may be used to overcome the destructive role of anisotropy in order to generate bright two-mode correlated twin-beams. In this work, we provide a rigorous theoretical description of the spatial properties of bright squeezed light in the presence of strong anisotropy. We investigate a single crystal and a system of two crystals with an air gap (corresponding to a nonlinear SU(1,1) interferometer) and demonstrate the generation of bright correlated twin-beams in such configurations at high gain due to anisotropy. We explore the mode structure of the generated light and show how anisotropy, together with crystal spacing, can be used for radiation shaping.

Pinning Effects of Exchange and Magnetocrystalline Anisotropies on Skyrmion Lattice

Reorientation of skyrmion crystal (SkX) with respect to crystallographic axes is believed to be insensitive to anisotropies of fourth order in spin-orbit coupling, for which sixth order terms are considered for explanation. Here, we show that this is wrong due to an oversimplified assumption that SkX possesses hexagonal symmetry. When the deformation of SkX is taken into account, fourth order anisotropies such as exchange anisotropy and magnetocrystalline anisotropy have pinning (in this work, the word ‘pinning’ refers to the reorientation effects of intrinsic anisotropy terms) effects on SkX. In particular, we reproduce some experiments of MnSi and Fe1−xCoxSi by considering the effect of fourth order magnetocrystalline anisotropy alone. We reproduce the 30∘ rotation of SkX in Cu2OSeO3 by considering the combined effects of the exchange and magnetocrystalline anisotropies. And we use the exchange anisotropy to explain the reorientation of SkX in VOSe2O5.

Magnetic phase diagram of single-layer CrBr3 * *Project supported by the National Natural Science Foundation of China (Grant No. 11625415). Z.-G. Fu acknowledges the Innovation Development Foundation of China Academy of Engineering Physics (Grant No. ZYCX1921-02).

We theoretically provide a magnetic phase diagram for the single-layer (SL) CrBr3, which could be effectively tuned by both strain engineering and charge doping in SL-CrBr3. Through systematical first-principles calculations and Heisenberg model Hamiltonian simulations, three different magnetic phases in SL-CrBr3, which are off-plane ferromagnetic, in-plane ferromagnetic and in-plane Néel-antiferromagnetic phases, are found in the strain and charge doping regimes we studied. Furthermore, our results show that higher order Heisenberg exchange parameters and anisotropy exchange parameters should be taken into account for accurately illustrating the magnetic phase transition in SL-CrBr3. As a result, we find from the SpinW simulation that the Curie temperature is about T c = 38.4 K, which is well consistent with the experimental result 34 K [Nano Lett. 19 3138 (2019)]. The findings here may be confirmed in future experiments, and may be useful for the potential applications of SL-CrBr3 in spintronics field.

Postgrowth Shaping and Transport Anisotropy in Two-Dimensional InAs Nanofins.

We report on the postgrowth shaping of free-standing two-dimensional (2D) InAs nanofins that are grown by selective-area epitaxy and mechanically transferred to a separate substrate for device fabrication. We use a citric acid-based wet etch that enables complex shapes, for example, van der Pauw cloverleaf structures, with patterning resolution down to 150 nm as well as partial thinning of the nanofin to improve local gate response. We exploit the high sensitivity of the cloverleaf structures to transport anisotropy to address the fundamental question of whether there is a measurable transport anisotropy arising from wurtzite/zincblende polytypism in 2D InAs nanostructures. We demonstrate a mobility anisotropy of order 2-4 at room temperature arising from polytypic stacking faults in our nanofins. Our work highlights a key materials consideration for devices featuring self-assembled 2D III-V nanostructures using advanced epitaxy methods.

