Metastability of Ising spin chains with nearest—neighbour and next—nearest—neighbour interactions in random fields

One-dimensional Ising systems in random fields (RFs) are studied taking into account the nearest-neighbour and next-nearest-neighbour interactions. We investigate two distributions of RFs: binary and Gaussian distributions. We consider four cases of the exchange couplings: ferro－ferromagnetic (F－F), ferro－antiferromagnetic (F－AF), antiferro－ferromagnetic (AF－F) and antiferro－antiferromagnetic (AF－AF). The energy minima of chains of no more than 30 spins with periodic boundary conditions are analysed exactly. We found that the average number of energy minima grows exponentially with the number of spins in both cases of RFs. The energy distributions across the corresponding energy minima are shown. The effects of RFs on both the average and density of metastable states are explained. For a weak RF, the energy distributions display a multipartitioned structure. We also discuss the frustration effect due to RFs and exchange fields. Finally, the distributions of magnetization are calculated. The absolute value of magnetization averaged over all metastable states decreases logarithmically with the number of spins.     

Spin-phonon coupling induced frustration in the exactly solved spin-1/2 Ising model on a decorated planar lattice

Spin-1/2 Ising model with a spin-phonon coupling on decorated planar lattices partially amenable to lattice vibrations is examined using the decoration-iteration transformation and harmonic approximation. It is shown that the magnetoelastic coupling gives rise to an effective antiferromagnetic next-nearest-neighbour interaction, which competes with the nearest-neighbour interaction and is responsible for a frustration of decorating spins. A strong enough spin-phonon coupling consequently leads to an appearance of striking partially ordered and partially disordered phase, where a perfect antiferromagnetic alignment of nodal spins is accompanied with a complete disorder of decorating spins. Thermal dependences of the specific heat are explored in detail.     

2D Ising Model with Layers of Quenched Spins

The model considered is a d=2 disordered Ising system on a square lattice with nearest neighbor interaction. The disorder is induced by layers (rows) of spins, randomly located, which are frozen in an antiferromagnetic order. It is assumed that all the vertical couplings take the same positive value J _v, while all the horizontal couplings take the same positive value J _h. The model can be exactly solved and the free energy is given as a simple explicit expression. The zero-temperature entropy can be positive because of the frustration due to the competition between antiferromagnetic alignment induced by the quenched layers and ferromagnetic alignment due to the positive couplings. No phase transition is found at finite temperature if the layers of frozen spins are independently distributed, while for correlated disorder one finds a low-temperature phase with some glassy properties.     

Spin, charge and lattice couplings in Cu-deficient oxysulphide BiOCu0.94S

The electrical and magnetic properties of slightly Cu-deficient BiOCu(0.94)S are investigated using neutron diffraction, ac magnetic susceptibility, magnetization and electrical resistivity measurements. The Cu spins order in a ferromagnetic arrangement below T(C) = 250 K. An antiferromagnetic component develops below 180 K when the crystalline unit cell experiences a sharp thermal contraction upon cooling, resulting in a canted ferromagnetic spin arrangement at low temperatures. In the magnetically ordered state the electrical transport can be described using three-dimensional variable range hopping conduction. An applied magnetic field can effectively reduce the hopping barrier. Spin-charge couplings are clearly revealed when the resistivity departs from the hopping conduction and begins to increase with increasing temperatures above 250 K where the Cu spins become disordered.     

Competing interactions in double-chains: Ising and spherical models

We investigate the thermodynamic properties of double chains of Ising and spherical spins with different first and a crossed second neighbour interaction in zero field. The interest is focussed on the region where different ground states are nearly degenerate due to competing interaction constants. The Ising system shows quasi-singular behaviour of the susceptibility for certain ratios of parameters. Moreover the nearest neighbour correlation function exhibits a sharp crossover from high-temperature “compensation-point” to low temperature ferro- or antiferromagnetic behaviour. An analogy is found between compensation points and tricritical points of higher dimensional systems.     

