Incommensurate Phases of the MgSiF6·6H2O Crystals: EPR and Group-Theoretical Studies

The group-theoretical study of the structural phase transition to incommensurate state of MgSiF₆·6H₂O crystals, revealed by the electron paramagnetic resonance (EPR) method, as well as analysis of the EPR results, are presented. The consideration of temperature dependences of Mn²⁺ admixture ion EPR spectrum symmetry and parameters leads to the conclusion that at T _i1 = 370 ± 0.3 K they undergo second-order structural phase transition to incommensurately modulated state, the order parameter of this transition may be the angle of [Mg(H₂O)₆]²⁺ octahedra rotation around crystal C ₃ axis. At temperature decreasing below T _i1 the gradual transformation of plane-wave modulation of lattice displacements into soliton mode occurs, which is interrupted by the first-order phase transition at T _i2 = 343 ± 0.3 K accompanied by abrupt decrease in modulation amplitude. At T _c = 298.5 ± 0.3 K the first-order improper ferroelastic phase transition into monoclinic phase occurs. The group-theoretical analysis of the phase transition at T _i1 in the investigated crystals, carried out for the first time, has shown that the existence of the incommensurately modulated phase is conditioned by the fundamental reasons (presence of Lifshitz invariant). The conclusions of this analysis on the nature of order parameter, the structural motifs of incommensurate phase and the possible character of temperature evolution of the structure are in agreement with the EPR investigation data.     

On the bethe approximation for the random bond Ising model

A random bond Ising model is considered in terms of the pair approximation, which is equivalent to the Bethe approximation, of the cluster variation method. On taking the configurational average over the random distribution of bonds ±J, we take into account the nearest neighbor correlations between effective fields and bonds. We investigate their effects to the phase transition temperature from the paramagnetic phase to the ferro- (or antiferro-) magnetic phase and to the spin glass phase for the Ising model on the square lattice. It turns out that the correlation effects act favorably to the spin glass phase and bend upward the line of transition temperature from the paramagnetic phase to the spin glass phase as the concentration being apart from 0.5. In the appendix, we derive the expression of free energy in the weak interaction limit.     

Longitudinal response of the spin system of a metal to modulated EPR saturation at arbitrary modulation frequency and detuning of the saturating field

The theory of the longitudinal (with respect to an external magnetic field) response of a combined spin system of localized paramagnetic centers (s subsystem) and free charge carriers (e subsystem) of a solid semiconductor to modulated saturation of EPR is developed. In contrast to relevant studies made earlier, the general case is considered of an arbitrary modulation frequency and arbitrary detuning of the saturating microwave field with respect to the central EPR frequency. A theoretical approach is used in which normal modes are considered in analyzing coupled oscillations of the spin magnetizations of the s and e subsystems. It is shown that, in the case of relaxation coupling between the subsystems, the longitudinal response recorded at the modulation frequency can be represented as the sum of the responses of the normal modes, each of which is described by a universal resonance lineshape that is different, in general, from the Lorentzian lineshape characteristic of EPR signals. In the extreme cases of weak and strong coupling, simple analytical formulas are derived. The results presented form a theoretical basis for applying the method of modulated longitudinal response for measuring very short longitudinal spin relaxation times in semiconductors with paramagnetic impurities. As an example, experimental data are presented for activated carbon containing stable free radicals.     

Phase diagram of the three states Potts model with next nearest neighbour interactions on the Bethe lattice

We have found an exact phase diagram of the Potts model with competing nearest neighbor and next nearest neighbor interactions on the Bethe lattice of order two. The diagram consists of five phases: ferromagnetic, paramagnetic, modulated, antiphase and paramodulated, all meeting at the multicritical point . We report on a new phase which we denote as paramodulated, found at low temperatures and characterized by zero average magnetization lying inside the modulated phase. Such a phase, inherent in the Potts model has no analogues in the Ising setting.     

