On the uniqueness of the equilibrium state for Ising spin systems

We show that for an Ising spin system of arbitrary spin with a ferromagnetic pair interaction and a periodic external magnetic field there is a unique equilibrium state if and only if the magnetization is continuous with respect to a uniform change in the external field. Hence, if the critical temperatureT _c is defined as the temperature where the spontaneous magnetization (which is a non-increasing function of the temperature) becomes positive, then the equilibrium state is unique forT>T _c and is non-unique forT<T _c (when the external field is zero). This implies that the correlation functions have a cluster property forT>T _c .We also show that for an anti-ferromagnet consisting of two sublattices there is a unique equilibrium state if and only if the staggered magnetization is continuous with respect to a change in the staggered field.Supported in part by U.S.A.F.O.S.R. under contract F 44620-71-C-0013, P001.     

Spherical Model in a Random Field

We investigate the properties of the Gibbs states and thermodynamic observables of the spherical model in a random field. We show that on the low-temperature critical line the magnetization of the model is not a self-averaging observable, but it self-averages conditionally. We also show that an arbitrarily weak homogeneous boundary field dominates over fluctuations of the random field once the model transits into a ferromagnetic phase. As a result, a homogeneous boundary field restores the conventional self-averaging of thermodynamic observables, like the magnetization and the susceptibility. We also investigate the effective field created at the sites of the lattice by the random field, and show that at the critical temperature of the spherical model the effective field undergoes a transition into a phase with long-range correlations ∼r ^4−d .     

Glassy phase and thermodynamics for random field Ising model on spherical lattice in magnetic field

Phase diagram and thermodynamic parameters of the random field Ising model (RFIM) on spherical lattice are studied by using mean field theory. This lattice is placed in an external magnetic field (B). The random field (hi) is assumed to be Gaussian distributed with zero mean and a variance     

The spontaneous magnetization of a one-dimensional model of a ferromagnetic toroid in a magnetic field

The paper deals with the derivation of the dependence of the spontaneous magnetization on the temperature and the intensity of the magnetic field for a one-dimensional model of a ferromagnetic toroid. For a chain formed of N10H ^–1/2 particles this dependence has the form of a half-power law modified by exponential dependence on H/T for temperatures and intensities of the magnetic field for which H/T10.     

Two-dimensional magnetic ordering in a multilayer structure

The effect of confinement from one, two or from all three directions on magnetic ordering has remained an active field of research for almost 100 years. The role of dipolar interactions and anistropy are important to obtain, the otherwise forbidden, ferromagnetic ordering at finite temperature for ions arranged in two-dimensional (2D) arrays (monlayers). We have demonstrated that conventional low-temperature magnetometry and polarized neutron scattering measurements can be performed to study short-range ferromagnetic ordering of in-plane spins in 2D systems using a multilayer stack of non-interacting monolayers of gadolinium ions formed by Langmuir-Blodgett (LB) technique. The spontaneous magnetization could not be detected in the heterogeneous magnetic phase observed here and the saturation value of the net magnetization was found to depend on the sample temperature and applied magnetic field. The net magnetization rises exponentially with lowering temperature and then reaches saturation following a T ln(βT) dependence. The T ln (βT) dependence of magnetization has been predicted from spinwave theory of 2D in-plane spin system with ferromagnetic interaction. The experimental findings reported here could be explained by extending this theory to a temperature domain of βT<1.     

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.     

New approaches inμ + SR studies on critical phenomena in Ni

The critical phenomena in Ni are probed by pulsedSR method under longitudinal- and zero external magnetic fields. The sample magnetization around the critical temperature is confirmed simultaneously by bulk magnetization measurement in situ, disappearance of transverseSR signal and recovery of asymmetry under longitudinal field. At the same time, the ratio of the ⁺ hyperfine field to the bulk magnetization in the ferromagnetic phase below the critical temperature is determined from the observables obtained only in the present experiment. The zero- and low-field longitudinal relaxation rate of muon does not diverge in approaching toT _c in the paramagnetic region, but seems to reach a saturation value.This work is supported by the Grand-in-Aid of the Japanese Ministry of Education, Culture and Science.     

Extremity of the disordered phase in the Ising model on the Bethe lattice

We prove that the disordered Gibbs distribution in the ferromagnetic Ising model on the Bethe lattice is extreme forTT _c ^SG , whereT _c ^SG is the critical temperature of the spin glass model on the Bethe lattice, and it is not extreme forT _c ^SG .     

