Ferromagnetic Lattice Research Articles

Low-lying spin excitations due to next-nearest neighbour interactions in a ferromagnetic lattice with a body-centred cubic (bcc) crystal structure

Spin excitations due to the next-nearest-neighbour interactions are investigated for a ferromagnetic lattice with a body-centred cubic (bcc) crystal structure. Using the three-dimensional Heisenberg spin model in a uniform external magnetic field, both the nearest-neighbour (NN) and next-nearest-neighbour (NNN) exchange interactions are considered. The spin wave energies at low temperatures are calculated for which the system is close to its ground state. From the dispersion plots, the additional exchange interactions by the NNN cause an increase in the spin excitation energies. Furthermore, there is a critical NNN/NN exchange ratio for which the effect of the NNN interactions becomes evident as characterized by the presence of two maximum energy peaks in the energy spectra.

Tunable Magnonic Spectra in Two‐Dimensional Magnonic Crystals with Variable Lattice Symmetry

AbstractTunable magnonic properties are demonstrated in two‐dimensional magnonic crystals in the form of artificial ferromagnetic nanodot lattices with variable lattice symmetry. An all‐optical time‐domain excitation and detection of the collective precessional dynamics is performed in the strongly magnetostatically coupled Ni80Fe20 (Py) circular dot lattices arranged in different lattice symmetry such as square, rectangular, hexagonal, honeycomb, and octagonal symmetry. As the symmetry changes from square to octagonal through rectangular, hexagonal and honeycomb, a significant variation in the spin wave spectra is observed. The single uniform collective mode in the square lattice splits in two distinct modes in the rectangular lattice and in three distinct modes in the hexagonal and octagonal lattices. However, in the honeycomb lattice a broad band of modes are observed. Micromagnetic simulations qualitatively reproduce the experimentally observed modes, and the simulated mode profiles reveal collective modes with different spatial distributions with the variation in the lattice symmetry determined by the magnetostatic field profiles. For the hexagonal lattice, the most intense peak shows a six‐fold anisotropy with the variation in the azimuthal angle of the external bias magnetic field. Analysis shows that this is due to the angular variation of the dynamical component of magnetization for this mode, which is directly influenced by the variation of the magnetostatic field on the elements in the hexagonal lattice. The observations are important for tunable and anisotropic propagation of spin waves in magnonic crystal based devices.

Ground States of Two-Dimensional Ising Spin Glasses: Fast Algorithms, Recent Developments and a Ferromagnet-Spin Glass Mixture

Using advanced numerical approaches based on optimization algorithms, much progress has been achieved for the study of the ground-state and low-temperature behavior of two-dimensional Ising spin glasses. Recent results led to a rather good understanding of these systems in the framework of the droplet-scaling theory. In this work, a pedagogical description of such an optimization-based approach is given and a short review of corresponding recent results is presented. Furthermore, original results are presented for a special type of system which combines a ferromagnetic sub lattice with a spin-glass sub lattice. Results for exact ground-state calculations up to system size N=1448×1448 are given. Past results of similar systems gave evidence that such a system might exhibit a spin-glass phase at finite temperatures. Nevertheless, the present results do not support this notion. But, for a suitable balance between ferromagnetic and ±J spin-glass couplings, extremely large finite-size effects occur. Thus, when considering intermediate system sizes, the system looks as if it orders. Furthermore, although the system exhibits only a discrete set of interactions, a power-law behavior for the stiffness energy can be observed clearly for a large range of system sizes. This is in contrast to past studies of systems with discrete sets of bond values.

A simple model for the magnetoelectric interaction in multiferroics

The (anti)ferromagnetic and ferroelectric transitions in some multiferroic compounds seem to be strongly correlated. Even for systems that do not show spontaneous ferroelectricity such as the LiMPO4 (M = Mn, Fe, Co, Ni) compounds, the coupling between magnetic and electric degrees of freedom is evident experimentally. Here, we present a simple numerical calculation to simulate this coupling that leads to the two transitions. We assume a magnetic sublattice consisting of classical magnetic moments coupled to a separated nonmagnetic sublattice consisting of classical electric dipoles. The coupling between them is realized through a phenomenological spin-lattice Hamiltonian, and the solution is obtained using the Monte Carlo technique. In the simplest version, the magnetic system is 2D Ising (anti)ferromagnetic lattice, with nearest neighbors interactions only, and the electric moments are permanent moments, coupled electrically. Within this approximation, the second order magnetic transition induces ferroelectricity in the electric dipoles. We show that these calculations can be extended to other magnetic systems, (x-y model and 3D Heisenberg) and to systems where the electric moments are created by strains, generated via spin-lattice coupling, so the model can be applied to model realistic systems such as the olivines mentioned above.