Dynamic compensation temperature in the kinetic spin-1 Ising model in an oscillating external magnetic field on alternate layers of a hexagonal lattice

The dynamic behavior of a two-sublattice spin-1 Ising model with a crystal-field interaction (D) in the presence of a time-varying magnetic field on a hexagonal lattice is studied by using the Glauber-type stochastic dynamics. The lattice is formed by alternate layers of spins σ=1 and S=1. For this spin arrangement, any spin at one lattice site has two nearest-neighbor spins on the same sublattice, and four on the other sublattice. The intersublattice interaction is antiferromagnetic. We employ the Glauber transition rates to construct the mean-field dynamical equations. Firstly, we study time variations of the average magnetizations in order to find the phases in the system, and the temperature dependence of the average magnetizations in a period, which is also called the dynamic magnetizations, to obtain the dynamic phase transition (DPT) points as well as to characterize the nature (continuous and discontinuous) of transitions. Then, the behavior of the total dynamic magnetization as a function of the temperature is investigated to find the types of the compensation behavior. Dynamic phase diagrams are calculated for both DPT points and dynamic compensation effect. Phase diagrams contain the paramagnetic (p) and antiferromagnetic (af) phases, the p+af and nm+p mixed phases, nm is the non-magnetic phase, and the compensation temperature or the L-type behavior that strongly depend on the interaction parameters. For D<2.835 and H₀>3.8275, H₀ is the magnetic field amplitude, the compensation effect does not appear in the system.     

Phase diagram of frustrated mixed-spin ladders in the strong-coupling limit

We study the ground-state properties of frustrated Heisenberg ferrimagnetic ladders with antiferromagnetic exchange interactions and two types of alternating sublattice spins. In the limit of strong rung couplings, we show that the mixed spin-1/2 and spin-1 ladders can be systematically mapped onto a spin-1/2 Heisenberg model with additional next-nearest-neighbor exchanges. The system is either in a ferrimagnetic state or in a critical spin-liquid state depending on the competition between the spin exchanges along the legs and the diagonal exchanges.     

Ferrimagnetism induced by asymmetrical ferromagnetic next-nearest-neighbour exchange interactions in an antiferromagnetic spin-1/2 zigzag chain

The magnetic properties of an antiferromagnetic bond alternating spin-1/2 zigzag chain with asymmetrical ferromagnetic next-nearest-neighbour exchange interactions at finite temperature are investigated by using the many-body Green's function theory. It is found that the ferrimagnetic ordering does not appear in the symmetrical next-nearest-neighbour coupling case, and takes place only for the asymmetrical next-nearest-neighbour case at finite temperature rather than the ground state. Furthermore, as the asymmetry degree of the next-nearest-neighbour exchange interactions increases, the ferrimagnetism becomes more and more dominant. It is shown that the elementary excitation spectra are responsible for the observed magnetic behaviour.     

Field-dependent nuclear relaxation of spins 1/2 induced by dipole-dipole couplings to quadrupole spins: LaF3 crystals as an example

A general theory of spin-lattice nuclear relaxation of spins I=1/2 caused by dipole-dipole couplings to quadrupole spins S1, characterized by a non-zero averaged (static) quadrupole coupling, is presented. In multispin systems containing quadrupolar and dipolar nuclei, transitions of spins 1/2 leading to their relaxation are associated through dipole-dipole couplings with certain transitions of quadrupole spins. The averaged quadrupole coupling attributes to the energy level structure of the quadrupole spin and influences in this manner relaxation processes of the spin 1/2. Typically, quadrupole spins exhibit also a complex multiexponential relaxation sensed by the dipolar spin as an additional modulation of the mutual dipole-dipole coupling. The proposed model includes both effects and is valid for an arbitrary magnetic field and an arbitrary quadrupole spin quantum number. The theory is applied to interpret fluorine relaxation profiles in LaF3 ionic crystals. The obtained results are compared with predictions of the 'classical' Solomon relaxation theory.     

