Phase diagram and exotic spin-spin correlations of anisotropic Ising model on the Sierpiński gasket

The anisotropic antiferromagnetic Ising model on the fractal Sierpiński gasket is intensively studied, and a number of exotic properties are disclosed. The ground state phase diagram in the plane of magnetic field-interaction of the system is obtained. The thermodynamic properties of the three plateau phases are probed by exploring the temperature-dependence of magnetization, specific heat, susceptibility and spin-spin correlations. No phase transitions are observed in this model. In the absence of a magnetic field, the unusual temperature dependence of the spin correlation length is obtained with 0 ≤ J_b/J_a< 1, and an interesting crossover behavior between different phases at J_b/J_a = 1 is unveiled, whose dynamics can be described by the J_b/J_a-dependence of the specific heat, susceptibility and spin correlation functions. The exotic spin-spin correlation patterns that share the same special rotational symmetry as that of the Sierpiński gasket are obtained in both the 1 / 3 plateau disordered phase and the 5/9 plateau partially ordered ferrimagnetic phase. Moreover, a quantum scheme is formulated to study the thermodynamics of the fractal Sierpiński gasket with Heisenberg interactions. We find that the unusual temperature dependence of the correlation length remains intact in a small quantum fluctuation.     

Simulation of the magnetic properties of manganese oxide Pb<Subscript>3</Subscript>Mn<Subscript>7</Subscript>O<Subscript>15</Subscript>

The magnetic susceptibility, heat capacity, and spin-spin correlation functions of manganese oxide Pb₃Mn₇O₁₅ are calculated by the Monte Carlo method. Two critical temperatures are determined: T ₁ ≈ 20 K, above which a modulated structure along the hexagonal axis is formed, and T ₂ ≈ 70 K, at which the long-range magnetic order disappears. The antiferromagnetic exchange interaction constant in a hexagonal plane is estimated to be J ₁ ～ 7 K, and the antiferromagnetic and ferromagnetic exchange interaction constants between hexagonal planes are calculated to be J ₂ ～ 3 K and K ～ 50 K, respectively.     

Unconventional spin-charge phase separation in a model 2D cuprate

In this work, we address a challenging problem of a competition of charge and spin orders for high-T _c cuprates within a simplified 2D spin-pseudospin model which takes into account both conventional Heisenberg Cu²⁺?Cu²⁺ antiferromagnetic spin exchange coupling (J) and the on-site (U) and intersite (V) charge correlations in the CuO₂ planes with the on-site Hilbert space reduced to only three effective charge states (nominally Cu^1+;2+;3+). We performed classical Monte Carlo calculations for large square lattices implying the mobile doped charges and focusing on a case of a small intersite repulsion V ? J. The on-site attraction (U < 0) does suppress the antiferromagnetic ordering and gives rise to a checkerboard charge order with the doped charge distributed randomly over a system in the whole temperature range. However, under the on-site repulsion (U > 0) the homogeneous ground state antiferromagnetic solutions of the doped system found in a mean-field approximation are shown to be unstable with respect to a phase separation with the charge and spin subsystems behaving like immiscible quantum liquids. Puzzlingly, with lowering the temperature one can observe two sequential phase transitions: first, an antiferromagnetic ordering in the spin subsystem diluted by randomly distributed charges, then, a charge condensation in the charge droplets. The effects are illustrated by the Monte Carlo calculations of the specific heat and longitudinal magnetic susceptibility.     

