Two-dimensional Magnetic Systems Research Articles

Crystallisation in a two-dimensional granular system at constant temperature

We study the crystallisation processes occurring in a nonvibrating two-dimensional magnetic granular system at various fixed values of the effective temperature. In this system, the energy loss due to dissipative effects is compensated by the continuous energy input coming into the system from a sinusoidal magnetic field. When this balance leads to high values of the effective temperature, no aggregates are formed, because particles’ kinetic energy prevents them from aggregating. For lower effective temperatures, formation of small aggregates is observed. The smaller the values of the applied field’s amplitude, the larger the number of these disordered aggregates. One also observes that when clusters form at a given effective temperature, the average effective diffusion coefficient decreases as time increases. For medium values of the effective temperature, formation of small crystals is observed. We find that the sixth bond-orientational order parameter and the number of bonds, when considering more than two, are very sensitive for exhibiting the order in the system, even when crystals are still very small.

Designing frustration in two-dimensional magnetic systems via the application of uniaxial strain

First principles are used and combined with Monte Carlo simulations to predict that the application of compressive uniaxial strains in two-dimensional $\mathrm{CrGe}{\mathrm{Te}}_{3}$ can tune the underlying magnetic parameters in such a way that the system undergoes a phase transition from ferromagnetic (FM) to antiferromagnetic (AFM) phases, with the border between these being a region of high frustration. Such latter region can be the playground for fine-tuning the system to exhibit exotic states. Moreover, we also show and explain that such uniaxial strains also dramatically tune the critical temperatures, namely N\'eel temperatures for the AFM phase and Curie temperatures for the FM phase, which is of obvious technological and fundamental significance.

On the Asymptotic Dynamics of 2-D Magnetic Quantum Systems

In this work we provide results on the long time localisation in space (dynamical localisation) of certain two-dimensional magnetic quantum systems. The underlying Hamiltonian may have the form $H=H_0+W$, where $H_0$ is rotationally symmetric, has dense point spectrum, and $W$ is a perturbation that breaks the rotational symmetry. In the latter case, we also give estimates for the growth of the angular momentum operator in time.

Fingerprints of Universal Spin-Stiffness Jump in Two-Dimensional Ferromagnets

Motivated by recent progress on synthesizing two-dimensional magnetic van der Waals systems, we propose a setup for detecting the topological Berezinskii-Kosterlitz-Thouless phase transition in spin-transport experiments on such structures. We demonstrate that the spatial correlations of injected spin currents into a pair of metallic leads can be used to measure the predicted universal jump of 2/π in the ferromagnet spin stiffness as well as its predicted universal square root dependence on temperature as the transition is approached from below. Our setup provides a simple route to measuring this topological phase transition in two-dimensional magnetic systems, something which up to now has proven elusive. It is hoped that this will encourage experimental efforts to investigate critical phenomena beyond the standard Ginzburg-Landau paradigm in low-dimensional magnetic systems with no local order parameter.

Great enhancement of Curie temperature and magnetic anisotropy in two-dimensional van der Waals magnetic semiconductor heterostructures

In two-dimensional (2D) magnetic systems, large magnetic anisotropy is needed to stabilize the magnetic order according to Mermin-Wagner theorem. Based on density functional theory (DFT) calculations, we propose that the magnetic anisotropic energy (MAE) of 2D ferromagnetic (FM) semiconductors can be strongly enhanced in van der Waals heterostructures by attaching a nonmagnetic semiconductor monolayer with large spin-orbit coupling. We studied Cr2Ge2Te6/PtSe2 bilayer heterostructures, where each layer has been realized in recent experiments. The DFT calculations show that the MAE of Cr2Ge2Te6/PtSe2 is enhanced by 70%, and the Curie temperature TC is increased far beyond room temperature. A model Hamiltonian is suggested to analyze the DFT results, showing that both the Dzyaloshinskii-Moriya interaction and the single-ion anisotropy contribute to the enhancement of the MAE. Based on the superexchange picture, we find that the decreased energy difference between 3d orbitals of Cr and 5p orbitals of Te contributes partially to the increase of TC. Our present work indicates a promising way to enhance the MAE and TC by constructing van der Waals semiconductor heterostructures, which will inspire further studies on the 2D magnetic semiconductor systems.

