Conical Phase Research Articles

Broadband reflective terahertz metalens employing Bessel beams for enhanced efficiency and depth of focus.

This paper presents a reflective terahertz (THz) Bessel metalens with broadband operation in the frequency range of 0.80-1 THz. The design employs a near-wavelength, polarization-insensitive resonator to achieve a wideband response. Optimized at 0.89 THz, the metalens integrates a hyperbolic phase configuration combined with a conical phase profile. By varying the cone angle, the metalens attains a focusing efficiency of up to 76% and an extended depth of focus of 21.7λ. Simulations demonstrate superior performance compared to conventional focusing metalenses. This design shows significant potential for applications in terahertz imaging, communications, and sensing technologies.

Weak-field FMR and magnetization near the collinear to conical ferrimagnetic phase transition in the U-type hexaferrite Sr4CoZnFe36O60 ceramics

ABSTRACT Temperature evolution of the ferromagnetic resonance (FMR) and its interference with other microwave (MW) magnons near the collinear to conical ferrimagnetic phase transition at T c2 = 305 K is found to correlate with the evolution of the weak-field magnetization: from two components in the conical phase to one component in the collinear phase. The FMR splitting above T c2 correlates with the splitting of the coercive fields of the two magnetization components. A high sensitivity of the FMR to the weak magnetic bias near T c2 is shown to be caused by the gradual transformation of the conical spin magnetic moments to the longitudinal ones. Application of the weak magnetic bias allows to adjust the MW absorption, and its level of above 30 dB is achieved near the FMR frequency (5.7–7.2 GHz), that allows to consider the Sr4CoZnFe36O60 hexaferrite ceramics as a possible MW absorbing material.

Controllable three-dimensional helical energy backflow in an optical focusing field.

The energy of light generally moves forward along the light propagation direction. However, in recent years, a counter-intuitive effect has been discovered that energy backflow can occur in certain special light fields. Presently, controlling the energy backflow of light for application requirements is becoming a significant challenge. Here we propose a method to generate and control a three-dimensional helical energy backflow (HEB) optical field. By designing an exponential helical conical phase mask, the energy backflow region in a common tightly focused field can be stretched into a three-dimensional helical shape with an ultra-long longitudinal length. The length of the HEB region can be flexibly extended up to 47.6λ by varying the exponential phase index and the initial topological charge. Furthermore, we demonstrate that nanoparticles within the HEB field are subjected to optical pulling forces, thereby drawing the nanoparticles back to the light source. This work presents a new, to the best of our knowledge, approach for the three-dimensional manipulation of the energy backflow field with potential applications in nanoparticle manipulation and detection.

Magnetostriction related to skyrmion-lattice formation in chiral magnet FeGe

The B20 type chiral magnet FeGe exhibits the formation of skyrmion-lattice (SkL) phases in the vicinity of the magnetic ordering temperature. The SkL is a magnetic superlattice composed of vortex-type topological spin objects, and it has experimentally been known that its formation requires the existence of an intermediate (IM) phase between SkL and the paramagnetic (PM) phases. We take interest in how the crystal lattice experiences the formation of these topological spin texture. In this study, we observed the so-called spin–orbit coupling induced magnetostriction related to these topological spin texture formation, in addition to the ac magnetization anomalies. The temperature and magnetic field dependences of the lattice parameter reflected the transformation of phases, such as helimagnetic (HM), SkL, IM, conical (CM), and PM phases. In the PM region, a phase characterized as gaseous skyrmions was detected similarly to the case of the same B20 type MnSi. Furthermore, the HM, CM, and IM phases were also divided into two regions. Thus, the precise phase diagram near Tc was reconstructed from the prospect of the magnetostriction such that we demonstrated that the stabilization of skyrmions needs a finite magnetic field.

