The Bethe lattice treatment of sound attenuation for a spin- 3/2 Ising model

The sound attenuation phenomena is investigated for a spin- 3/2 Ising model on the Bethe lattice in terms of the recursion relations by using the Onsager theory of irreversible thermodynamics. The dependencies of sound attenuation on the temperature (T$T$), frequency (w$w$), Onsager coefficient (γ$\gamma$) and external magnetic field (H$H$) near the second-order (_Tc)$\left(T_c\right)$ and first-order (_Tt)$\left(T_t\right)$ phase transition temperatures are examined for given coordination numbers q$q$ on the Bethe lattice. It is assumed that the sound wave couples to the order-parameter fluctuations which decay mainly via the order-parameter relaxation process, thus two relaxation times are obtained and which are used to obtain an expression for the sound attenuation coefficient (α)$\left(\alpha \right)$. Our investigations revealed that only one peak is obtained near _Tt$T_t$ and three peaks are found near _Tc$T_c$ when the Onsager coefficient is varied at a given constant frequency for q=3$q=3$. Fixing the Onsager coefficient and varying the frequency always leads to two peaks for q=3,4$q=3,4$ and 6 near _Tc$T_c$. The sound attenuation peaks are observed near _Tt$T_t$ at lower values of external magnetic field, but as it increases the sound attenuation peaks decrease and eventually disappear.     

The influence of 3d-impurities on magnetic and transport properties of CoSiB metallic glasses

Temperature dependencies of magnetic susceptibility and electric resistivity of Co-based metallic glasses (MGs) of the general composition _Co(72-x)Mex(Si,B₎₂₈${\mathrm{Co}}_{(72-x)}{\mathrm{Me}}_x(\mathrm{Si},\mathrm{B}{)}_{28}$(Me=Fe,Cr,Si:B=18:10)$(\mathrm{Me}=\mathrm{Fe},\mathrm{Cr},\mathrm{Si}:\mathrm{B}=18:10)$ have been studied up to 950 K. The studied MGs were found to be ferromagnets at the room temperature and their Curie point _TC$T_{\mathrm{C}}$ ranges within 260–560 K depending on the dopant contents. At the temperatures higher than _TC$T_{\mathrm{C}}$, a wide paramagnetic region exists. The regularities of magnetic moment variation upon Cr doping evidence a formation of antiferromagnetic clusters, which determine the anomalous behavior of resistivity.     

On the propensity of magnetism in 3d transition-metal-MgCNi3 alloys

The effects of disorder and incipient magnetism in MgC(_Ni1-xTx)3$\mathrm{MgC}({\mathrm{Ni}}_{1-x}{\mathrm{T}}_x{)}_3$ (T≡Fe$\mathrm{T}\equiv \mathrm{Fe}$, Co or Cu) alloys are studied using coherent-potential approximation and Ginzburg–Landau coefficients. The first-principles, local-density-functional-based calculations for substitutionally disordered Fe and Co impurities in the Ni sub-lattice of MgCNi₃, in low concentrations, show that incipient magnetism resides in these materials. The overestimation of the calculated magnetic properties points to the limitations of the local-density approximation. However, using a phenomenological approach based on Ginzburg–Landau coefficients and the fixed-spin moment method, we show that MgC(_Ni1-xTx)3$\mathrm{MgC}({\mathrm{Ni}}_{1-x}{\mathrm{T}}_x{)}_3$ alloys remain paramagnetic. At expanded volumes, we also find the possibility of a ferromagnetic state for MgC(_{Ni0.95Fe0.05)3}$\mathrm{MgC}({\mathrm{Ni}}_{0.95}{\mathrm{Fe}}_{0.05}{)}_3$ and MgC(_{Ni0.90Co0.10)3}$\mathrm{MgC}({\mathrm{Ni}}_{0.90}{\mathrm{Co}}_{0.10}{)}_3$ alloys.     