Real space renormalization group approach to the two-dimensional antiferromagnetic Heisenberg model (I) – The singlet triplet gap

The low energy behaviour of the two-dimensional antiferromagnetic Heisenberg model is studied in the sector with total spins S = 0,1,2 by means of a renormalization group procedure, which generates a recursion formula for the interaction matrix Δ_S ⁽ⁿ⁺¹⁾ of 4 neighbouring “n clusters” of size 2ⁿ × 2ⁿ, n = 1,2,3,... from the corresponding quantities Δ_S ⁽ⁿ⁾. Conservation of total spin S is implemented explicitly and plays an important role. It is shown, how the ground state energies E_S ⁽ⁿ⁺¹⁾, S = 0,1,2 approach each other for increasing n, i.e. system size. The most relevant couplings in the interaction matrices are generated by the transitions 〈S’,m’;n+1|S_q ^*|S,m;n+1〉 between the ground states |S,m;n+1〉 (m = -S,...,S) on an (n+1)-cluster of size 2ⁿ⁺¹ × 2ⁿ⁺¹, mediated by the staggered spin operator S_q ^*.     

Approaching the ground state of the kagomé antiferromagnet

Y0.5Ca0.5BaCo4O7 contains kagomé layers of Co ions, whose spins are strongly coupled, with a Curie-Weiss temperature of -2200 K. At low temperature, T=1.2 K, our diffuse neutron scattering study with polarization analysis reveals characteristic spin correlations close to a predicted two-dimensional coplanar ground state with staggered chirality. The absence of three-dimensional long-range antiferromagnetic order indicates negligible coupling between the kagomé layers. The scattering intensities are consistent with high spin S=3/2 states of Co2+ in the kagomé layers and low spin S=0 states for Co3+ ions on interlayer sites. Our observations agree with previous Monte Carlo simulations indicating a ground state of effectively short range, staggered chiral spin order.     

Incommensurate magnetic ordering in Cu2Te2O5X2 (X = Cl,Br) studied by neutron diffraction

We present the results of the first neutron powder and single crystal diffraction studies of the coupled spin tetrahedra systems Cu2Te2O5X2 (X = Cl,Br). Incommensurate antiferromagnetic order with the propagation vectors kCl approximately [0.150,0.422,1/2], kBr approximately [0.158,0.354,1/2] sets in below TN = 18 K for X = Cl and 11 K for X = Br. No simple collinear antiferromagnetic or ferromagnetic spin arrangements within Cu2+ tetrahedra fit these observations. Fitting the diffraction data to more complex but physically reasonable models with multiple helices leads to a moment of 0.67(1)microB/Cu2+ at 1.5 K for the Cl compound. The reason for such a complex ground state may be geometrical frustration of the spins due to the intratetrahedral and intertetrahedral couplings having similar strengths. In neither compound has any evidence for a structural transition accompanying the magnetic ordering been found.     

Spin order due to orbital fluctuations: cubic vanadates

We investigate the highly frustrated spin and orbital superexchange interactions in cubic vanadates. The fluctuations of t(2g) orbitals trigger a novel mechanism of ferromagnetic interactions between spins S = 1 of V3+ ions along one of the cubic directions which operates already in the absence of Hund's rule exchange J(H), and leads to the C-type antiferromagnetic phase in LaVO3. The Jahn-Teller effect can stabilize the orbital ordering and the G-type antiferromagnetic phase at low temperatures, but large entropy due to orbital fluctuations favors again the C phase at higher temperatures, as observed in YVO (3).     

Influence of an interface layer on the effective coupling at a ferromagnet/antiferromagnet interface

We examine the exchange anisotropy induced at a ferromagnetic/antiferromagnetic interface when an antiferromagnetic interface layer exists. We show that competition between exchange couplings in the interface layer can result in a ferrimagnetic-like compensation point. This leads to a reversal of the effective field acting on the ferromagnet, and a consequent sign change of the exchange bias for temperatures near the Néel temperature of the antiferromagnet. A surprising result is the sensitive dependence of the compensation point on exchange interactions. Even minute modifications of the exchange interactions near the interface can result in a reversal of the effective field, provided certain conditions are met.     