Thermodynamics of the frustrated J<Subscript>1</Subscript>-J<Subscript>2</Subscript> Heisenberg ferromagnet on the body-centered cubic lattice with arbitrary spin

We use the spin-rotation-invariant Green’s function method as well as thehigh-temperature expansion to discuss the thermodynamic properties of the frustratedspin-S J ₁-J ₂ Heisenbergmagnet on the body-centered cubic lattice. We consider ferromagnetic nearest-neighborbonds J ₁<0 and antiferromagnetic next-nearest-neighbor bonds J ₂ ≥ 0 andarbitrary spin S. We find that the transition point\hbox{$J_2^c$}J2cbetween the ferromagnetic ground state and theantiferromagnetic one is nearly independent of the spin S, i.e., it is very closeto the classical transition point\hbox{$J_2^{c,{\rm clas}}= \frac{2}{3}|J_1|$}J2c,clas=23|J1|. At finite temperatures we focus on the parameterregime\hbox{$J_2<J_2^c$}J2<J2cwith a ferromagnetic ground-state. We calculate theCurie temperature T _C (S, J ₂)and derive an empirical formula describing the influence of the frustration parameterJ ₂ and spin S on T _C . We find that theCurie temperature monotonically decreases with increasing frustration J ₂, where veryclose to\hbox{$J_2^{c,{\rm clas}}$}J2c,clasthe T _C (J ₂)-curveexhibits a fast decay which is well described by a logarithmic term\hbox{$1/\textrm{log}(\frac{2}{3}|J_1|-J_{2})$}1/log(23|J1|?J2). To characterize the magnetic ordering below and aboveT _C , we calculate thespin-spin correlation functions ?S ₀ S _R ?, the spontaneous magnetization, the uniform static susceptibilityχ ₀ as well as the correlation lengthξ.Moreover, we discuss the specific heat C _V and the temperaturedependence of the excitation spectrum. As approaching the transition point\hbox{$J_2^c$}J2csome unusual features were found, such as negativespin-spin correlations at temperatures above T _C even though theground state is ferromagnetic or an increase of the spin stiffness with growingtemperature.     

Band structure and the magnetic and elastic properties of SrFeO<Subscript>3</Subscript> and LaFeO<Subscript>3</Subscript> perovskites

The band structure and the magnetic and elastic characteristics of SrFeO₃ and LaFeO₃ perovskites with ferromagnetic and antiferromagnetic collinear spin configurations (of the A, C, and G types) are investigated using the ab initio pseudopotential method (the VASP program package) with the inclusion of the single-site Coulomb correlations (the LSDA + U formalism). It is shown that, in the pressure range 0–50 GPa, the most stable states are the ferromagnetic metal state for the SrFeO₃ compound and the antiferromagnetic insulator state of the G type for the LaFeO₃ compound.     

Periodic Striped Ground States in Ising Models with Competing Interactions

We consider Ising models in two and three dimensions, with short range ferromagnetic and long range, power-law decaying, antiferromagnetic interactions. We let J be the ratio between the strength of the ferromagnetic to antiferromagnetic interactions. The competition between these two kinds of interactions induces the system to form domains of minus spins in a background of plus spins, or vice versa. If the decay exponent p of the long range interaction is larger than d + 1, with d the space dimension, this happens for all values of J smaller than a critical value J_c(p), beyond which the ground state is homogeneous. In this paper, we give a characterization of the infinite volume ground states of the system, for p > 2d and J in a left neighborhood of J_c(p). In particular, we prove that the quasi-one-dimensional states consisting of infinite stripes (d = 2) or slabs (d = 3), all of the same optimal width and orientation, and alternating magnetization, are infinite volume ground states. Our proof is based on localization bounds combined with reflection positivity.     

Electronic structures of ternary iron arsenides <Emphasis Type="Italic">A</Emphasis>Fe<Subscript>2</Subscript>As<Subscript>2</Subscript> (<Emphasis Type="Italic">A</Emphasis> = Ba,Ca, or Sr)

We have studied the electronic and magnetic structures of the ternary iron arsenides AFe₂As₂ (A = Ba, Ca, or Sr) using the first-principles density functional theory. The ground states of these compounds are in a collinear antiferromagnetic order, resulting from the interplay between the nearest and the next-nearest neighbor superexchange antiferromagnetic interactions bridged by As 4p orbitals. The correction from the spin-orbit interaction to the electronic band structure is given. The pressure can reduce dramatically the magnetic moment and diminish the collinear antiferromagnetic order. Based on the calculations, we propose that the low energy dynamics of these materials can be described effectively by a t-J _H -J ₁-J ₂-type model [2008, arXiv: 0806.3526v2].     

