Ferromagnetic Chain Research Articles

Quasi-one-dimensional magnetism in [formula omitted] compounds: From Heisenberg to Ising chains

A series of MnxFe1-xNb2O6 compounds (0⩽x⩽1) is investigated by both X-ray and neutron powder diffraction, as well as specific-heat and magnetic measurements. The samples present orthorhombic Pbcn crystal symmetry, and exhibit weakly coupled magnetic chains. These chains are of Heisenberg type (weak anisotropy) on the Mn-rich side, and Ising-like (strong anisotropy) on the Fe-rich side. Except for 100% Fe (x=0), which has weakly-interacting ferromagnetic Ising chains, a negative Curie-Weiss temperature is obtained from the magnetic susceptibility, indicating dominant antiferromagnetic interactions. At the lowest probed temperature, T=1.5K, true long-range magnetic order is only observed for x=1, 0.8, and 0. Although the ordering is globally antiferromagnetic in all cases, the first two are characterized by a two-sublattice structure with propagation vector k=(0,0,0), while the latter presents alternatingly oriented ferromagnetic chains described by k=(0,12,0). For other compositions, short-range magnetic correlations are extracted from diffuse neutron-scattering data.

Role of dipolar interactions on morphologies and tunnel magnetoresistance in assemblies of magnetic nanoparticles

We undertake comprehensive simulations of 2d arrays (Lx×Ly) of magnetic nanoparticles (MNPs) with dipole-dipole interactions by solving LLG equations. Our primary interest is to understand the correspondence between equilibrium spin (ES) morphologies and tunnel magnetoresistance (TMR) as a function of Θ – the ratio of the dipolar to the anisotropy strength, sample size Lx, aspect ratio Ar=Ly/Lx and the direction of the applied field H→=HêH. The parameter Θ is varied by choosing three distinct particles: (i) α-Fe2O3(Θ≃0), (ii) Co (Θ≃0.37) and (iii) Fe3O4(Θ≃1.28). Our main observations are as follows: (a) For weakly interacting spins (Θ≃0), the morphology has randomly oriented magnetic moments for all sample sizes and aspect ratios. The TMR exhibits a peak value of 50% at the coercive field Hc. It is robust with respect to Lx and Ar, and isotropic with respect to êH. (b) For strong interactions (Θ>1), the moments order in the plane of the sample. The ES morphology comprises of magnetically aligned regions interspersed with flux closure loops. For fields along x or y, the maximum TMR amplitude decrease to ∼30%. For êH=ẑ, it drops to ∼3%. The TMR is robust with respect to Lx and Ar and isotropic in the x and y directions only. (c) In strongly interacting samples (Θ>1) with Lx comparable to the size of a flux closure loop, increasing Ar creates ferromagnetic chains in the sample oriented along y or -y. Consequently, for êH=ŷ, the TMR magnitude for Ar=1 is ∼33% while that for Ar=32 drops to ∼16%. For êH=x̂ on the other hand, it is ∼30% and independent of Ar. The TMR of long ribbons of MNPs has a strong dependence on Ar and is anisotropic in all three directions.

Some new exact solutions of (2+1)-dimensional nonlinear Heisenberg ferromagnetic spin chain with the conformable time fractional derivative

There are various types of fractional derivatives in literature e.g. Caputo, Riemann–Liouville, conformable and so on. In the present paper, a new integrable nonlinear Schrodinger type equation in (2+1)-dimensions is investigated, which describes the spin dynamics of Heisenberg ferromagnetic spin chains. Some bright and dark solitons and other exact solutions of this equation with conformable time fractional derivative are reported. Then, fractionalize effects of this model are graphically investigated. Moreover, the simplest equation method and Nucci’s method are utilized for differential equations with conformable fractional derivatives.

Chirality Transitions in Frustrated Ferromagnetic Spin Chains: A Link with the Gradient Theory of Phase Transitions

We study chirality transitions in frustrated ferromagnetic spin chains, in view of a possible connection with the theory of Liquid Crystals. A variational approach to the study of these systems has been recently proposed by Cicalese and Solombrino, focusing close to the helimagnet-ferromagnet transition point corresponding to the critical value of the frustration parameter $\alpha=4$. We reformulate this problem for any $\alpha\geq0$ in the framework of surface energies in nonconvex discrete systems with nearest neighbors ferromagnetic and next-to-nearest neighbors antiferromagnetic interactions and we link it to the gradient theory of phase transitions, by showing a uniform equivalence by $\Gamma$-convergence on $[0,4]$ with Modica-Mortola type functionals.

A [Cr2Ni] coordination polymer: slow relaxation of magnetization in quasi-one-dimensional ferromagnetic chains.