Investigation of magnetocaloric effect in La0.45Pr0.25Ca0.3MnO3 by magnetic,differential scanning calorimetry and thermal analysis

We investigated magnetocaloric effect in La_0.45Pr_0.25Ca_0.3MnO₃ by direct methods (changes in temperature and latent heat) and indirect method (magnetization isotherms). This compound undergoes a first-order paramagnetic to ferromagnetic transition with T_C=200 K upon cooling. The paramagnetic phase becomes unstable and it transforms into a ferromagnetic phase under the application of magnetic field, which results in a field-induced metamagnetic transition (FIMMT). The FIMMT is accompanied by release of latent heat and temperature of the sample as evidenced from differential scanning calorimetry and thermal analysis experiments. A large magnetic entropy change of ΔS_m=−7.2 J kg⁻¹ K⁻¹ at T=212.5 K and refrigeration capacity of 228 J kg⁻¹ are found for a field change of ΔH=5 T. It is suggested that destruction of magnetic polarons and growth of ferromagnetic phase accompanied by a lattice volume change with increasing magnetic field is responsible for the large magnetocaloric effect in this compound.     

Modulated phases and the mean-field theory of magnetism with competing interactions

The mean-field theory of an Ising magnet with infinitely weak, infinitely long-range potentials of arbitrary sign is presented in terms of a variational principle for the magnetization. Previous studies of the theory have revealed paramagnetic, ferromagnetic, and modulated phases. For a particular choice of potential, which is an obvious continuous version of the between-plane ANNNI model interaction, exact solutions of the stationary condition implied by the variational principle are obtained. This leads us to formulate a trial magnetization to well describe the modulated phase in general. To illustrate the utility of the trial magnetization, both analytic and numerical calculations are performed, which determine the wavenumber in certain portions of the modulated phase for the above-mentioned potential.     

Magnetic properties of nanoparticles of cobalt chromite

Magnetic properties of cobalt chromite nanoparticles of size 8-12 nm synthesized through conventional coprecipitation route are reported. Magnetization versus temperature measurement plot reveals a transition from paramagnetic to superparamagnetic (SPM) phase in contrast with the transition from paramagnetic to long-range ferrimagnetic phase at Curie temperature, T_c, reported in bulk. The blocking temperature, T_b, of SPM phase is found to be 50-60 K. On cooling in the presence of 10 kOe field these nanoparticles show an enhancement in coercivity and shifting of loop at 10 K, which is absent at 50 K. While the later observation supports the blocking temperature of the SPM phase, the former one is attributed to a disordered spin configuration at the surfaces and the distribution of nanoparticle sizes.     

Temperature and concentration dependences of the electronic etructure of copper oxides in the generalized tight binding method

The electronic structure of p-type doped HTSC cuprates is calculated by explicitly taking into account strong electron correlations. The smooth evolution of the electronic structure from undoped antiferro-magnetic to optimally and heavily doped paramagnetic compositions is traced. For a low doping level, in-gap impurity-type states are obtained, at which the Fermi level is pinned in the low-doping region. These states are separated by a pseudogap from the valence band. The Fermi surfaces calculated for the paramagnetic phase for various concentrations of holes are in good agreement with the results of ARPES experiments and indicate a gradual change in the Fermi surface from the hole type to the electron type.     

Resonance enhancement of electron-phonon interaction

A superconducting state near the phase transition curve from paramagnetic phase to superconducting phase for perovskites La_{2 ? x} Sr _x CuO₄ and YBa₂Cu₃O₆ is considered. Expressions for effective parameters of electron-spin-phonon interaction are obtained. It is shown that the critical temperature of the phase transition from paramagnetic phase to superconducting phase T _c is determined by the enhancement of electron-phonon interaction by spin fluctuations of exchange type.     

Dynamische Spinsuszeptibilität für die paramagnetische Phase im Modell schmaler Energiebänder

A calculation of the reduced spin susceptibility χ _zz (k, Ω) of the paramagnetic phase of a system of interacting electrons in a narrows band is presented. The treatment is based on a linear response technique for the perturbed system using the Hubbard decoupling scheme within a Greens function method. The result has the property of reducing to a modified random phase result in the weak-interaction limit and is intended to be a valid interpolation formula for all values ofI/Δ. Also presented are conditions for the instability of the paramagnetic phase against the ferromagnetic and the antiferromagnetic state.     

