Green function theory of Curie and order—order transitions in ferromagnetic systems

Dipolar critical temperatures in ferromagnetic systems with isotropic bilinear and biquadratic exchange are investigated by means of the Green function technique. Expressions are found for both the familiar Curie temperature, T_c, and the less well known order-order transition temperature, T_o, at which, under appropriate conditions, the magnetic ordering undergoes a change between fully aligned and canted ferromagnetism. At T = 0, a fully aligned state has <s_i^z = s for spin s and all lattice sites i, while a canted state has 〈s_i^z〉<s. It is shown independently of the Green function analysis that the T = 0 ground state is fully aligned if α, the ratio of biquadratic to bilinear exchange integrals, obeys ?[2s(s?1)]^?1<α< [2s²?2s+1]^?1. The region below the lower limit is identified as the range in which canted ferromagnetism can occur and is a range that does not appear to have been considered previously via the Green function formalism.The temperature dependence of the magnetic ordering is investigated by means of the double-time temperature-dependent Green function formalism. A new decoupling scheme is derived and used to reduce higher order Green functions to lowest order. It is found that a canted state, occuring at low temperatures, undergoes a transition to a fully aligned state at a temperature T₀ and subsequently becomes disordered at temperature T_c. Transitions to paramagnetism are found to be second order for α<α_c and first order for α?α_c where α_c is a critical value that depends on the atomic spin and weakly on the lattice structure. A phase diagram is given to illustrate the results, and a comparison is made with the corresponding results found in mean field theory.     

Properties of the Ising magnet confined in a corner geometry

The properties of Ising square lattices with nearest neighbor ferromagnetic exchange confined in a corner geometry, are studied by means of Monte Carlo simulations. Free boundary conditions at which boundary magnetic fields ±h are applied, i.e., at the two boundary rows ending at the lower left corner a field +h acts, while at the two boundary rows ending at the upper right corner a field −h acts. For temperatures T less than the critical temperature T_c of the bulk, this boundary condition leads to the formation of two domains with opposite orientation of the magnetization direction, separated by an interface which for T larger than the filling transition temperature T_f(h) runs from the upper left corner to the lower right corner, while for T<T_f(h) this interface is localized either close to the lower left corner or close to the upper right corner. It is shown that for T=T_f(h) the magnetization profile m(z) in the z-direction normal to the interface simply is linear and the interfacial width scales as w∝L, while for T>T_f(h) it scales as . The distribution P(?) of the interface position ? (measured along the z-direction from the corners) decays exponentially for T<T_f(h) from either corner, is essentially flat for T=T_f(h), and is a Gaussian centered at the middle of the diagonal for T>T_f(h). Unlike the findings for critical wetting in the thin film geometry of the Ising model, the Monte Carlo results for corner wetting are in very good agreement with the theoretical predictions.     

Inelastic neutron scattering study of spin waves in MnO

The dispersion relation E(q) for spin waves in MnO has been measured at 4.2°K by neutron inelastic scattering. The isotropic exchange integrals as well as the anisotropy constants have been determined by fitting the Hamiltonian to the data. It is found that the exchange striction plays main role in the anomaly in the magnetic interactions in MnO and the biquadratic exchange interaction j₁(S₁·S₂)² is almost absent (j₁/J₁ ? 0.002).     

Density correlations of hadron gas and the origin of early multiplicity scaling

We will define a sequence of functions called density correlations which measure statistical correlations between momentum space densities of particles in the ensemble of inelastic final states produced by scattering a pair of hadrons. Then we will show that early multiplicity scaling of the distribution of charged particles produced by pp collisions can primarly be explained by the assumption that fluctuations of the density of charged particles are quite random and therefore higher correlation functions are small in an appropriate sense, combined with the assumption that the first three density correlations fulfill an approximate form of Feyman scaling at small values of x. These assumptions will aslo be used to derive an expression for the scaling function Ψ(η) which is completely determined by <N²>_S/<N>_S² and <N³>_S/<N>_S³, and recursion relation to calculate <N^m>_S/<N>_S^m, m ? 4, from <N²>_S/<N>_S² and <N³>_S/<N>_S³. The prediction for Ψ(η) accurately reproduces data in the interval 0.2 ? η ? 3.1, 50 GeV/c ? p_L ? 303 GeV/c, and the predictions for <N_S>^m/<N>_S^m, 4 ? m ? 10, agree with observed values in the interval 50 GeV/c ? p_L ? 303 GeV/c.     