The reaction of [Cr3IIIO(OAc)6(H2O)3]NO3·AcOH with 2-hydroxynaphthaldehyde, 2-amino-isobutyric acid and NiCl2·6H2O in MeOH, under basic and solvothermal conditions, led to the formation of the quasi-1D coordination polymer {[CrIII2NiII(L)4(MeOH)2]}n (where L = the dianion of the Schiff base between 2-hydroxynaphthaldehyde and 2-amino-isobutyric acid), which behaves as a ferromagnetic chain, displaying slow relaxation of magnetization.

Investigation of various soliton solutions to the Heisenberg ferromagnetic spin chain equation

This study uses two mathematical approaches in constructing dark, bright, kink-type and singular soliton solutions to the Heisenberg ferromagnetic spin chain equation. The (2+1)-dimensional Heisenberg ferromagnetic spin chain equation describes nonlinear dynamics of magnets. The acquired results in this study may help in explaining some physical meanings of some nonlinear physical models arising in electromagnetic waves. For instance, the hyperbolic tangent arises in the calculation of magnetic moment and rapidity of special relativity, the hyperbolic cotangent arises in the Langevin function for magnetic polarization. The 2-, 3-dimensional and the contour plots of all the acquired solutions are presented.

Domain walls in single-chain magnets

The topology and creation energy of domain walls in different magnetic chains (called Single-Chain Magnets or SCMs) are discussed. As these domain walls, that can be seen as ``defects'', are known to control both static and dynamic properties of these one-dimensional systems, their study and understanding are necessary first steps before a deeper discussion of the SCM properties at finite temperature. The starting point of the paper is the simple regular ferromagnetic chain for which the characteristics of the domain walls are well known. Then two cases will be discussed (i) the ``mixed chains'' in which isotropic and anisotropic classical spins alternate, and (ii) the so-called ``canted chains'' where two different easy axis directions are present. In particular, we show that ``strictly narrow'' domain walls no longer exist in these more complex cases, while a cascade of phase transitions is found for canted chains as the canting angle approaches ${45}^{\ensuremath{\circ}}$. The consequence for thermodynamic properties is briefly discussed in the last part of the paper.

Dark, bright and other soliton solutions to the Heisenberg ferromagnetic spin chain equation

In this study, the applications of the extended sinh-Gordon equation expansion method to a nonlinear Schrödinger equation that describes the nonlinear spin dynamics of (2 + 1)-dimensional Heisenberg ferromagnetic spin chains with bilinear and anisotropic interactions in the semiclassical limit is presented. We successfully construct dark, bright, combined dark-bright, singular and combined singular soliton solutions to this equation. We give the parametric conditions for the existence of valid soliton to each of the obtained solutions. We plot the 2D and 3D graphics to some of the obtained solutions. The reported results of this study may be helpful in explaining the physical meaning of the studied model.

Lax pair, infinitely many conservation laws and solitons for a (2+1)-dimensional Heisenberg ferromagnetic spin chain equation with time-dependent coefficients

Under investigation in this paper is a (2+1)-dimensional Heisenberg ferromagnetic spin chain equation with time-dependent coefficients. Based on the symbolic computation, Lax pair and infinitely many conservation laws are constructed. Multi-soliton solutions are derived by virtue of the Darboux transformation. Propagation and interaction properties of the solitons are discussed. Amplitude of the soliton is determined by the spectral parameter and wave number, while the velocity is related to both these parameters and the time-dependent coefficients. Elastic interactions between the two solitons are displayed, and their amplitudes keep unchanged after the interaction except for the phase shifts.

Anholonomy according to three formulations of non-null curve evolution

In this paper, we present three anholonomy densities and three geometric phases for three formulations of curve evolution in Minkowski 3-space and give applications of three formulation for ferromagnetic and antiferromagnetic spin chains.

Magnetic helices as metastable states of finite XY ferromagnetic chains: An analytical study

We investigated a simple but non trivial model, consisting of a chain of N classical XY spins with nearest neighbor ferromagnetic interaction, where each of the two end-point spins is assumed to be exchange-coupled to a fully-pinned fictitious spin. In the mean field approximation, the system might be representative of a soft ferromagnetic film sandwiched between two magnetically hard layers. We show that, while the ground state is ferromagnetic and collinear, the system can attain non-collinear metastable states in the form of magnetic helices. The helical solutions and their stability were studied analytically in the absence of an external magnetic field. There are four possible classes of solutions. Only one class is metastable, and its helical states contain an integer number of turns. Among the remaining unstable classes, there is a class of helices which contain an integer number of turns. Therefore, an integer number of turns in a helical configuration is a necessary, but not a sufficient, condition for metastability. These results may be useful to devise future applications of metastable magnetic helices as energy-storing elements.