Magnetic, electrical, and optical properties of electron-doped Ca1 − x LaxMnO3 − δ(x ≤ 0.12) single crystals

The magnetic, electrical, and optical properties of Ca_{1 ? x} La_xMnO_{3 ? δ}(x ≤ 0.12) manganite single crystals have been studied. The state with a spatially inhomogeneous electron distribution has been found. Interrelations between the electric and magnetic subsystems are analyzed. The obtained magnetic data show evidence for the formation of a G-type antiferromagnetic (G-AFM) phase with a spin-canted structure in the crystal with x = 0.05, for which the Curie and Néel temperatures are T _C = T _N(G) = 115 K. On cooling from the paramagnetic state, the crystals with x = 0.10 and 0.12 exhibit transitions from the paramagnetic to a C-type antiferromagnetic (C-AFM) phase in a part of the volume at T _N(C) = 150 and 200 K, and from the paramagnetic to the G-type antiferromagnetic (G-AFM) phase in the remaining volume at T _N(G) = 110 and 108 K, respectively. The onset of the C-type magnetic phase nucleation in crystals is observed at lower dopant (La) concentrations than in polycrystalline samples, which is explained by the deviation of single crystals from the stoichiometry with respect to oxygen. The magnetic phase transitions are manifested by anomalies in the electric resistance and magnetoresistance of doped crystals. An analysis of the electrical and optical properties of the samples shows evidence of (i) the formation of a charge energy gap in the C-AFM phase with retained paramagnetic metallic regions and (ii) the presence of ferromagnetic “metallic” droplets in the insulating G-AFM phase. The multiphase state of Ca_{1 ? x} La_xMnO_{3 ? δ} manganite single crystals featuring the coexistence of two magnetic phases, the regions with orbital/charge ordering, and the FM “metallic” droplets is related to a competition of exchange interactions by the superexchange and double exchange mechanisms.     

Electronic structure and spin fluctuations in the helical ferromagnet MnSi

The influence of spin fluctuations on the magnetic properties of the ferromagnetic helimagnet MnSi has been studied in the Hubbard model taking into account the antisymmetric relativistic Dzyaloshinskii–Moriya interaction for band electrons. The obtained equations of the magnetic state indicate the correlation between the fine structure of the density of electronic states and the magnetization and coefficient of mode–mode coupling. It has been shown that the position of the Fermi energy in the immediate proximity on the point of the local minimum of the density of electronic states leads to large zero spin fluctuations at low magnetization of the helimagnet. When approaching from down the Néel point (approximately, at 0.9T_N), the zero fluctuation disappear, and the temperature rise of thermal spin fluctuation is accompanied by the change in the sign of the coefficient of mode–mode coupling. A magnetic field perpendicular to the helicoids plane brings about the formation and subsequent “collapse” of the helimagnetic cone. However, the condition of the change in the sign of the coefficient of mode–mode coupling divides the MnSi phase diagram into two parts, one of which corresponds to the ferromagnetic state induced by the field, and the other corresponding to the paramagnetic state. In this case, the h–T diagram has a specific region, inside which the paramagnetic and the ferromagnetic state are instable. The boundaries of the region agree with the experimental data on the boundaries of the anomalous phase (a phase). It has been found that the results of calculations of the temperature dependence of the magnetic susceptibility agree with the experimental data.     

Spin-glass and spin-crystal phase transition of a regular Ising model on the Cayley tree

A regular Ising model with nearest-neighbour interaction of +J and -J on a Cayley tree is reported to show a phase transition from the paramagnetic phase to the spin-glass and spin-crystal phase in a uniform external field below a critical value h_c.     

Effects of a magnetic field on a modulated phase

The effects of a magnetic field on a modulated phase are studied. A modulated phase is found to have two critical fields H₁ and H₂. For a large enough magnetic field, H₁ and H₂ can be approximated by a linear law. As a result, the minimum magnetic field needed to destroy a modulated phase is a constant. The minimum magnetic field also greatly depends on the order of a commensurate phase. A very high order commensurate phase and an incommensurate phase cannot survive a magnetic field. The behaviour of a magnetoelastic chain in a magnetic field can be described by a harmless devil's staircase. The inverse temperature is found to play a role similar to that of a special magnetic field. The deeper physics underlying these new phenomena is the breaking of the left-right symmetry of a phase diagram. As a result a controllable path to a modulated phase is found.     