The effect of a surface on the dynamic and thermodynamic properties of S=1 Heisenberg ferromagnet with biquadratic exchange

Properties of semi-infinite (S=1) Heisenberg ferromagnet with biquadratic exchange were studied in terms of surface exchange (=I_S/I) and biquadratic coupling (a). It was shown that a strict correlation exists, depending on , between the type of surface spin waves (acoustic or optical) and the mean-field (MF) critical temperature, bulk (T_c) and surface T_c^S>T_c (for ). Within the framework of the Landau–Ginsburg theory for semi-infinite simple cubic ferromagnet, a detailed study is presented of the critical behaviour of the system, in particular in the vicinity of the tricritical point which is the consequence of the biquadratic interaction. It is shown that tricritical exponents satisfy exactly the scaling relations for d=3. The analysis of the spin–spin correlation function within the framework of the same theory, shows that there occurs the critical magnetic scattering of low-energy electrons (LEED) from the surface in the case , when the ordering temperature T_c^S is approached from above (from paramagnetic phase). In the opposite case, , there occurs no surface critical scattering. It was also shown that in the vicinity of the tricritical point, the biquadratic interaction increases the range of validity of the MF approximation.     

Hysteresis effects at a cooperative high-spin (5T2) ⇌ low-spin (1A1) transition in dithiocyanatobis (4, 7-dimethyl-1, 10-phenanthroline) iron (II)

Hysteresis has been observed at the cooperative high-spin (⁵T₂) ? low-spin (¹A₁) transition in Fe (4, 7-(CH₃)₂-phen)₂(NCS)₂ where phen = 1, 10-phenanthroline. The transition is centered on T_c> = 121.7 K for rising and on T_c< = 118.6 K for lowering of temperature. The observations are in only qualitative agreement with the thermodynamic theory of Slichter and Drickamer.     

αS(KT2) versus αS(K2) in QCD jet development: Some quantitative remarks

Properties of QCD jets for two proposed choices of the variable appearing in the QCD running coupling constant, α_S(K²) or α_S(K_T²) with K_T²=z(1?z)K², have been studied in detail by the use of Monte Carlo techniques. Contrary to expectations based on approximate analytic calculations it is found that when substituting K² with K_T² in α_S the growth with energy of the multiplicity of the quanta is not sensibly altered, and it is even slowed down for extreme values of the non-perturbative cutoff, which delimits the minimum virtual mass of the quanta. It appears, therefore, that the analysis of subleading effects may be totally misleading if phase-space constraints are not taken into account exactly, which is possible to do in Monte Carlo calculations.     

Spin autocorrelation of Ni in K2Mn0.975Ni0.025F4 studied by nuclear spin-lattice relaxation

From the nuclear spin-lattice relaxation of the out-of-layer ¹⁹F nuclei in magnetic fields perpendicular to the c-axis the low-frequency component of the autocorrelation function 〈S^z(t)S^z(O)〉 of Ni in ordered K₂Mn_0.975Ni_0.025F₄ is found to be substantially reduced relative to the Mn host. The experimental rates vs temperature are in accord with those for relaxation involving two spin excitations calculated with local Green's functions.     

Effects of Cr doping in bilayered manganite LaSr2Mn2O7: Resistivity, thermoelectric power, and thermal conductivity

Systematic studies of resistivity, thermoelectric power, and thermal conductivity have been performed on polycrystalline bilayered manganites LaSr₂Mn_2−xCr_xO₇ (0≤x≤0.2). It is found that the temperature dependence of both Seebeck coefficient S(T) and resistivity ρ(T) in the high temperature region follows the small polaron transport mechanism for all the samples. But in the low temperature region, variable-range-hopping (VRH) model matches the experimental data better. In addition, the maximum of absolute S(T) at low temperatures is gradually suppressed for the sample with Cr-doping level of x>0.04, implying that a new FM order probably arises. With decreasing the temperatures further, S(T) has a sign change and becomes positive for the sample with Cr-doping level of x>0.04, indicating that there may occur a variation of the type of charge carrier. As to thermal conduction κ(T), the low-temperature peak is suppressed due to Cr-doping. The variation of κ(T) is analyzed based on the combined effect due to the suppression of local Mn³⁺O₆ Jahn-Teller (JT) lattice distortion because of the substitution of Cr³⁺ ions for Mn³⁺ ions, which results in the increase in thermal conduction, and the introduction of the disorder due to Cr-doping, which contributes to the decrease in thermal conduction.     