Proposed realization of itinerant ferromagnetism in optical lattices

We propose a scheme to realize the itinerant ferromagnetism of two-component cold fermionic atoms in the $p$-orbital bands in optical lattices. The band flatness in the two-dimensional honeycomb lattice dramatically amplifies the interaction effect, driving the ferromagnetic transition even with a relatively weak repulsive interaction. This scheme has the advantage that the stability of the system can be maintained without causing decay to the molecular state as one approaches the Feshbach resonance from the side with the positive scattering length. Experimental signatures and detections are also discussed.

Electromagnetic wave diffraction by lattices of magnetic nanowires and geometry and scale effects in the terahertz frequency range

The TEM wave diffraction by a periodic lattice of magnetic nanowires has been simulated mathematically in the terahertz frequency range. The computational algorithm based on autonomous blocks with virtual Floquet channels loaded by magnetic nanoinclusions has been developed and used to perform the electrodynamic analysis of the scattering matrix parameters constructed for a 2D periodic lattice of longitudinally magnetized ferromagnetic (iron) nanowires at a frequency of 30 THz. It is demonstrated that the maximum of the transmission coefficient of a TEM wave propagating through a ferromagnetic nanowire lattice can be controlled by the constant magnetizing field near the antiresonance point and depends on the geometry and dimensions of nanowires and the lattice.

Magnetic Interactions of the 15‐Electron Nb6F12 Clusters in Nb6F15

AbstractThe crystal structure of Nb6F15 consists of Nb6F12 clusters that are corner‐shared through linear Nb–F–Nb bridges to form two simple cubic lattices, which interpenetrate each other with F···F van der Waals contacts only. With 15 valence electrons in Nb–Nb bonding states each cluster carries one unpaired spin. 19F NMR and EPR spectroscopic measurements suggest antiferromagnetic ordering in Nb6F15 below 6 K. A spin‐dimer analysis based on tight binding calculations shows that the correct magnetic structure of Nb6F15 associated with this ordering should have the spin arrangement in which two interpenetrating ferromagnetic simple cubic lattices are antiferromagnetically coupled.

Survival of short-range order in the Ising model on negatively curved surfaces

We examine the ordering behavior of the ferromagnetic Ising lattice model defined on a surface with a constant negative curvature. Small-sized ferromagnetic domains are observed to exist at temperatures far greater than the critical temperature, at which the inner-core region of the lattice undergoes a mean-field phase transition. The survival of short-range order at such high temperatures can be attributed to strong boundary-spin contributions to the ordering mechanism as a result of which boundary effects remain active even within the thermodynamic limit. Our results are consistent with the previous finding of disorder-free Griffiths phase that is stable at temperatures lower than the mean-field critical temperature.

Possible negative refraction in two dimensional ferromagnetic wire lattice

In this paper, we present theoretical and experimental results for the indication of negative refraction in ferromagnetic metallic wire lattice. We have studied microwave transmission through a two dimensional wire lattice made of ferromagnetic metallic wires under the applied static magnetic field. We have found that, the microwave transmission were significantly changed at ferromagnetic resonance frequency region. Thus the magnetic permeability can be tuned by external dc magnetic field. Since the dielectric permittivity of metallic wire lattice is negative and can take a value close to unity then the crystal exhibits negative index of refraction at microwave region under the external magnetic field.

GPU accelerated Monte Carlo simulation of the 2D and 3D Ising model

The compute unified device architecture (CUDA) is a programming approach for performing scientific calculations on a graphics processing unit (GPU) as a data-parallel computing device. The programming interface allows to implement algorithms using extensions to standard C language. With continuously increased number of cores in combination with a high memory bandwidth, a recent GPU offers incredible resources for general purpose computing. First, we apply this new technology to Monte Carlo simulations of the two dimensional ferromagnetic square lattice Ising model. By implementing a variant of the checkerboard algorithm, results are obtained up to 60 times faster on the GPU than on a current CPU core. An implementation of the three dimensional ferromagnetic cubic lattice Ising model on a GPU is able to generate results up to 35 times faster than on a current CPU core. As proof of concept we calculate the critical temperature of the 2D and 3D Ising model using finite size scaling techniques. Theoretical results for the 2D Ising model and previous simulation results for the 3D Ising model can be reproduced.