Quark-antiquark composite systems: The Bethe-Salpeter equation in the spectral-integration technique

The Bethe-Salpeter equations for the quark-antiquark composite systems, q\(\bar q\), are written in terms of spectral integrals. For the q\(\bar q\) mesons characterized by the mass M, spin J, and radial quantum number n, the equations are presented for the following (n, M²) trajectories: π _J , η _J , a _J , f _J , ρ _J , ω _J , h _J , and b _J .     

Phase transitions in a two-dimensional antiferromagnetic Potts model on a triangular lattice with next-nearest neighbor interactions

Phase transitions (PTs) and frustrations in two-dimensional structures described by a three-vertex antiferromagnetic Potts model on a triangular lattice are investigated by the Monte Carlo method with regard to nearest and next-nearest neighbors with interaction constants J₁ and J₂, respectively. PTs in these models are analyzed for the ratio r = J₂/J₁ of next-nearest to nearest exchange interaction constants in the interval |r| = 0–1.0. On the basis of the analysis of the low-temperature entropy, the density of states function of the system, and the fourth-order Binder cumulants, it is shown that a Potts model with interaction constants J₁ < 0 and J₂ < 0 exhibits a first-order PT in the range of 0 ? r < 0.2, whereas, in the interval 0.2 ? r ? 1.0, frustrations arise in the system. At the same time, for J₁ > 0 and J₂ < 0, frustrations arise in the range 0.5 < |r| < 1.0, while, in the interval 0 ? |r| ? 1/3, the model exhibits a second-order PT.     

Frustrated antiferromagnetism in the Sr<Subscript>2</Subscript>YRuO<Subscript>6</Subscript> double perovskite

The spins of Ru⁵⁺ ions in Sr₂YRuO₆ form a face-centered cubic lattice with antiferromagnetic nearest neighbor interaction J≈25 meV. The antiferromagnetic structure of the first type experimentally observed below the Néel temperature T _N =26 K corresponds to four frustrated spins of 12 nearest neighbors. In the Heisenberg model in the spin-wave approximation, the frustrations already cause instability of the antiferromagnetic state at T=0 K. This state is stabilized by weak anisotropy D or exchange interaction I with the next-nearest neighbors. Low D/J～I/J～10^?3 values correspond to the experimental T _N and sublattice magnetic moment values.     

Determination of the Spin–Spin Coupling Constant in Hydrogen Deuteride HD and Estimates of the Manifestation of Axion-Like Particles

An experimental value of the spin–spin coupling constant in deuterated molecular hydrogen HD has been obtained, J _pd = (43.112 ± 0.005) Hz (300 K), while investigating two gaseous samples at pressures of 95 and 155 atm. The experimental result does not coincide with Jpd = (43.31 ± 0.05) Hz that was calculated theoretically by Helkager et al. The observed discrepancy ΔJ _pd ≈ (0.20 ± 0.05 Hz) may point to a manifestation of the involvement of light pseudo-scalar (axion-like) bosons with a mass m _a ≈ 1 keV/c² in the spin–spin coupling of the HD proton and deuteron.     

Asymmetric Anderson model and spin excitations in the Kondo insulator YbB<Subscript>12</Subscript>

A cluster problem is analyzed as an example demonstrating that the observed three-mode behavior of spin-triplet excitations in YbB₁₂ can be described by the asymmetric Anderson model with insulating singlet ground state. In the case of an infinite system, it is argued that the behavior of the f subsystem can be analyzed by using an effective Hamiltonian ? _J with direct antiferromagnetic f-f exchange interaction. The spin excitation spectrum is shown to have a minimum at the antiferromagnetic vector, as observed experimentally. A distinctive feature of the analysis is the use of singlet and triplet basis operators.     