Switching of magnetoelectric states in the Y-type hexaferrite Ba0.5Sr1.5CoMgFe11AlO22

The multiferroic Y-type hexaferrites BaxSr2−xMe2Fe12−yAlyO22 (Me = Zn2+, Co2+, Mg2+, etc.) have attracted much attention due to their giant magnetoelectric (ME) effect up to room temperature and low modulated magnetic field by the chemical doping control of the complex magnetic phases. However, the research of substitution between the Me ions is rare. As doping at the Me ion site can combine the advantages of both, e.g., higher magnetic ordering temperature in Co2 and stronger ME coefficient in Mg2 Y-type hexaferrites, herein, we report the stability and switching of magnetoelectric states in the Y-type hexaferrites Ba0.5Sr1.5CoMgFe11AlO22 single crystals. Our results demonstrate that substituting half of the Mg2+ with Co2+ enhances the transition temperature of the alternating longitudinal conical phase to proper screw spin order up to room temperature compared to those Mg2 Y-type hexaferrites. Simultaneous occurrence of in-plane and out-of-plane ferroelectric polarization is observed, alongside comparable spontaneous magnetization. It was found that the in-plane spin-driven polarization can be reversible below 50 K with a substantial ME coefficient α = −8000 ps/m but becomes irreversible at 100 K. This reversal in the sign of the ME coefficient signifies the transition between two distinct ME states at high temperature. The reversibility and irreversibility of spin-induced polarization are discussed within the framework of free energy based on the ferroelectric phase, which prevail in numerous Y-type hexaferrites. Our results provide insights into understanding the role of the Me ions in the magnetoelectric coupling in Y-type hexaferrites.

Magnetic sublattice disorder mediated exchange bias at the interfaces of Ho/Er multilayers in their conical phases

Magnetic sublattice disorder mediated exchange bias at the interfaces of Ho/Er multilayers in their conical phases

Exchange coupling in the conical phase of Ho within Ho/Tb multilayers due to Ho magnetic sublattice disorder

Exchange coupling in the conical phase of Ho within Ho/Tb multilayers due to Ho magnetic sublattice disorder

Electron paramagnetic resonance probing of the spin fluctuation transition in the conical spiral phase of MnSi

In the spiral conical phase of manganese monosilicide, MnSi, the EPR spectra are studied at a frequency of 9.3 GHz in the temperature range of 5–30 K for an external magnetic field oriented along the crystallographic direction [100]. It is found that in the temperature range T < T* = 25 K, located 4 K below the paramagnetic phase-conical phase transition temperature TC = 29 K, a complex EPR spectrum consisting of several lines appears. A procedure is proposed for decomposing experimental spectra into components, which makes it possible to find for each spectral line the temperature dependences of the resonance magnetic field, line width, and integrated intensity. At Tf ∼16 K, one of the main lines in the EPR spectrum with the highest integrated intensity demonstrates a maximum in the temperature dependence of the line width W(T), corresponding to a change in W by a factor of ∼2.8. We argue that this unusual behavior appears as a consequence of a spin fluctuation transition in the conical spiral magnetic phase with long range magnetic order.

Field-controlled dynamics of skyrmions and monopoles.

Magnetic monopoles, despite their ongoing experimental search as elementary particles, have inspired the discovery of analogous excitations in condensed matter systems. In chiral condensed matter systems, emergent monopoles are responsible for the onset of transitions between topologically distinct states and phases, such as in the case of transitions from helical and conical phase to A-phase comprising periodic arrays of skyrmions. By combining numerical modeling and optical characterizations, we describe how different geometrical configurations of skyrmions terminating at monopoles can be realized in liquid crystals and liquid crystal ferromagnets. We demonstrate how these complex structures can be effectively manipulated by external magnetic and electric fields. Furthermore, we discuss how our findings may hint at similar dynamics in other physical systems and their potential applications.

Task-adaptive physical reservoir computing

Reservoir computing is a neuromorphic architecture that may offer viable solutions to the growing energy costs of machine learning. In software-based machine learning, computing performance can be readily reconfigured to suit different computational tasks by tuning hyperparameters. This critical functionality is missing in ‘physical’ reservoir computing schemes that exploit nonlinear and history-dependent responses of physical systems for data processing. Here we overcome this issue with a ‘task-adaptive’ approach to physical reservoir computing. By leveraging a thermodynamical phase space to reconfigure key reservoir properties, we optimize computational performance across a diverse task set. We use the spin-wave spectra of the chiral magnet Cu2OSeO3 that hosts skyrmion, conical and helical magnetic phases, providing on-demand access to different computational reservoir responses. The task-adaptive approach is applicable to a wide variety of physical systems, which we show in other chiral magnets via above (and near) room-temperature demonstrations in Co8.5Zn8.5Mn3 (and FeGe).