A quadrature-free Legendre polynomial approach for the fast modelling guided circumferential wave in anisotropic fractional order viscoelastic hollow cylinders

Compared to the traditional integer order viscoelastic model, a fractional order derivative viscoelastic model is shown to be advantageous. The characteristics of guided circumferential waves in an anisotropic fractional order Kelvin–Voigt viscoelastic hollow cylinder are investigated by a quadrature-free Legendre polynomial approach combining the Weyl definition of fractional order derivatives. The presented approach can obtain dispersion solutions in a stable manner from an eigenvalue/eigenvector problem for the calculation of wavenumbers and displacement profiles of viscoelastic guided wave, which avoids a lot of numerical integration calculation in a traditional polynomial method and greatly improves the computational efficiency. Comparisons with the related studies are conducted to validate the correctness of the presented approach. The full three dimensional spectrum of an anisotropic fractional Kelvin–Voigt hollow cylinder is plotted. The influence of fractional order and material parameters on the phase velocity dispersion and attenuation curves of guided circumferential wave is discussed in detail. Moreover, the difference of the phase velocity dispersion and attenuation characteristics between the Kelvin–Voigt and hysteretic viscoelastic models is also illustrated. The presented approach along with the observed wave features should be particularly useful in non-destructive evaluations using waves in viscoelastic waveguides.

Temperature dependence of London penetration depth anisotropy in superconductors with anisotropic order parameters

We study the effects of anisotropic order parameters on the temperature dependence of London penetration depth anisotropy $\gamma_\lambda(T)$. After MgB$_2$, this dependence is commonly attributed to distinct gaps on multi-band Fermi surfaces in superconductors. We have found, however, that the anisotropy parameter may depend on temperature also in one-band materials with anisotropic order parameters $\Delta(T,k_F)$, a few such examples are given. We have found also that for different order parameters, the temperature dependence of $\Delta(T)/\Delta(0)$ can be represented with good accuracy by the interpolation suggested by D. Einzel, J. Low Temp. Phys, {\bf 131}, 1 (2003), which simplifies considerably the evaluation of $\gamma_\lambda(T)$. Of particular interest is mixed order parameters of two symmetries for which $\gamma_\lambda(T)$ may go through a maximum for a certain relative weight of two phases. Also, for this case, we find that the ratio $\Delta_{max}(0)/T_c$ may exceed substantially the weak coupling limit of 1.76. It, however, does not imply a strong coupling, rather it is due to significantly anisotropic angular variation of $\Delta$.

Magnetization processes and magnetic domain structures in Ta/CoFeB/MgO stacks

Magnetization processes and magnetic domain structures in Ta/CoFeB/MgO stacks were studied in a series of samples with various CoFeB thicknesses d ranging from 1.24 to 1.60 nm with a step of 0.04 nm, using polar magneto-optical Kerr effect (PMOKE) magnetometry and microscopy. Thickness dependence of the magnetic anisotropy was evaluated and the first and second order anisotropy constants were quantified for each thickness. Accordingly, this dependence was deduced to result in magnetization reorientation from out-of-plane to in-plane through an easy-cone magnetization region (1.39 nm ≤ d ≤ 1.41 nm) as d was increased. PMOKE imaging of the magnetization reversal processes for stacks with out-of-plane easy axis indicated both a significant increase of the density of nucleation centers and a change in domain morphology with increasing d up to the magnetization reorientation thickness. Magnetization reversal dynamics was described by a thermal activation model consistent with a Barkhausen length of about 120 nm. The thinnest films with d = 1.24 and 1.28 nm exhibited straightened narrow stripe domains resulting from magnetic dipolar repulsion. A thorough study of narrow stripe domains was performed via direct and indirect magnetization reversal processes. The application of such structures as spin wave nano-channels could be promising.

Liquid-crystal-based topological photonics

Liquid crystals are complex fluids that allow exquisite control of light propagation thanks to their orientational order and optical anisotropy. Inspired by recent advances in liquid-crystal photo-patterning technology, we propose a soft-matter platform for assembling topological photonic materials that holds promise for protected unidirectional waveguides, sensors, and lasers. Crucial to our approach is to use spatial variations in the orientation of the nematic liquid-crystal molecules to emulate the time modulations needed in a so-called Floquet topological insulator. The varying orientation of the nematic director introduces a geometric phase that rotates the local optical axes. In conjunction with suitably designed structural properties, this geometric phase leads to the creation of topologically protected states of light. We propose and analyze in detail soft photonic realizations of two iconic topological systems: a Su-Schrieffer-Heeger chain and a Chern insulator. The use of soft building blocks potentially allows for reconfigurable systems that exploit the interplay between topological states of light and the underlying responsive medium.