Deconfinement phase transition in a two-dimensional model of interacting 2 × 2 plaquettes

The low energy behaviour of the two-dimensional antiferromagnetic Heisenberg model is studied in the sector with total spins S = 0,1,2 by means of a renormalization group procedure, which generates a recursion formula for the interaction matrix Δ_S ⁽ⁿ⁺¹⁾ of 4 neighbouring “n clusters” of size 2ⁿ × 2ⁿ, n = 1,2,3,... from the corresponding quantities Δ_S ⁽ⁿ⁾. Conservation of total spin S is implemented explicitly and plays an important role. It is shown, how the ground state energies E_S ⁽ⁿ⁺¹⁾, S = 0,1,2 approach each other for increasing n, i.e. system size. The most relevant couplings in the interaction matrices are generated by the transitions 〈S’,m’;n+1|S_q ^*|S,m;n+1〉 between the ground states |S,m;n+1〉 (m = -S,...,S) on an (n+1)-cluster of size 2ⁿ⁺¹ × 2ⁿ⁺¹, mediated by the staggered spin operator S_q ^*.     

Magnetization curves of a spin- bilayer system (A2) (ApB1−p)1 (B)2 with disordered interfaces

A calculation is presented for the component magnetizations of an infinite multilayer Ising system, consisting periodically of two layers of spin- A ions, two layers of spin- B ions, and a disordered layer interface in between that is characterized by a random arrangement of A and B ions like a two-dimensional A_pB_1−p alloy. The system is a simple cubic Ising-type structure with a coordination number z = 6. The model is general for ferro- and for antiferromagnetic A-B exchange couplings. The A-A and B-B exchange couplings are regarded as ferromagnetic. An effective field theory that goes beyond mean field, is employed to calculate the bulk-like transition temperature, the different component magnetizations as well as the total bulk-like magnetization. The component magnetizations are calculated for different realistic model values of ferro- and antiferromagnetic A-B exchange constants, as a function of temperature and of the concentration parameter p that characterizes the disorder in the interface. We show that the presence of a disordered interface may significantly affect the component and total magnetizations. In particular, for the case of antiferromagnetic exchange couplings, it is shown that the system can acquire a compensation temperature for certain domains of values of the concentration parameter p in the disordered interface.     

Kondo screening in a magnetically frustrated nanostructure: exact results on a stable non-fermi-liquid phase

Triangular symmetry stabilizes a novel non-Fermi-liquid phase in the three-impurity Kondo model with frustrating antiferromagnetic interactions between half-integer impurity spins. The phase arises without fine-tuning of couplings, and is stable against magnetic fields and particle-hole symmetry breaking. We find a conformal field theory describing this phase, verify it using the numerical renormalization group, and extract various exact, universal low-energy properties. Signatures predicted in electrical transport may be testable in scanning tunneling microscopy or quantum-dot experiments.     

The competition between CDW and SDW in quasi-one-dimensional organic magnetic polymer with interchain coupling interaction

Based on a theoretical model proposed for interchain-coupled quasi-one-dimensional organic magnetic polymer, the effects of the interchain couplings and electron–electron interactions on the charge density wave (CDW) and spin density wave (SDW) that exist in the system are studied. It is found that the amplitude of the SDW along the main chain will decrease with increasing of the oscillatory term of the interchain couplings in the system, which is unfavorable to the ferromagnetic ground state of the system. Moreover, with different interchain couplings, there will all exist a critical value of the inter-site electron–electron Coulomb repulsion, and at this value, the system will experience a transformation from strong SDW state to strong CDW one, which will weaken the mediating function of the antiferromagnetic SDW along the main chain. As a result, the ferromagnetic correlation intensity between the spins of the side radicals will be affected and consequently the stability of the ferromagnetic state in the system will be weakened.     

Magnon bands in twisted bilayer honeycomb quantum magnets

We study the magnon bands of twisted bilayer honeycomb quantum magnets using linear spin wave theory. Although the interlayer coupling can be ferromagnetic or antiferromagnetic, we keep the intralayer one ferromagnetic to avoid possible frustration. For the interlayer ferromagnetic case, we find the magnon bands have similar features with the corresponding electronic energy spectrums. Although the linear dispersions near the Dirac points are preserved in the magnon bands of twisted bilayer magnets, their slopes are reduced with the decrease of the twist angles. On the other hand, the interlayer antiferromagnetic couplings generate quite different magnon spectra. The two single-layered magnon spectra are usually decoupled due to the opposite orientations of the spins in the two layers. We also develop a low-energy continuous theory for very small twist angles, which has been verified to fit well with the exact tight-binding calculations. Our results may be experimentally observed due to the rapid progress in two-dimensional magnetic materials.