Dynamical quadrupole structure factor of frustrated ferromagnetic chain

We investigate the dynamical quadrupole structure factor of a spin-1/2 J1-J2 Heisenberg chain with competing ferromagnetic J1 and antiferromagnetic J2 in a magnetic field by exploiting density-matrix renormalization group techniques. In a field-induced spin nematic regime, we observe gapless excitations at q=π according to quasi-long-range antiferro-quadrupole correlations. The gapless excitation mode has a quadratic form at the saturation, while it changes into a linear dispersion as the magnetization decreases.

Optical solitons and modulation instability analysis of an integrable model of (2+1)-Dimensional Heisenberg ferromagnetic spin chain equation

This paper addresses the nonlinear Schrödinger type equation (NLSE) in (2+1)-dimensions which describes the nonlinear spin dynamics of Heisenberg ferromagnetic spin chains (HFSC) with anisotropic and bilinear interactions in the semiclassical limit. Two integration schemes are employed to study the equation. These are the complex envelope function ansatz and the generalized tanh methods. Dark, dark-bright or combined optical and singular soliton solutions of the equation are derived. Furthermore, the modulational instability (MI) is studied based on the standard linear-stability analysis and the MI gain is got. Numerical simulation of the obtained results are analyzed with interesting figures showing the physical meaning of the solutions.

Thermal transport through a spin-phonon interacting junction: A nonequilibrium Green's function method study

Using the nonequilibrium Green's function method, we consider heat transport in an insulating ferromagnetic spin chain model with spin-phonon interaction under an external magnetic field. Employing the Holstein-Primakoff transformation to the spin system, we treat the resulted magnon-phonon interaction within the self-consistent Born approximation. We find the magnon-phonon coupling can change qualitatively the magnon thermal conductance in the high-temperature regime. At a spectral mismatched ferromagnetic-normal insulator interface, we also find thermal rectification and negative differential thermal conductance due to the magnon-phonon interaction. We show that these effects can be effectively tuned by the external applied magnetic field, a convenient advantage absent in anharmonic phonon and electron-phonon systems studied before.

Nonautonomous multi-peak solitons and modulation instability for a variable-coefficient nonlinear Schrödinger equation with higher-order effects

In this paper, we study a variable-coefficient nonlinear Schrodinger (vc-NLS) equation with fourth-order effects describing an inhomogeneous one-dimensional continuum anisotropic Heisenberg ferromagnetic spin chain or alpha helical protein. The first-order nonautonomous breather solution of the fourth-order vc-NLS equation is derived. The state transition between nonautonomous breather and nonautonomous multi-peak soliton can be realized when group velocity dispersion (GVD) coefficient is proportional to the fourth-order dispersion (FOD) coefficient. We also display how the higher-order effects influence the nonautonomous multi-peak solitons. Our results show that the velocity and localization of the nonautonomous multi-peak soliton are affected by the FOD coefficient, and the peak number is controlled by the GVD coefficient. Further, we also show the compression effect and motion with variable velocity of nonautonomous multi-peak soliton in two kinds of dispersion management systems. Finally, we reveal the relation between the state transition and the modulation instability (MI) analysis.

Healing of defects in random antiferromagnetic spin chains

We study the effects of a weakened link in random antiferromagnetic spin chains. We show that healing occurs, and that homogeneity is restored at low energy, in a way that is qualitatively similar to the fate of impurities in clean ferromagnetic spin chains, or in Luttinger liquids with attractive interactions. Healing in the random case occurs even without interactions, and is characteristic of the random singlet phase. Using real-space renormalization group and exact diagonalization methods, we characterize this universal healing crossover by studying the entanglement across the weak link. We identify a crossover healing length that separates a regime where the system is cut in half by the weak link from a fixed point where the spin chain is healed. Our results open the way to the study of impurity physics in disordered spin chains.

Chaotic dynamics of Heisenberg ferromagnetic spin chain with bilinear and biquadratic interactions

We investigate the chaotic dynamics of one dimensional Heisenberg ferromagnetic spin chain by constructing the Hamiltonian equations of motion. We present the trajectory and phase plots of the system with bilinear and also biquadratic interactions. The stability of the system is analysed in both cases by constructing the Jacobian matrix and by measuring the Lyapunov exponents. The results are illustrated graphically.