Out-of-plane magnetic anisotropy engineered via band distortion in two-dimensional materials

We unveil the connection between magnetic anisotropy and band structures in $\mathrm{\ensuremath{\Gamma}}$-specialized ${\mathrm{In}}_{2}{\mathrm{Se}}_{3}/{\mathrm{Fe}}_{3}{\mathrm{GeTe}}_{2}$ heterostructure, through first-principles calculations. A significant band distortion occurs near the $\mathrm{\ensuremath{\Gamma}}$ point with a formed valley. As the band-distortion-caused valley moves relative to the quasivalence band maximum, the magnetic anisotropy switches between in-plane and out-of-plane magnetic anisotropy. Such a rule applies to either the strained or polarization-switched ${\mathrm{In}}_{2}{\mathrm{Se}}_{3}/{\mathrm{Fe}}_{3}{\mathrm{GeTe}}_{2}$ heterostructure. These findings demonstrate the feasibility of predicting the magnetic anisotropy by band structure modification in two-dimensional magnetic systems.

Performance Analysis and Optimization of Spatially Coupled Protograph-Based Low-Density Parity-Check Codes for Two-Dimensional Magnetic Recording Systems

As a class of convolutional-based low-density parity-check (LDPC) codes, spatially coupled protograph (SC-P) codes not only can exhibit outstanding error performance but also can realize low-complexity implementation. Motivated by the prominent superiorities, SC-P codes have been intensively investigated in various communication environments. However, no research works regarding SC-P codes in the magnetic recording (MR) scenarios have been done so far. To explore such an issue mentioned previously, this article carries out a comprehensive study on the SC-P codes in the two-dimensional magnetic recording (TDMR) systems. Specifically, a turbo-like extrinsic information transfer (EXIT) algorithm is conceived for the SC-P-coded TDMR systems. With the help of such an algorithm, we evaluate the convergence performance (i.e., decoding thresholds) for conventional SC-P codes over TDMR channels with turbo equalization and illustrate that such codes should be re-constructed to attain better performance. Therefore, we develop an optimization scheme to generate a novel class of SC-P codes, called enhanced SC-P codes, which can exhibit promising decoding thresholds without losing the linear-minimum-distance superiority. The convergence-performance analyses and simulated results reveal that such enhanced SC-P codes can obtain more desirable coding gains in contrast to the conventional SC-P codes and the state-of-the-art protograph codes for the whole signal-to-noise-ratio (SNR) range under study. The excellent performance and simple implementation make the enhanced SC-P codes a very competitive error-correction solution for the next-generation TDMR devices.

Structure, chromium vacancies, and magnetism in a Cr12−xTe16 compound

Binary Cr-Te compounds are known to exhibit various structures and interesting physical properties, which are very sensitive to Cr content and arrangement. We report the structure and physical properties of a compound $\mathrm{C}{\mathrm{r}}_{12\ensuremath{-}x}\mathrm{T}{\mathrm{e}}_{16}$ with $x\ensuremath{\sim}2.65$. $\mathrm{C}{\mathrm{r}}_{9.35}\mathrm{T}{\mathrm{e}}_{16}$ crystallizes in the trigonal structure with the space group $P\overline{3}m1$ (No. 164), consisting of four different Cr sites (Cr1, Cr2, Cr3, Cr4) with an ordered Cr4 vacant layer. The electrical resistivity, magnetization, specific heat, and neutron diffraction measurements indicate that there is a ferromagnetic transition at ${T}_{\mathrm{C}1}\ensuremath{\sim}160$ K with the first-order nature, and an anomaly at ${T}_{\mathrm{C}2}\ensuremath{\sim}67$ K. At 5 K, the magnetic moments of Cr2 and Cr3 are aligned along the $c$ axis with $2.78\phantom{\rule{0.16em}{0ex}}{\ensuremath{\mu}}_{\mathrm{B}}/\mathrm{Cr}$. Detailed neutron diffraction refinement suggests that ordered magnetic moments on Cr1 (fully occupied) and Cr4 (partially occupied) are negligible. The different magnetic response stems from different valence states and different magnetic interactions between Cr2/Cr3 and Cr1/Cr4 as evidenced by the x-ray absorption fine-structure measurements. This creates a unique two-dimensional magnetic system with ordered moments confined in the Cr2/Cr3 layer.