Period doubling in maps with a maximum of order z

We consider the scaling behaviour in period-doubling systems, exemplified by the one-dimensional map χ_n+1 = 1 − λ|χ_n|^z, which has a maximum of order z (z > 1). The Feigenbaum scaling factors α and δ are studied as functions of z, and more generally the scaling functions 1/σ and ƒ(a). In particular, using the universal functions g(x) and h(x) we establish the inequality δ < α^z, which implies that δ remains finite (≲ 30) in the limit z → ∞.     

Quantization and confinement effects in superconducting nanostructures

The confinement of the flux lines by a lattice of submicron holes (‘antidots’) has been studied in nanostructured superconducting Pb/Ge multilayers. By introducing regular arrays of sufficiently large antidots, multi-quanta vortex lattices have been stabilized. Sharp cusp-like magnetization (M) anomalies, appearing at matching fieldsH_m=mφ₀/Sin superconducting films with the antidot lattices having a unit cell areaS, are successfully explained. These anomalies are, analogues of the well-knownM(H) cusp atH_c1, but for the onset of multi-quanta (m+1)φ₀-vortices penetration at each subsequent matching fieldH_m. It is shown that theM(H) curve between the matching fieldsH_m<H<H_m+1follows a simpleM∝ln(H−H_m) dependence. These experimental observations have revealed an unusual expansion of validity of the London limit in superconductors with lattices of relatively large antidots. The successful high quality fit of theM(H,T) curves convincingly demonstrates that a new type of the critical stateB=const (‘single-terrace critical state’) can be realized in superconductors with the antidot lattices.     

Spectral dependence of photoinduced optical absorption in doped yttrium iron garnet single crystals

The photoinduced optical absorption α of doped yttrium iron garnets (YIG) is investigated. It is found that the optical absorption α at a wavelength of 1.1 μm depends on the wavelength of irradiating light in the range 0.6–1.9 μm. It is demonstrated that, in the Y₃Fe₅O₁₂ crystal with an acceptor Ba impurity, the photoinduced increase in α is due to the formation of Fe⁴⁺ ions in octahedral sites. The charge transfer occurs through photoexcitation of the ⁶ A _1g (⁶ S) → ⁴ T _1g (⁴ G) and ⁶ A _1g (⁶ S) → ⁴ T _2g (⁴ G) transitions of octahedral Fe³⁺ ions. In the crystal with a donor Si impurity, the increase in α is caused by the formation of Fe²⁺ ions upon photoionization of silicon. __________ Translated from Fizika Tverdogo Tela, Vol. 43, No. 7, 2001, pp. 1233–1235. Original Russian Text Copyright ? 2001 by Doroshenko, Nadezhdin.     

Distribution of pseudo-critical temperatures and lack of self-averaging in disordered Poland-Scheraga models with different loop exponents

According to recent progresses in the finite size scaling theory of disordered systems, thermodynamic observables are not self-averaging at critical points when the disorder is relevant in the Harris criterion sense. This lack of self-averageness at criticality is directly related to the distribution of pseudo-critical temperatures T_c(i,L) over the ensemble of samples (i) of size L. In this paper, we apply this analysis to disordered Poland-Scheraga models with different loop exponents c, corresponding to marginal and relevant disorder. In all cases, we numerically obtain a Gaussian histogram of pseudo-critical temperatures T_c(i,L) with mean T_c^av(L) and width ΔT_c(L). For the marginal case c=1.5 corresponding to two-dimensional wetting, both the width ΔT_c(L) and the shift [T_c(∞)-T_c^av(L)] decay as L^-1/2, so the exponent is unchanged (ν_random=2=ν_pure) but disorder is relevant and leads to non self-averaging at criticality. For relevant disorder c=1.75, the width ΔT_c(L) and the shift [T_c(∞)-T_c^av(L)] decay with the same new exponent L^-1/νrandom (where ν_random ∼2.7 > 2 > ν_pure) and there is again no self-averaging at criticality. Finally for the value c=2.15, of interest in the context of DNA denaturation, the transition is first-order in the pure case. In the presence of disorder, the width ΔT_c(L) ∼L^-1/2 dominates over the shift [T_c(∞)-T_c^av(L)] ∼L^-1, i.e. there are two correlation length exponents ν=2 and that govern respectively the averaged/typical loop distribution.     