Partial Ferrimagnetism in S = 1/2 Heisenberg Ladders with a Ferromagnetic Leg, an Antiferromagnetic Leg, and Antiferromagnetic Rungs

Ground-state and finite-temperature properties of $S=1/2$ Heisenberg ladders with a ferromagnetic leg, an antiferromagnetic leg, and antiferromagnetic rungs are studied. It is shown that a partial ferrimagnetic phase extends over a wide parameter range in the ground state. The numerical results are supported by an analytical calculation based on a mapping onto the nonlinear $\sigma$ model and a perturbation calculation from the strong-rung limit. It is shown that the partial ferrimagnetic state is a spontaneously magnetized Tomonaga--Luttinger liquid with incommensurate magnetic correlation, which is confirmed by a DMRG calculation. The finite-temperature magnetic susceptibility is calculated using the thermal pure quantum state method. It is suggested that the susceptibility diverges as $T^{-2}$ in the ferrimagnetic phases as in the case of ferromagnetic Heisenberg chains.

Zigzag spin structure in layered honeycomb Li3Ni2SbO6 : A combined diffraction and antiferromagnetic resonance study

The magnetic structure of $\mathrm{L}{\mathrm{i}}_{3}\mathrm{N}{\mathrm{i}}_{2}\mathrm{Sb}{\mathrm{O}}_{6}$ has been determined by low-temperature neutron diffraction, and the crystal structure has been refined by a combination of synchrotron and neutron powder diffraction. The monoclinic ($C2/m$) symmetry, assigned previously to this pseudohexagonal layered structure, has been unambiguously proven by peak splitting in the synchrotron diffraction pattern. The structure is based on essentially hexagonal honeycomb-ordered $\mathrm{N}{\mathrm{i}}_{2}\mathrm{Sb}{\mathrm{O}}_{6}$ layers alternating with $\mathrm{L}{\mathrm{i}}_{3}$ layers, all cations and anions being in an octahedral environment. The compound orders antiferromagnetically below ${T}_{\mathrm{N}}=15\phantom{\rule{0.16em}{0ex}}\mathrm{K}$, with the magnetic supercell being a $2a\ifmmode\times\else\texttimes\fi{}2b$ multiple of the crystal cell. The magnetic structure within the honeycomb layer consists of zigzag ferromagnetic spin chains coupled antiferromagnetically. The ordered magnetic moment amounts to $1.62(2)\phantom{\rule{0.16em}{0ex}}{\ensuremath{\mu}}_{\mathrm{B}}/\mathrm{Ni}$, which is slightly lower than the full theoretical value. Upon cooling below ${T}_{\mathrm{N}}$, the spins tilt from the $c$ axis, with a maximum tilting angle of $15.{6}^{\ensuremath{\circ}}$ at $T=1.5\phantom{\rule{0.16em}{0ex}}\mathrm{K}$. Our data imply non-negligible ferromagnetic interactions between the honeycomb layers. The observed antiferromagnetic resonance modes are in agreement with the two-sublattice model derived from the neutron data. Orthorhombic anisotropy shows up in zero-field splitting of $\mathrm{\ensuremath{\Delta}}=198\ifmmode\pm\else\textpm\fi{}4$ and $218\ifmmode\pm\else\textpm\fi{}4\phantom{\rule{0.16em}{0ex}}\mathrm{GHz}$. Above ${T}_{\mathrm{N}}$, the electron spin resonance data imply short-range antiferromagnetic order up to about 80 K.

Crossover from an incommensurate singlet spiral state with a vanishingly small spin gap to a valence-bond solid state in dimerized frustrated ferromagnetic spin chains

Motivated by the magnetic properties of the spin-chain compounds LiCuSbO$_4$$\equiv$LiSbCuO$_4$ and Rb$_2$Cu$_2$Mo$_3$O$_{12}$, we study the ground state of the Heisenberg chain with dimerized nearest-neighbor ferromagnetic (FM)($J_1, J_1^\prime<0$) and next-nearest-neighbor antiferromagnetic ($J_2>0$) couplings. Using the density-matrix renormalization group technique and spin-wave theory we find a first-order transition between a fully-polarized FM and an incommensurate spiral state at $2\alpha=\beta/(1+\beta)$, where $\alpha$ is the frustration ratio $J_2/|J_1|$ and $\beta$ the degree of dimerization $J_1^\prime/J_1$.In the singlet spiral state the spin-gap is vanishingly small in the vicinity of the FM transition, corresponding to a situation of LiCuSbO$_4$. For larger $\alpha$, corresponding to Rb$_2$Cu$_2$Mo$_3$O$_{12}$, and smaller $\beta$ there is a crossover from this frustration induced incommensurate state to an Affleck-Lieb-Kennedy-Tasaki-type valence bond solid state with substantial spin-gaps.