Magnetism and Optical Anisotropy in van der Waals Antiferromagnetic Insulator CrOCl.

van der Waals (vdW) magnetic insulators are of significance in both fundamental research and technological application, but most two-dimensional (2D) vdW magnetic systems are unstable and of high lattice symmetry. Stable 2D vdW magnetic insulators with anisotropic structure are needed to modulate the properties and unlock potential applications. Here we present a stable vdW antiferromagnetic material, CrOCl, with low-symmetry orthorhombic structure, and investigate systematically its magnetism, phase transition behavior, and optical anisotropy. Spin-phonon coupling effects are uncovered by the abnormal frequency shifts of Raman-active modes, suggesting the formation of a magnetic superstructure. The sizable abnormal change of interplanar spacing indicates the presence of a structural transition at around 27 K. Further in-plane vibrational, reflectional, and absorptional anisotropic properties are explored both experimentally and theoretically, revealing a highly polarization sensitive characteristic and linear dichroism in 2D CrOCl. Meanwhile, the particularly high polarization dependency of the second-harmonic generation and the nonlinear susceptibility of ∼2.24 × 10-11 m/V make it suitable in the field of polarization-dependent nonlinear optics. The findings on the intricate properties of 2D CrOCl lay foundations for future applications of low-symmetry vdW magnets in spin-dependent electronic and optoelectronic devices.

Confinement of magnetism in atomically thin La0.7Sr0.3CrO3/La0.7Sr0.3MnO3 heterostructures

At crystalline interfaces where a valence-mismatch exists, electronic, and structural interactions may occur to relieve the polar mismatch, leading to the stabilization of non-bulk-like phases. We show that spontaneous reconstructions at polar La0.7Sr0.3MnO3 interfaces are correlated with suppressed ferromagnetism for film thicknesses on the order of a unit cell. We investigate the structural and magnetic properties of valence-matched La0.7Sr0.3CrO3/La0.7Sr0.3MnO3 interfaces using a combination of high-resolution electron microscopy, first principles theory, synchrotron X-ray scattering and magnetic spectroscopy and temperature-dependent magnetometry. A combination of an antiferromagnetic coupling between the La0.7Sr0.3CrO3 and La0.7Sr0.3MnO3 layers and a suppression of interfacial polar distortions are found to result in robust long-range ferromagnetic ordering for ultrathin La0.7Sr0.3MnO3. These results underscore the critical importance of interfacial structural and magnetic interactions in the design of devices based on two-dimensional oxide magnetic systems.

Structural stability and control at high speed regime of two-dimensional active magnetic bearing systems

An extensive and complete theoretical background useful while taking relevant decisions in the designing and controlling process of two-dimensional (2D) active magnetic bearings (AMBs) are proposed. By means of the Hamiltonian of the associated conservative system, a state diagram of stability of the system is established and the critical parameters describing boundaries of each domain analytically derived. It appears that the system exhibits seven domains of stability ranging from a totally unstable domain to a fully stable one depending on the delicate balance between the control parameters, the bearings parameters and the bias current. The results indicate that the 2D-configuration of the system enlarges its stability domain in the working range of the precontrol current parameter and contributes also to upgrade the loading capacity of the system. Nonlinear oscillations of the shaft in the high speed regime are also investigated in the domain of possible stability of the system and the analytical expression of the frequency response of the system derived. The analysis of the results shows that the lowest amplitude of vibrations are obtained for the small value of the proportional gain of the PD controller. Numerical simulations performed confirmed the accuracy of theses obtained results.

A sum rule of uniaxial anisotropy and external magnetic field for formation of Néel-type skyrmion lattices in two-dimensional ferromagnets

It is generally believed that the perpendicular magnetic anisotropy (PMA) plays an important role in stabilizing skyrmion lattices (SkL) in two-dimensional (2D) magnetic systems in which both Heisenberg exchange and Dzyaloshinskii–Moriya interactions co-exist, and the skyrmion sizes in SkLs are mainly determined by the strengths of these two intrinsic interactions. To investigate the details, we employ here a quantum computational approach we develop in recent years to simulate the Néel-type skyrmion lattices formed on a 2D PdFe/Ir(1 1 1)-like film. From our simulated results, we find that: within an external magnetic field applied normal to the film plane, the PMA is indeed able to help induce Néel-type SkLs in a wider field range; however, to stabilize the SkLs, the PMA cannot be too strong, the strengths of the external magnetic field and the maximal PMA must satisfy a sum rule since the effective perpendicular magnetic field generated by these two interactions cannot exceed a largest value. We also notice that the periodical boundary condition imposed on the FM system in simulations is able to facilitate SkL formations, and it can also modify the skyrmion size in a certain extend.