Phase transition in Ising, XY and Heisenberg magnetic films

The phase transition and magnetic properties of a ferromagnet spin-S, a disordered diluted thin and semi-infinite film with a face-centered cubic lattice are investigated using the high-temperature series expansions technique extrapolated with Padé approximants method for Heisenberg, XY and Ising models. The reduced critical temperature of the system τ_c is studied as function of the thickness of the thin film and the exchange interactions in the bulk, and within the surfaces J_b, J_s and J_⊥, respectively. It is found that τ_c increases with the exchange interactions of surface. The magnetic phase diagrams (τ_c versus the dilution x) and the percolation threshold are obtained. The shifts of the critical temperatures T_c(l) from the bulk value (T_c(∞)/T_c(l) − 1) can be described by a power law l^−λ, where λ = 1/υ is the inverse of the correlation length exponent.     

On the connectivity index for lattices of nonintegral dimensionality

We define the connectivity indexc for an infinite graph by the requirement that to disconnect a subset of at leastV points from the rest of the graph requires the deletion of a minimum ofS(V) bonds whereS(V) ∼V ^(c−1)/c for largeV. For ad-dimensional hypercubical lattice withd integral,c=d. We construct explicit examples of lattices with nonintegral connectivity indexc, 1<c<∞. It is argued that the connectivity index is an important parameter determining the critical behaviour of Hamiltonians on these lattices.     

Two-dimensional critical behaviour in antiferrodistortive Al ur6(CIO4)3 and Ga ur6(ClO4)3

Critical behaviour with dimensionality d = 2 has been observed for the 300 K antiferrodistortive phase transition in Al ur₆(ClO₄)₃ and Ga ur₆(ClO₄)₃ by means of the temperature dependence of the ESR parameter D. The systems exhibited d = 2 behaviour in the static critical behaviour for T<T_c?40 K for T>T_c + 40 K. From the ESR data including line width measurements the local order parameter relaxation rate ω₁ has been obtained for various temperatures above T_c, with a lowest value of ω₁ = 150 MHz at T_c + 15 K     

Estimation of T1 for Co2+ ions from temperature variation of the EPR linewidths for Gd3+ in Ce2Co3(NO3)12.24H2O single crystals

EPR of Gd³⁺ doped in Ce₂M″₃(NO₃)₁₂.24H₂O (M″ = Mg, Zn, Co) single crystals has been studied at various temperatures from room temperature to 77 K using ∼ 9.45 GHz EPR spectrometer. The observation of resolved Gd³⁺ spectra at room temperature in Ce₃Co₂(NO₃)₁₂.24H₂O has been interpreted in terms of a random modulation of the interaction between the Gd³⁺ and the Co²⁺ ions by the rapid spin-lattice relaxation of Co²⁺ ions. It is found that the effective spin-lattice relaxation time T₁ ∝ T⁻ⁿ where n = 1.85 (B∥z axis) and n = 1.75 (B⊥z axis) if 103 < T < 283 K.     

The nature of anharmonicity and anomalous piezoelectric properties of ferroelectric SbSBr crystal

The contribution of soft mode at Sb atom's sites, to the temperature dependences of Sb atom's equilibrium position's difference Δz(T) has been studied theoretically, when SbSBr crystal is deformed along a(x), b(y) and c(z)-axis in paraelectric phase and is deformed along c(z)-axis in ferroelectric phase. The largest change of Δz₃₃(T) occurs in the ferroelectric phase near the phase transition temperature in the range from 16 K to 21 K. The temperature dependence of Sb atom's equilibrium position's displacements Δz₃₃ is very similar to the temperature dependence of experimental piezoelectric modulus, when SbSBr crystal is deformed in the direction of c(z)-axis in ferroelectric phase.     

Haldane gap in a S=1 exchange model with long-range interactions

The ground-state properties of the S = 1 Haldane- Shastry model are studied using a modified Lanczos algorithm and diagonalizing exactly small chains. We find evidence that, as for the antiferromagnetic Heisenberg model, the spectrum shows a gap, in contrast to the {ie1-1} case. The correlation functions < S ^z(0)S ^z(m) > decay exponentially for large m. We find that the correlation functions for the Haldane-Shastry model decay faster than for the Heisenberg model. We estimate the infinite system limit for the groundstate energy, value of the gap and correlation functions.