Terahertz Bessel metalens with an extended non-diffractive length and a high efficiency.

In this paper, we propose a reflective terahertz (THz) Bessel metalens that utilizes polarization-insensitive sub-wavelength metal resonator-dielectric-metal structures. The Bessel metalens is configured with the superposition of hyperboloidal and conical phase profiles, resulting in a high-efficiency and long non-diffractive length Bessel beam. Our experimental results demonstrate that the proposed Bessel metalens has a focusing efficiency of 72.1% and a non-diffractive length of 239λ. This device has promising aspects in the fields of THz imaging systems and other miniaturized and integrated scenes that require non-diffractive Bessel beams.

Pair interaction of localized topological structures in confined chiral media.

We study pairwise interactions between localized topological structures in chiral magnetic and cholesteric liquid crystal (CLC) systems confined in the planar geometry. Our calculations for magnetics are based on the lattice model that takes into account the bulk and surface anisotropies along with the exchange and the Dzyaloshinskii-Moriya interactions. In CLC cells, these anisotropies describe the energy of interaction with an external magnetic or electric field and the anchoring energy assuming that the magnetic or electric anisotropy is negative and the boundary conditions are homeotropic. We have selected the region of the phase diagram, where various localized solitonlike structures, including skyrmion tubes, torons, and leeches, embedded in the ground state of the z-cone (conical phase) coexist, and carried out numerical analysis of the distance dependencies of the effective intersoliton interaction potentials. For skyrmions and torons, the potentials are found to be attractive in the large separation region. It turned out that for these potentials, the effects of axial asymmetry are negligible. By contrast, it turned out that for the intermediate structures between the skyrmions and torons known as the leeches, the leech-leech potentials generally depend on the orientation of the intersoliton separation vector and their large distance parts may become repulsive at certain directions of the vector. All the potentials have the short distance repulsive parts and the local minima located at the equilibrium separations. It is found that the skyrmion-skyrmion potential has an additional metastable configuration shifted towards the short-distance region.

Exchange coupling due to spin-imbalance in Er magnetic sublattice within Er/Tb multilayers

Topologically stable spin spiral structures in rare-earth (RE) can form the basis of realizing all-spin-based technology as strong exchange coupling has been reported earlier at the ferromagnet (FM)–RE or RE–RE interfaces around the temperature range where both layers are essentially ferromagnetic. Owing to the small number of irreversible spins in the non-collinear configuration within the RE layer, very weak coupling is rendered around the temperature range of the helical phase. Competing anisotropies in Er result in a conical c-axis ferromagnetic structure below 20 K while Tb orders ferromagnetically with an easy axis along the a-axis below 221 K. Here, we grow heteroepitaxial Er/Tb multilayers and find an exchange coupling of up to +170±10 Oe, particularly below 20 K. This exchange bias phenomenon can be due to the effect of spin spiral to conical phase fraction within Er below 20 K. Additionally, we find inter-domain magnetic AC frequency-responsive magnetic interaction behavior which does not comply with the spin-freezing/blocking like ordering around the crossover range of helical to conical phase. Empirically, this can be explained in terms of the increased spin-imbalance in each Er magnetic sublattice due to the atomic disorder induced during the field cooling process. This unconventional exchange coupling could essentially enable us to tailor non-collinear spintronic devices in the future with induced spin-imbalance in the RE sublattice.

Distinguishing the Focal-Conic Fan Texture of Smectic A from the Focal-Conic Fan Texture of Smectic B

This publication presents methods of distinguishing the focal texture of the conical smectic phase A (SmA) and the crystalline smectic B phase (CrB). Most often, characteristic transition bars are observed in polarized light at the temperature point of the SmA–CrB phase transition. TOApy software transforms each image from a series of images recorded during POM observation to a function of light intensity versus temperature. Thermo-optical analysis is a powerful quantitative tool to notice this phase transition, but it has some limitations. The other applied method, the local binary pattern (LBP) algorithm, with high probability, detects differences between the textures of the conical focal fan of the SmA and CrB phases. The LBP algorithm is an efficient tool for texture classification.