Crystal growth, microstructure, and physical properties of SrMnSb2

We report on the crystal and magnetic structures, magnetic, and transport properties of SrMnSb$_2$ single crystals grown by the self-flux method. Magnetic susceptibility measurements reveal an antiferromagnetic (AFM) transition at $T_{\rm N} = 295(3)$ K. Above $T_{\rm N}$, the susceptibility slightly increases and forms a broad peak at $T \sim 420$ K, which is a typical feature of two-dimensional magnetic systems. Neutron diffraction measurements on single crystals confirm the previously reported C-type AFM structure below $T_{\rm N}$. Both de Haas-van Alphen (dHvA) and Shubnikov-de Haas (SdH) effects are observed in SrMnSb$_2$ single crystals. Analysis of the oscillatory component by a Fourier transform shows that the prominent frequencies obtained by the two different techniques are practically the same within error regardless of sample size or saturated magnetic moment. Transmission electron microscopy (TEM) reveals the existence of stacking faults in the crystals, which result from a horizontal shift of Sb atomic layers suggesting possible ordering of Sb vacancies in the crystals. Increase of temperature in susceptibility measurements leads to the formation of a strong peak at $T \sim {570}$ K that upon cooling under magnetic field the susceptibility shows a ferromagnetic transition at $T_{\rm C} \sim 580$ K. Neutron powder diffraction on crushed single-crystals does not support an FM phase above $T_{\rm N}$. Furthermore, X-ray magnetic circular dichroism (XMCD) measurements of a single crystal at the $L_{2,3}$ edge of Mn shows a signal due to induced canting of AFM moments by the applied magnetic field. All evidence strongly suggests that a chemical transformation at the surface of single crystals occurs above 500 K concurrently producing a minute amount of ferromagnetic impurity phase.

General theory of the topological Hall effect in systems with chiral spin textures

We present a consistent theory of the topological Hall effect (THE) in two-dimensional magnetic systems with a disordered array of chiral spin textures, such as magnetic skyrmions. We focus on the scattering regime when the mean-free path of itinerant electrons exceeds the spin texture size, and THE arises from the asymmetric carrier scattering on individual chiral spin textures. We calculate the resistivity tensor on the basis of the Boltzmann kinetic equation taking into account the asymmetric scattering on skyrmions via the collision integral. Our theory describes both the adiabatic regime when THE arises from a spin Hall effect and the nonadiabatic scattering when THE is due to purely charge transverse currents. We analyze the dependence of THE resistivity on a chiral spin texture structure, as well as on material parameters. We discuss the crossover between spin and charge regimes of THE driven by the increase of skyrmion size, the features of THE due to the variation of the Fermi energy, and the exchange interaction strength; we comment on the sign and magnitude of THE.

Structural and optical properties of two-dimensional gadolinium stearate Langmuir monolayer

Langmuir-Blodgett (LB) films having large stack of amphiphilic-fatty-acids bearing rare-earth-ions are ideal two-dimensional magnetic systems to study spin-vortex ordering as the distances of the magnetic-ions along the out-of-plane and in-plane directions differ by an order of magnitude. Here we present results of in-situ X-ray scattering measurements on Langmuir monolayer of the amphiphilic stearic acid on the water surface containing Gadolinium ions to understand the formation process of monolayer and multilayer LB films on the substrates. Infrared spectroscopy and microscopy measurements were also carried out to understand the growth and transfer mechanism of the LB films.