Equilibrium magnetic properties of dipolar interacting ferromagnetic nanoparticles

We use Monte Carlo simulations to study the influence of dipolar interaction on the equilibrium magnetic properties of monodisperse single-domain ferromagnetic nanoparticles. Low field magnetizations simulated in zero field cooling (ZFC)/field cooling (FC) procedures and field-dependent magnetization curves above the blocking temperatures show strong dependence on the concentration and the spatial arrangement (cubic or random) of the magnetic particles. The field-dependent magnetizations can not be simply described by the T^* model at relative low temperatures due to the interplay between anisotropy and dipolar interactions, as well as the spatial arrangement effect.     

Magnetic properties of electron-doped La0.23Ca0.77MnO3 nanoparticles

Magnetic properties of electron-doped La_0.23Ca_0.77MnO₃ manganite nanoparticles, with average size of 12 and 60?nm, prepared by the glycine?Cnitrate method, have been investigated in the temperature range 5?C300?K and magnetic fields up to 90?kOe. It is suggested that weak ferromagnetic moment results from ferromagnetic shells of the basically antiferromagnetic nanoparticles and from domains of frustrated disordered phase in the core. Assumption of two distinct sources of ferromagnetism is supported by the appearance of two independent ferromagnetic contributions in the fit of the T ^3/2 Bloch law to spontaneous magnetization. The ferromagnetic components, which are more pronounced in smaller particles, occupy only a small fraction of the nanoparticle volume and the antiferromagnetic ground state remains stable. It is found that the magnetic hysteresis loops following field cooled processes, display size-dependent horizontal and vertical shifts, namely, exhibiting exchange bias effect. Time-dependent magnetization dynamics demonstrating two relaxation rates were observed at constant magnetic fields upon cooling to T?<?100?K.     

Quantum spherical model in a random field: coherent state path integral approach

By introducing boson operators, a quantum spherical XY model in the presence of a random field has been studied by the coherent state path integral approach. The phase diagram is obtained, and the effects of the random-field fluctuations on the possibilities of the existence of a ferromagnetic phase are discussed. At the critical point, , the order parameter M describing the ordered ferromagnetic phase disappears as .Since the model is equivalent to a Bose system, we also show that the phase transition at zero temperature between the superfluid and the disordered Mott insulator phases occurs at the chemical potential , where J₀ is the strength of the exchange interaction. As the temperature T goes to zero, the asymptotic behavior of the entropy and the specific heat are and , respectively. Received: 20 May 1997 / Accepted: 20 October 1997     

The Ising model in a random magnetic field

The existence of a spontaneous magnetization in the three-dimensional Ising model in a weak random magnetic field (RFIM) is investgated. Following Imry and Ma, we consider the energy change, E, from the fully aligned ferromagnetic state caused by flipping all the spins inside a connected surface, . It is proved rigorously that with high probability, E is positive forall enclosing the origin. Under the unproven assumption that the expectation value of the spin at one site is weakly correlated with the random fields at far away sites (which is true if surfaces within surfaces can be ignored) it follows that the three-dimensional RFIM has a spontaneous magnetization at low temperatures. The proof works for all dimensions greater than two, providing support for the conjecture that two is the lower critical dimension.Work supported in part by NSF grant No. DMR 8100417.     

Inhomogeneous magnetic states in the Nd(Mn<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>Cr<Subscript>x</Subscript>)O<Subscript>3</Subscript> system

The crystal structure and magnetic properties of the Nd(Mn_?xCr_x)O₃ system (x≤0.85) have been studied. Substitution of chromium for manganese was shown to induce a transition from the antiferromagnetic to ferromagnetic state (x≈0.2) and a decrease in the critical temperature followed, conversely, by an increase in the Néel temperature and decay of spontaneous magnetization. At low temperatures, the magnetization was found to behave anomalously as a result of magnetic interaction between the ferromagnetic and antiferromagnetic phases. The formation of the ferromagnetic phase is attributed to destruction of cooperative static orbital ordering, while the coexistence of different magnetic phases is most probably due to internal chemical inhomogeneity of the solid solutions.     