Ferromagnetic interaction between [Ni(bdt) 2] − anions in [Mn 2(Saloph) 2( μ-OH)][Ni(bdt) 2](CH 3CN) 2

A new molecule-based magnetic material [Mn 2(Saloph) 2( μ-OH)][Ni(bdt) 2](CH 3CN) 2 was prepared by the metathesis of [Mn(Saloph)(H 2O)(ClO 4)] ( S = 2) and TBA[Ni(bdt) 2] ( S = 1/2). In the crystal, [Ni(bdt) 2] − anions form square lattices which are separated from each other by the layers of antiferromagnetically coupled binuclear cations [Mn 2(Saloph) 2( μ-OH)] +. The magnetic susceptibility of the material coincides with the sum of the S = 2 van Vleck dimer model and S = 1/2 Heisenberg ferromagnetic square lattice model with 2 J = −92.4 and +4.5 K, respectively. The origin of the ferromagnetic interaction can be explained by the T-shaped intermolecular overlap mode of SOMOs which spreads to the ends of [Ni(bdt) 2] − molecules.

Path-integral representation for quantum spin models: Application to the quantum cavity method and Monte Carlo simulations

The cavity method is a well-established technique for solving classical spin models on sparse random graphs (mean-field models with finite connectivity). Laumann et al. [Phys. Rev. B 78, 134424 (2008)] proposed recently an extension of this method to quantum spin-1/2 models in a transverse field, using a discretized Suzuki-Trotter imaginary-time formalism. Here we show how to take analytically the continuous imaginary-time limit. Our main technical contribution is an explicit procedure to generate the spin trajectories in a path-integral representation of the imaginary-time dynamics. As a side result we also show how this procedure can be used in simple heat bath Monte Carlo simulations of generic quantum spin models. The replica symmetric continuous-time quantum cavity method is formulated for a wide class of models and applied as a simple example on the Bethe lattice ferromagnet in a transverse field. The results of the methods are confronted with various approximation schemes in this particular case. On this system we performed quantum Monte Carlo simulations that confirm the exactness of the cavity method in the thermodynamic limit.

High-precision thermodynamic and critical properties from tensor renormalization-group flows

The recently developed tensor renormalization-group (TRG) method provides a highly precise technique for deriving thermodynamic and critical properties of lattice Hamiltonians. The TRG is a local coarse-graining transformation, with the elements of the tensor at each lattice site playing the part of the interactions that undergo the renormalization-group flows. These tensor flows are directly related to the phase diagram structure of the infinite system, with each phase flowing to a distinct surface of fixed points. Fixed-point analysis and summation along the flows give the critical exponents, as well as thermodynamic functions along the entire temperature range. Thus, for the ferromagnetic triangular lattice Ising model, the free energy is calculated to better than 10(-5) along the entire temperature range. Unlike previous position-space renormalization-group methods, the truncation (of the tensor index range D) in this general method converges under straightforward and systematic improvements. Our best results are easily obtained with D=24, corresponding to 4624-dimensional renormalization-group flows.

Comment on “Ferromagnetic wire lattice with a tunable negative index of refraction for microwaves using an external magnetic field” by Yun-Song Zhou et al.

Comment on “Ferromagnetic wire lattice with a tunable negative index of refraction for microwaves using an external magnetic field” by Yun-Song Zhou et al.

Spin reversal and magnetization jumps in ErMe xMn 1−xO 3 perovskites (Me=Ni, Co)