Development of High-resolution Two-dimensional Magnetic Field Measurement System by Use of Printed-circuit Technology

Development of High-resolution Two-dimensional Magnetic Field Measurement System by Use of Printed-circuit Technology

Collective magnetism in an artificial 2D XY spin system

Two-dimensional magnetic systems with continuous spin degrees of freedom exhibit a rich spectrum of thermal behaviour due to the strong competition between fluctuations and correlations. When such systems incorporate coupling via the anisotropic dipolar interaction, a discrete symmetry emerges, which can be spontaneously broken leading to a low-temperature ordered phase. However, the experimental realisation of such two-dimensional spin systems in crystalline materials is difficult since the dipolar coupling is usually much weaker than the exchange interaction. Here we realise two-dimensional magnetostatically coupled XY spin systems with nanoscale thermally active magnetic discs placed on square lattices. Using low-energy muon-spin relaxation and soft X-ray scattering, we observe correlated dynamics at the critical temperature and the emergence of static long-range order at low temperatures, which is compatible with theoretical predictions for dipolar-coupled XY spin systems. Furthermore, by modifying the sample design, we demonstrate the possibility to tune the collective magnetic behaviour in thermally active artificial spin systems with continuous degrees of freedom.

Structural characterization of a magnetic granular system under a time-dependent magnetic field: Voronoi tessellation and multifractal analysis

The structure of a two-dimensional magnetic granular system was determined by multifractal and Voronoi polygon analysis for a wide range of particle concentrations. Randomizing of the particle motions are produced by applying to the system a time-dependent sinusoidal magnetic field directed along the vertical direction. Both repulsive and attractive short-range interactions between the particles are induced. A direct observation of such system shows qualitatively that, as particle concentration increases, the structure evolves from being liquid-like at low particle concentrations to solid-like at high concentrations. We observe the formation of clusters which are small and weakly bonded and short-lived at low concentrations. Above a threshold particle concentration, clusters grow larger and are more strongly attached. In the system, one can distinguish the mobile particles from the immobile particles belonging to clusters, they can be considered separately as two different phases, a fluid and a solid. We determined the information entropy of the system as a whole and separately from each phase as particle concentration increases. The distribution of the Voronoi polygon areas are well fitted by a two-parameter gamma distribution and we have found that the regularity factor shows a notable change when pieces of the solid phase start to form. The methods we use here show that they can use even when the system is heterogeneous and they provide information when changes start.

Polar Channel Coding Schemes for Two-Dimensional Magnetic Recording Systems

This paper proposes new two-dimensional magnetic recording (TDMR) systems using polar channel coding as practical error correction coding. It is known that the time and space complexities of the encoding/decoding algorithms based on polar channel coding are $\mathcal {O}(N \log N)$ , where $N$ is the codeword (block) length. If we compare the error-correction performance of a polar code with that of a low-density parity-check (LDPC) code in the same rate, it is known that the polar code has a longer length and its decoder still has a lower implementation complexity than the LDPC decoder. Therefore, relatively low-complexity coding schemes are preferable for any TDMR systems under high rates and relatively long codeword lengths. In this paper, the proposed TDMR system serially concatenates a two-dimensional (2-D) modulation code with one-dimensional (1-D) polar codes in each down-track direction. These element polar codes are designed on the fundamentals of the channel polarization theory, which are applied for channels with memory. Actually, it evaluates the performance of the signal processing scheme with concatenated coding and generalized partial response equalization for the proposed TDMR system using bit-patterned media by computer simulations. As a result, it shows that the block error rate performance of the proposed TDMR system with the 2-D modulation and polar channel coding schemes is superior to that of the 1-D system with the conventional 1-D high rate modulation and LDPC coding schemes.

Asymmetrical DC bias analysis of the no‐load series transformer by using the TPFEM

The time-periodic finite element method (TPFEM) is coupled with circuit equations to study the asymmetrical DC bias problems of series transformer in this study. The periodic characteristics of the current and the magnetic field are taken as the restraint conditions. Taking into account the external voltages and determining the equivalent thickness of the two-dimensional magnetic system by calculating the magnetic field energy, the field–circuit coupled time-periodic finite element equations are built. The locally convergent fixed-point method is used to solve the non-linear time-varying equations by updating the fixed reluctivity. The calculated results agree well with those measured on a no-load low-voltage series transformer prototype under asymmetrical DC bias, which verifies the effectiveness of TPFEM in the DC bias calculation. The characteristics of the no-load series transformer prototype under asymmetrical DC bias are analysed based on this method.