Harnessing Skyrmion Hall Effect by Thickness Gradients in Wedge-Shaped Samples of Cubic Helimagnets.

The skyrmion Hall effect, which is regarded as a significant hurdle for skyrmion implementation in thin-film racetrack devices, is theoretically shown to be suppressed in wedge-shaped nanostructures of cubic helimagnets. Under an applied electric current, ordinary isolated skyrmions with the topological charge 1 were found to move along the straight trajectories parallel to the wedge boundaries. Depending on the current density, such skyrmion tracks are located at different thicknesses uphill along the wedge. Numerical simulations show that such an equilibrium is achieved due to the balance between the Magnus force, which instigates skyrmion shift towards the wedge elevation, and the force, which restores the skyrmion position near the sharp wedge boundary due to the minimum of the edge-skyrmion interaction potential. Current-driven dynamics is found to be highly non-linear and to rest on the internal properties of isolated skyrmions in wedge geometries; both the skyrmion size and the helicity are modified in a non-trivial way with an increasing sample thickness. In addition, we supplement the well-known theoretical phase diagram of states in thin layers of chiral magnets with new characteristic lines; in particular, we demonstrate the second-order phase transition between the helical and conical phases with mutually perpendicular wave vectors. Our results are useful from both the fundamental point of view, since they systematize the internal properties of isolated skyrmions, and from the point of view of applications, since they point to the parameter region, where the skyrmion dynamics could be utilized.

Propagation of intense electromagnetic pulse with a small conical phase shift induced by Axicon optics.

The conical phase shift induced by the axicon generates a non-diffracting Bessel beam. In this paper, we examine the propagation property of an electromagnetic wave focused by a thin lens and axicon waveplate combination, which induces a small amount of conical phase shift less than one wavelength. A general expression describing the focused field distribution has been derived under the paraxial approximation. The conical phase shift breaks the axial symmetry of intensity and shows a focal spot-shaping capability by controlling the central intensity profile within a certain range near focus. The focal spot-shaping capability can be applied to form a concave or flattened intensity profile, which can be used to control the concavity of a double-sided relativistic flying mirror or to generate the spatially uniform and energetic laser-driven proton/ion beams for hadron therapy.

Spin nematics meet spin liquids: Exotic quantum phases in the spin-1 bilinear-biquadratic model with Kitaev interactions

Spin liquid crystals are magnetic analogs of liquid crystals, possessing properties of both liquids and solids, a typical example of which are spin nematics. Spin nematics share many features with spin liquids, and the interplay between them is a promising, but little explored, route to uncovering new phases of matter. Here, we address this question in the context of a spin-$1$ magnet on the honeycomb lattice, by considering a model with both biquadratic interactions, favouring spin-nematic states, and Kitaev-like interactions, supporting spin liquids. Accompanying these, where dipole and quadrupole moments compete, we find a plethora of exotic phases, including multiple-$q$ states with nonzero scalar spin chirality; a quasi-one-dimensional coplanar phase; a twisted conical phase; and a noncoplanar order state which gives way to a chiral spin liquid at finite temperature. The implication of these results for experiment is discussed.

Highly tunable spin Hall magnetoresistance in room-temperature magnetoelectric multiferroic, Sr3Co2Fe24O41|Pt hybrids