The erbium-based manganite ErMnO 3 has been partially substituted at the manganese site by the transition-metal elements Ni and Co. The perovskite orthorhombic structure is found from x(Ni)=0.2–0.5 in the nickel-based solid solution ErNi x Mn 1− x O 3, while it can be extended up to x(Co)=0.7 in the case of cobalt, provided that the synthesis is performed under oxygenation conditions to favor the presence of Co 3+. Presence of different magnetic entities (i.e., Er 3+, Ni 2+, Co 2+, Co 3+, Mn 3+, and Mn 4+) leads to quite unusual magnetic properties, characterized by the coexistence of antiferromagnetic and ferromagnetic interactions. In ErNi x Mn 1− x O 3, a critical concentration x crit(Ni)=1/3 separates two regimes: spin-canted AF interactions predominate at x< x crit, while the ferromagnetic behavior is enhanced for x> x crit. Spin reversal phenomena are present both in the nickel- and cobalt-based compounds. A phenomenological model based on two interacting sublattices, coupled by an antiferromagnetic exchange interaction, explains the inversion of the overall magnetic moment at low temperatures. In this model, the ferromagnetic transition-metal lattice, which orders at T c, creates a strong local field at the erbium site, polarizing the Er moments in a direction opposite to the applied field. At low temperatures, when the contribution of the paramagnetic erbium sublattice, which varies as T −1, gets larger than the ferromagnetic contribution, the total magnetic moment changes its sign, leading to an overall ferrimagnetic state. The half-substituted compound ErCo 0.50Mn 0.50O 3 was studied in detail, since the magnetization loops present two well-identified anomalies: an intersection of the magnetization branches at low fields, and magnetization jumps at high fields. The influence of the oxidizing conditions was studied in other compositions close to the 50/50=Mn/Co substitution rate. These anomalies are clearly connected to the spin inversion phenomena and to the simultaneous presence of Co 2+ and Co 3+ magnetic moments. Dynamical aspects should be considered to well identify the high-field anomaly, since it depends on the magnetic field sweep rate.

New PLAD apparatus and fabrication of epitaxial films and junctions of functional materials: SiC, GaN, ZnO, diamond and GMR layers

Abstract We have developed a new pulsed laser ablation–deposition (PLAD) apparatus and techniques for fabricating films of high-temperature or functional materials, including two short-wavelength lasers: (a) a YAG 5th harmonic (213 nm) and (b) Raman-shifted lasers containing vacuum ultraviolet light; also involved are (c) a high-temperature heater with a maximum temperature of 1350 °C, (d) dual-target simultaneous ablation mechanics, and (e) hybrid PLAD using a pico-second YAG laser combined with (c) and/or (d). Using the high-T heater, hetero-epitaxial films of 3C–, 2H– and 4H–SiC have been prepared on sapphire-c. In situ p-doping for GaN epitaxial films is achieved by simultaneous ablation of GaN and Mg targets by (d) during film growth. Junctions such as pGaN (Mg-doped)-film/n-SiC(0 0 0 1) substrate and pGaN/n-Si(1 1 1) show good diode characteristics. Epitaxial films with a diamond lattice can be grown on the sapphire-c plane by hybrid PLAD (e) with a high-T heater using a 6H-SiC target. High quality epitaxial films of ZnO are grown by PLAD by introducing a low-temperature self-buffer layer; magnetization of ferromagnetic materials is enforced by overlaying on a ferromagnetic lattice plane of an anti-ferromagnetic material, showing the value of the layer-overlaying method in improving quality. The short-wavelength lasers are useful in reducing surface particles on functional films, including superconductors.

How to compute loop corrections to the Bethe approximation

We introduce a method for computing corrections to the Bethe approximation for spinmodels on arbitrary lattices. Unlike cluster variational methods, the new approach takesinto account fluctuations on all length scales.The derivation of the leading correction is explained and appliedto two simple examples: the ferromagnetic Ising model ond-dimensional lattices, and the spin glass on random graphs (both in their high-temperaturephases). In the first case we rederive the well known Ginzburg criterion and the uppercritical dimension. In the second, we compute finite-size corrections to the free energy.

Dissipation of Spin Angular Momentum in Magnetic Switching

Applying one ultrashort magnetic field pulse, we observe up to 10 precessional switches of the magnetization direction in single crystalline Fe films of 10 and 15 atomic layers. We find that the rate at which angular momentum is dissipated in uniform large angle spin precession increases with time and film thickness, surpassing the intrinsic ferromagnetic resonance spin lattice relaxation of Fe by nearly an order of magnitude.

Mean field, long-range ferromagnets and periodic boundary conditions

Periodic boundary conditions are applied to a ferromagnetic spin lattice. A symmetrical lattice and its contributions all over space are being used. Results, for the Ising model with ferromagnetic interaction that decays as a 1/ r D+ ν law, are discussed in the mean field approximation.

Interacting networks and spin reversal in (RE, Ca)MnO 3

Magnetic properties of (RE, Ca)MnO 3 perovskites (RE=Gd, Dy) have been studied in the ordered state. The remanent magnetization M rem reverses its magnetic moment, as if the external field was applied opposite to the initial direction. Results are interpreted in terms of two interacting networks, with negative exchange interaction between the RE and the ferromagnetic Mn lattices.