Models of spin structures in Sr<Subscript>2</Subscript>RuO<Subscript>4</Subscript>

The mean-field method is used to calculate the bands, Fermi surfaces, and spin susceptibilities of a three-band model of the RuO₄ plane of Sr₂RuO₄ rutinate for states with different spin structures. In particular, the spiral state is studied with the “incommensurate” vector Q=2π(1/3, 1/3) corresponding to the nesting of bands with the population n=4. This state proves to be the lowest with respect to energy among other (paramagnetic, ferromagnetic, antiferromagnetic, and periodic) solutions. In the spiral state, in addition to the main α, β, and γ sheets of the Fermi surface, shadow Fermi boundaries along the Γ(0, 0)-M(π, 0) line (previously observed in the ARPES experiments) are revealed and explained. This may change the interpretation of the data on dispersionless peaks in photoemission, previously ascribed to surface states. The spin susceptibilities of the spiral state exhibit peaks in the dependence Im?(q, ω) at q=Q in accordance with the observed magnetic peak in neutron scattering. The hypothesis of the presence of spin structures with q=Q in the normal state of Sr₂RuO₄ and the methods of checking this hypothesis are discussed.     

Properties of InGaAs/GaAs quantum wells with a δ〈Mn〉-doped layer in GaAs

A method of formation of two-dimensional structures containing a δ〈Mn〉-doped layer in GaAs and an In_xGa_1?x As quantum well (QW) separated by a GaAs spacer of thickness d = 4–6 nm is developed using laser evaporation of a metallic target during MOS hydride epitaxy. It is shown that, up to room temperature, these structures have ferromagnetic properties most likely caused by MnAs clusters. At low temperatures (T _m ～ 30 K), the anomalous Hall effect is revealed to occur. This effect is related to hole scattering by Mn ions in GaAs and to the magnetic exchange between these ions and QW holes, which determines the spin polarization of the holes. The behavior of the negative magnetoresistance of these structures at low temperatures indicates the key role of quantum interference effects.     

Pressure-induced antiferromagnetism in La<Subscript>0.75</Subscript>Ca<Subscript>0.25</Subscript>MnO<Subscript>3</Subscript> manganite

The crystal and magnetic structures of La_0.75Ca_0.25MnO₃ manganite are studied under high pressures up to 4.5 GPa in the temperature range 12–300 K by the neutron diffraction method. At normal pressure and temperature T _C = 240 K, a ferromagnetic state is formed in La_0.75Ca_0.25MnO₃. At high pressures P ≥ 1.5 GPa and at temperatures T < T _N ≈ 150 K, a new A-type antiferromagnetic state appears. A further increase in pressure leads to an increase in the volume fraction of the antiferromagnetic phase, which coexists with the initial ferromagnetic phase. The effect of high pressure causes a considerable increase in T _C with the slope dT _C /dP ≈ 12 K/GPa. Calculations performed in the framework of the double exchange model with allowance for the electron-phonon interaction make it possible to explain this pressure dependence of T _C on the basis of experimental data.     

Monte Carlo determination of the low-energy constants for a two-dimensional spin-1 Heisenberg model with spatial anisotropy

The low-energy constants, namely the spin stiffness ρ _s , the staggered magnetization density ? _s per area, and the spinwave velocity c of the two-dimensional (2D) spin-1 Heisenberg model on the square and rectangular lattices are determined using the first principles Monte Carlo method. In particular, the studied models have different antiferromagnetic couplings J ₁ and J ₂ in the spatial 1- and 2-directions, respectively. For each considered J ₂∕J ₁, the aspect ratio of the corresponding linear box sizes L ₂∕L ₁ used in the simulations is adjusted so that the squares of the two spatial winding numbers take the same values. In addition, the relevant finite-volume and -temperature predictions from magnon chiral perturbation theory are employed in extracting the numerical values of these low-energy constants. Our results of ρ _s1 are in quantitative agreement with those obtained by the series expansion method over a broad range of J ₂∕J ₁. This in turn provides convincing numerical evidence for the quantitative correctness of our approach. The ? _s and c presented here for the spatially anisotropic models are new and can be used as benchmarks for future related studies.     