Separate quantitative evaluation of degree of order and perpendicular magnetic anisotropy for disorder and order portion in FePt granular films

The dependence of the degree of order and perpendicular magnetic anisotropy (Ku⊥) on magnetic layer thickness (dmag) for FePt granular films with various grain boundary materials (GBMs) were investigated. According to the analysis for granular films with a constant GBM volume of 30 vol%, the order, disorder, and non-epitaxial portions co-existed in the FePt granular films. From the separate quantitative evaluation for these portions, the following was found; 1) the degree of order and magnitudes of Ku⊥ for disorder and order portions against dmag were constant, while the film average evaluation resulted in the dependence of the degree of order and Ku⊥ on dmag and the positive correlation between the grain diameter and the degree of order, 2) for the order portion, Ku⊥ had linear correlation with the degree of order, 3) the magnitude of Ku⊥ and the degree of order for the order portion depended on GBM.

Highly Saturated Glassy Liquid Crystal Films Having Nano- and Microscale Thicknesses for High-Power Laser Applications

The optical properties of glassy liquid crystals (GLC’s) designed to provide high resistance to laser-induced damage are explored. GLC’s readily enable freezing of the anisotropic ordering of liqui...

Ferromagnetic thin Films with Simple Cubic Structure as Described by Fourth Order Perturbed Heisenberg Hamiltonian

For the first time, fourth order perturbed Heisenberg Hamiltonian has been applied to study the properties of simple cubic structured ferromagnetic ultrathin films with two spin layers. Only the spin exchange interaction, second order magnetic anisotropy constant and the short-range magnetic dipole interaction were taken into account. Only when the second order anisotropy constant varies from one spin plane to the other spin plane, perturbation becomes nonzero. 3-D plots of total energy versus spin exchange interaction and angle, total energy versus second order anisotropy constant in bottom spin layer and angle, and total energy versus second order anisotropy constant in top layer and angle were plotted. Peaks in the plots are closely packed in fourth order perturbed case compared to the plots obtained using third order perturbed case. All the graphs were plotted using MATLAB program

Distributions of anisotropic order and applications to H-distributions

We define distributions of anisotropic order on manifolds, and establish their immediate properties. The central result is the Schwartz kernel theorem for such distributions, allowing the representation of continuous operators from [Formula: see text] to [Formula: see text] by kernels, which we prove to be distributions of order [Formula: see text] in [Formula: see text], but higher, although still finite, order in [Formula: see text]. Our main motivation for introducing these distributions is to obtain the new result that H-distributions (Antonić and Mitrović), a recently introduced generalization of H-measures are, in fact, distributions of order 0 (i.e. Radon measures) in [Formula: see text], and of finite order in [Formula: see text]. This allows us to obtain some more precise results on H-distributions, hopefully allowing for further applications to partial differential equations.

Competing spin modulations in the magnetically frustrated semimetal EuCuSb

The competing magnetic ground states of the itinerant magnet EuCuSb, which has a hexagonal layered structure, were studied via magnetization, resistivity, and neutron diffraction measurements on single-crystal samples. EuCuSb has a three-dimensional semimetallic band structure as confirmed by band calculation and angle-resolved photoelectron spectroscopy, consistent with the nearly isotropic metallic conductivity in the paramagnetic state. However, below the antiferromagnetic transition temperature of TN1 (8.5 K), the resistivity, especially along the hexagonal axis, increases significantly. This implies the emergence of anisotropic magnetic ordering coupled to the conducting electrons. Neutron diffraction measurements show that the Eu spins, which order ferromagnetically within each layer, are collinearly modulated (up-up-down-down) along the hexagonal axis below TN1, followed by the partial emergence of helical spin modulation below TN2 (6 K). Based on the observation of anomalous magnetoresistance with hysteretic behavior, we discuss the competing nature of the ground state inherent in a frustrated Heisenberg-like spin system with a centrosymmetric structure.

Oxygen-Mediated Superexchange Interactions and Their Impact on the Structural Stability, Magnetic Order, and Magnetocrystalline Anisotropy of One-Dimensional Co-Oxide Chains on Rh(553) Step-Surfaces

First-principles calculations in the framework of the generalized gradient approximation together with U on-site Coulomb corrections in the GGA + U approach to density functional theory (DFT) are p...