We present spin transport studies on a low-field, room-temperature magnetoelectric multiferroic polycrystalline Sr3Co2Fe24O41|Pt heterostructure wherein a highly tunable transverse conical magnetic phase is responsible for static and dynamic magnetoelectric coupling. We measured angular dependence of spin Hall magnetoresistance (SMR) at constant magnetic fields (H) in the range; 50–100 kOe. Application of field below the critical value (Hc1 ≈ 2.5 kOe), yielded negative SMR and the H-evolution of normalized SMR ((ΔR∕R0) × 100 %) exhibited a negative gradient. Further, an increase in H resulted in the positive slope of (ΔR∕R0) × 100 % Vs. H and later at higher H around 14 kOe, a crossover from negative to positive SMR was observed. We employed a simple model for estimating the equilibrium magnetic configuration and computed the SMR modulation at various values of H. We argue that the tilting of the cone is dominant and in turn responsible for the observed nature of SMR below 2.5 kOe while, the closing of the cone-angle is pronounced at higher fields causing a reversal in sign of the SMR from negative to positive. Importantly, SMR experiments revealed that a change in the helicity with a reversal of the magnetic field has no influence on the observed SMR. Longitudinal spin Seebeck effect (LSSE) signal was measured to be ≈ 500 nV at 280 K, under application of thermal gradient, ΔT = 23 K and field, 60 kOe. The observed LSSE signal, originating from pure magnon spin current, showed a similar H-dependent behavior as that of the magnetization of Sr3Co2Fe24O41. Our detailed spin transport studies on polycrystalline Sr3Co2Fe24O41|Pt heterostructure demonstrate high tunability of the amplitude and the sign of the SMR, highlighting its potential for novel spintronic devices such as SMR-based spin valves and voltage-controlled spin transport devices.

Small-angle neutron scattering of long-wavelength magnetic modulations in reduced sample dimensions.

Magnetic small-angle neutron scattering (SANS) is ideally suited to providing direct reciprocal-space information on long-wavelength magnetic modulations, such as helicoids, solitons, merons or skyrmions. SANS of such structures in thin films or micro-structured bulk materials is strongly limited by the tiny scattering volume vis a vis the prohibitively high background scattering by the substrate and support structures. Considering near-surface scattering just above the critical angle of reflection, where unwanted signal contributions due to substrate or support structures become very small, it is established that the scattering patterns of the helical, conical, skyrmion lattice and fluctuation-disordered phases in a polished bulk sample of MnSi are equivalent for conventional transmission and near-surface SANS geometries. This motivates the prediction of a complete repository of scattering patterns expected for thin films in the near-surface SANS geometry for each orientation of the magnetic order with respect to the scattering plane.

Anomalous Hall effect in conical helimagnetic crystals

Spin-spiral texture can substantially change charge transport properties in helimagnets. We find the anomalous Hall effect (AHE) exhibiting the dramatic behavior with respect to chemical potential $\ensuremath{\mu}$ in conical magnetic structures. The direct conductivity demonstrates kinks, and the anomalous Hall current exhibits minima and maxima changing the sign. We analytically derive the expression for energy bands and eigenstates in the most general case. Because of the conical potential, the energy bands are split into two nonparabolic bands where the lower band can have one- or two-minima shapes in the ${k}_{z}$ direction ($\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathbit{z}}$ is a direction of the spiral axis). We prove that the origin of the anomalous Hall effect is not topological and is due to the interplay between the asymmetry of energy bands in the $x$ and $z$ directions and spin restrictions in the phase space due to the conical potential. We also investigate the dependence of transport properties on cone half- angle $\ensuremath{\theta}$, and find that the effects are most pronounced at $\ensuremath{\theta}=\ensuremath{\pi}/2$ (a helical state). Electric current is calculated using the Boltzmann equation where the relaxation is caused by electron-acoustic phonon interaction. The transition probability is found to be a $2\ifmmode\times\else\texttimes\fi{}2$ matrix with nonvanishing off-diagonal elements indicating the strong interband transitions. The origin of interband transitions is because of the nature of the conical potential where conduction electron spins interact with localized magnetic moments. To verify the proposed theory, we calculate the temperature dependence of resistivity for $\mathrm{MnSi}$ crystals and find the discontinuity at the phase transition between conical and paramagnetic phases. The calculations are in the excellent agreement with the experimental data. In addition, we predict the discontinuity behavior for the anomalous Hall resistivity at the phase transition where the resistivity exhibits the abrupt change at $T={T}_{C}$, (a) to zero if the relativistic effects for the conduction electrons are small or (b) to a nonzero value if Rashba/Dresselhaus effects are taken into account.