A study of the critical properties of the Ising model on body-centered cubic lattice taking into account the interaction of next behind nearest neighbors

The replica Monte Carlo method has been used to investigate the critical behavior of a threedimensional antiferromagnetic Ising model on a body-centered cubic lattice, taking into account interactions of the adjacent behind neighbors. Investigations are carried out for the ratios of the values of exchange interactions behind the nearest and next nearest neighbors k = J ₂/J ₁ in the range of k ∈ [0.0, 1.0] with the step Δk = 0.1. In the framework of the theory of finite-dimensional scaling the static critical indices of heat capacity α, susceptibility γ, of the order parameter β, correlation radius ν, and also the Fisher index η are calculated. It is shown that the universality class of the critical behavior of this model is kept in the interval of k ∈ [0.0, 0.6]. It is established that a nonuniversal critical behavior is observed in the range k ∈ [0.8, 1.0].     

Ferromagnetic and spin-wave resonance in Co/Pd/CoNi multilayer films

It has been found that the magnitude and sign of exchange interaction between Co(5 nm) and CoNi(5 nm) ferromagnetic layers through Pd depend on magnetization orientation of ferromagnetic layers. If magnetization is oriented in a layer plane, exchange interaction can be both ferromagnetic and antiferromagnetic. If magnetization orientation is orthogonal to a layer plane, the exchange constant is always positive at d_Pd<d _c and equals zero at d_Pd>d _c (d _c is the characteristic length).     

Magnetic and crystal structures of iron-ion-doped TbBaCo<Subscript>2</Subscript>O<Subscript>5 + γ</Subscript>

Neutron diffraction and magnetic studies of a TbBaCo₂O_{5 + γ} polycrystalline sample with a perovskite-like layered structure have revealed that spontaneous magnetization appears at 305 K and decreases sharply below 200 K. It has been shown that the crystal structure is described by space group Pmmm with a 2a _p · a _tp · 2a _p unit cell. The magnetic structure in the high-temperature magnetic phase consists of the G-type antiferromagnetic and ferromagnetic components, whereas the magnetic structure in the low-temperature phase is a G-type antiferromagnetic. The ferromagnetic component appears due to the noncollinearity of the magnetic moments of Co³⁺ ions, which are in the high-spin state in pyramids and in the low-spin state in octahedrons. The antiferromagnetic component is present in the octahedral sublattice, because oxygen vacancies are partially ordered.     

Magnetic and electrical properties of the ZnGeAs<Subscript>2</Subscript>: Mn chalcopyrite

Doping of the ZnGeAs₂ semiconductor with manganese has produced compositions with spontaneous magnetization and high Curie temperatures of up to 367 K for the composition 3.5 wt% Mn. Their magnetic properties are characteristic of spin glasses at temperatures T < T _S and magnetic fields H < 11 kOe. In stronger fields, the spin glass state transforms into a phase with a spontaneous magnetization 4–5 times weaker than that to be expected under ferromagnetic ordering of all Mn ions. This is obviously a singly-connected ferromagnetic phase containing regions with frustrated bonds. The frustrated regions and the spin glass phase have inclusions of noninteracting ferromagnetic clusters, because these regions and the spin glass phase at low temperatures exhibit a strong increase in the magnetization M, with the dependence M(T) being described by the Langevin function. Measurements of the electrical resistivity ρ and the Hall effect have revealed that, for T < 30 K, the resistivity ρ of compositions with 1.5 and 3.5 wt % Mn is higher that at 30 K, which makes superexchange dominant and gives rise to the onset of the spin glass state. The nonuniform distribution of Mn ions in the spin glass phase accounts for the existence of isolated ferromagnetic clusters, their ferromagnetism being generated by carrier-mediated exchange. As the temperature increases still more, the increase in the mobility occurs faster than the decrease in the concentration, thus promoting an enhancement of the carrier-mediated exchange and growth of the ferromagnetic clusters in size, which at T = T _S come in contact. This signifies a transition from a multiply-to a singly-connected ferromagnetic phase, which contains microregions with frustrated bonds.