An asymmetric single-channel color image encryption based on Hartley transform and gyrator transform

A novel asymmetric single-channel color image encryption using Hartley transform and gyrator transform is proposed. A color image is segregated into R, G, and B channels and then each channel is independently Hartley transformed. The three transformed channels are multiplied and then phase- and amplitude truncated to obtain first encrypted image and first decryption key. The encoded image is modulated with a conjugate of random phase mask. The modulated image is gyrator transformed and then phase- and amplitude truncated to get second encrypted image and second decryption key. The asymmetric (decryption) keys, random phase mask, and transformation angle of gyrator transform serve as main keys. The optoelectronic encryption and decryption systems are suggested. Numerical simulation results have been demonstrated to verify the performance and security of the proposed security system.     

Magnetic circular dichroism in the luminescence of F-centres in KI

Magnetic field induced circular polarization of the F-centre emission has been measured in KI at 1.9 K in fields up to 80 kG. Both the diamagnetic (field dependent) and the paramagnetic contributions (dependent upon the spin polarization of the relaxed excited state) have been detected. The spin polarization is produced by a pump beam modulated between left and right circular polarization. The expected behaviour of the spin polarization as a function of the frequency of the modulation has been observed. Knowledge of these small dichroic effects gives further insights into the nature of the relaxed excited state.     

The effect of competition between the frequency of the field and the frequency of the spin flipping on the kinetics of Ising metamagnet

We consider the effect of a variable representing the competition between the frequency of the field and the frequency of the spin flipping (Ω) on the dynamics of the metamagnetic Ising model in a cubic lattice under the presence of a time varying (oscillating) external magnetic field. The system is modelled with a formalism of master equation at a mean-field level. The time averaged staggered magnetization (Ms) acts as the order parameter and divides temperature field plane into three regions: anti-ferromagnetic, paramagnetic and coexistence of anti-ferromagnetic and paramagnetic phases. It is observed that the topology of the dynamical phase diagram depends strongly on Ω as well as the ratio between interlayer and intralayer couplings.     

Exact Solution of a Generalized ANNNI Model on a Cayley Tree

We consider the Ising model on a rooted Cayley tree of order two with nearest neighbor interactions and competing next nearest neighbor interactions restricted to spins belonging to the same branch of the tree. This model was studied by Vannimenus who found a new modulated phase, in addition to the paramagnetic, ferromagnetic, antiferromagnetic phases and a (+ + - -) periodic phase. Vannimenus’s results are based on an analysis of the recurrence equations (relating the partition function of an n ? generation tree to the partition function of its subsystems containing (n ?1) generations) and most results are obtained numerically. In this paper we analytically study the recurrence equations and obtain some exact results: critical temperatures and curves, number of phases, partition function.     

Reentrant phases in the ± J spin glass

We consider an enlarged phase space of the ±J spin glass which includes the dilute Ising model and the frustrated system. The three orthogonal axes in this space are: (i) The fraction of ferro- to antiferro-magnetic bonds, p; (ii) the ratio of the strengths of the antiferro- to ferromagnetic interacions, q; and (iii) the temperature, T. Within this phase space we observe extended regions of the low-temperature spin-glass phase which is characterized by a unique distribution of the local-order parameter. We observe reentrant phase transitions: for fixed p and q with varying T the distribution of the local order parameter shows paramagnetic, ferromagnetic and then spin-glass phases; for fixed p and T and varying q the distribution shows ferromagnetic to paramagnetic and then spin-glass phases.     

Ultrasonic study of dysprosium in a magnetic field

The ultrasonic attenuation of longitudinal waves propagating along the c axis of single crystal dyprosium is reported, as a function of the applied basal plane field in the paramagnetic region, and as a function of the temperature, at constant applied basal plane field, in the spin-spiral region. In the paramagnetic region, anomalous attenuation behavior is explained on the basis of competing spin-polarization and spin-fluctuation effects. Two anomalous maxima in the temperature dependence of the attenuation were observed: one near T_N is attributed to spin fluctuations associated with short range ferromagnetic ordering; another one at 130 K is attributed to a magnetic phase transition from a fanstructure phase, intermediate between the spin-spiral and ferromagnetically ordered phase