Magnetostriction domain structure in a periodic system of magnetoelastic and elastic nonmagnetic layers

The spectrum of magnetoelastic waves in a periodic structure of alternating ferromagnetic and nonmagnetic layers was studied. In the case of ferromagnetic layers with easy magnetization axes parallel to the layer surfaces, an orientational phase transition induced by an external tangential magnetic field H_e was considered. The formation of an inhomogeneous phase with a spatially modulated order parameter, which is caused by the magnetization being coupled through magnetostriction to lattice strains near the interfaces separating the magnetoelastic from elastic media, is predicted. It is shown that at a certain critical field in excess of the orientational phase transition field in the system without magnetostriction, a magnetoelastic wave propagating in a direction parallel to the in-plane magnetization vector M becomes unstable at finite values of the wave vector and condenses into a magnetostriction domain structure. A phase diagram in the (L, T, H_e) coordinates is constructed, and the regions of existence of thermodynamically equilibrium collinear, canted, and domain phases are established (L and T are the thicknesses of the ferromagnetic and nonmagnetic layers, respectively).     

On the equivalence of different order parameters and coexistence of phases for Ising ferromagnet. II

We investigate Ising spin systems with general ferromagnetic, translation invariant interactions,H=–J _BB,J _B0. We show that the critical temperatureT _i for the order parameterp _i defined as the temperature below whichp _i>0, is independent of the way in which the symmetry breaking interactions approach zero from above. Furthermore, all the equivalent correlation functions have the same critical exponents asT T_i from below, e.g. for pair interactions all the odd correlations have the same critical index as the spontaneous magnetization. The number of fluid and crystalline phases (periodic equilibrium states) coexisting at a temperatureT at which the energy is continuous is shown to be related to the number of symmetries of the interactions. This generalizes previous results for Ising spins with even (and non-vanishing nearest-neighbour) ferromagnetic interactions. We discuss some applications of these results to the triangular lattice with three body interactions and to the Ashkin-Teller model. Our results give the answer to the question raised by R.J. Baxter et al. concerning the equality of some critical exponents.Supported by NSF Grant PHY 77-22302     

Curietemperatur und Kollektivmagnetisierung bei ein- und vielkristallinen dünnen Nickelschichten

With a method of observing the temperature dependence of therf-permeability the Curie temperatureΘ of evaporated thin films (thicknessD from 30 to 300 Å) of nickel with various structures was investigated. Monocrystalline samples withD about 50 Å showedΘ-values comparable to the bulk material. The behaviour of some polycrystalline and several granulated films depends to a large extent on the structure (varied by conditions of deposition). It may be explained with a model that treats aggregates of small ferromagnetic particles with a high spontaneous magnetization but an interaction that may be considerably weaker than the full ferromagnetic exchange coupling. There appears a transition (to superparamagnetism) temperatureT _A which can be much lower than the Curie temperature. The expected dependence of T_A on particle size fits approximately with the experimental results from therf-method and electron diffraction data at samples of various structures.     

Large-n limit of the Heisenberg model: The decorated lattice and the disordered chain

The critical temperature of the generalized spherical model (large-component limit of the classical Heisenberg model) on a cubic lattice, whose every bond is decorated byL spins, is found. WhenL, the asymptotics of the temperature isT _c aL ^–1. The reduction of the number of spherical constraints for the model is found to be fairly large. The free energy of the one-dimensional generalized spherical model with random nearest neighbor interaction is calculated.     

Magnetic and optical properties of Zn1– x Fe x O ( x = 0.05 and 0.10) diluted magnetic semiconducting nanoparticles

We have investigated the magnetic and optical properties of chemically low temperature-synthesized Zn_{1– x} Fe _x O (x = 0.05 and 0.10) diluted magnetic semiconducting nanoparticles (～7 nm). Observed magnetic behaviour of x = 0.05 samples showed that the net magnetic interaction was antiferromagnetic-like, a feature established by Curie–Weiss fit, concave Arrott–Belov–Kouvel (ABK) plots with the absence of spontaneous magnetization even at 5 K and stretched exponential-type time-dependent magnetization behaviour. Optimization of the Fe(x) dopant concentration in Zn_{1– x} Fe _x O gave the most favourable room-temperature ferromagnetism for x = 0.10, as supported by finite coercive field (～94.4 Oe) and remanent magnetization (0.011 µ_B/Fe ion) from strong hysteretic magnetization vs. magnetic-field curves at room temperature. The Curie temperature of the x = 0.10 sample was estimated at ～388 K. The existence of a room-temperature ferromagnetic phase was further established by the convex nature of the ABK plots with finite spontaneous magnetization. The observed magnetic behaviour for different x values is best explained by a magnetic polaron model.