On the theory of the dynamical properties of nematics

The Leslie–Ericksen coefficients of a thermotropic nematic are determined by using an approximate solution of the Fokker–Planck equation for the one-particle distribution function over orientations of the nematic molecules. The results show that the well-known Doi–Edwards theory of the dynamical properties of nematics leads to a qualitatively wrong result for the Leslie angle. The “isotropic medium - nematic” (I–N$I–N$) transition induced by the shear flow is considered. When the temperature decreases, the I–N$I–N$ transition in the shear flowing system takes place at the temperature _T1$T_1$ higher than the temperature _Tc$T_c$ of the equilibrium transition in the motionless system. The interface boundary in this case is parallel to the plane formed by the flow velocity and its gradient. When the shear flowing nematic phase is heated, the N–I$N–I$ transition occurs at another temperature _T2$T_2$, and the following inequalities _T1>_T2>_Tc$T_1>T_2>T_c$ hold. In this case the boundary between the isotropic and nematic phases is perpendicular to the flow velocity. Thus, unlike the equilibrium phase transition, a temperature hysteresis of the phase transition is expected.     

Terahertz spectroscopy of multiferroic EuFe3(BO3)4

The terahertz spectra of a rare-earth iron borate with the huntite structure are obtained for the first time. We study the low-temperature (4.0–90 K) α-polarized transmittance spectra of the EuFe₃(BO₃)₄ single crystal in the region 0.9–6.0 THz. Pronounced shifts of phonon frequencies and appearance of new phonon modes at the temperature _TS=58 K$T_S=58\text{K}$ of the R32→P₃₁21$R32\to P{3}_{1}21$ structural phase transition are observed. Additional shifts of phonon frequencies occur at the temperature _TN=34 K$T_N=34\text{K}$ of the magnetic ordering of the Fe subsystem, thus evidencing the spin–phonon coupling in this multiferroic material.     

Transitions involving conical magnetic phases in a model with bilinear and biquadratic interactions

In a previous work a model was proposed for the phase transitions of crystals with localized magnetic moments which at low temperature have a “conical” arrangement that at higher T transforms into a more symmetrical structure (depending on the compound) before becoming totally disordered. The model assumes bilinear and biquadratic interactions between magnetic moments up to the fifth neighbours, and for any given T the structure with the least free energy is obtained by a mean-field approximation (MFA). The interaction constants are derived from ab initio   energy calculations. In this work we improve upon that model modifying the MFA in such a way that a continuous (instead of discontinuous) spectrum of excited states is available to the system. In the previous work, which dealt with _LaMn2Ge2${\mathrm{LaMn}}_2{\mathrm{Ge}}_2$ and _LaMn2Si2${\mathrm{LaMn}}_2{\mathrm{Si}}_2$, we found that transitions to different structures can be obtained for increasing T, in good qualitative agreement with experiment. The critical temperatures, however, were exaggeratedly high. With the new MFA we obtain essentially the same behaviour concerning the phase transitions, and critical temperatures much closer to the experimental ones.     

Surface magnetic phase transitions in films

Using a simple Landau model, we discuss the different possibilities of generating magnetic effects at a second-order transition for films. Varying the sample size d$d$ and/or surface coupling γ$\gamma$ one can decrease or increase substantially the surface critical temperature _Ts$T_{\mathrm{s}}$ and the saturation magnetization _Ms$M_{\mathrm{s}}$. In the case of γ>0$\gamma >0$, _Ms$M_{\mathrm{s}}$ and _Ts$T_{\mathrm{s}}$ decrease from the bulk values as the film thickness is reduced. These theoretical results are in nice agreement with the experimental data on superconducting _MgB2${\mathrm{MgB}}_2$ thin films. By contrast, for γ<0$\gamma <0$, an enhancement of both quantities is expected. This extraordinary transition has rarely been observed experimentally and, usually, the situation is far from being clear. We analyze a new experiment on _NiFe2O4${\mathrm{NiFe}}_2{\mathrm{O}}_4$ ultra-thin films, where a very strong enhancement of the saturation magnetization is observed.     

Magnetic,dielectric and magnetoelectric properties of new family of orthorhombic multiferroic Eu1−xYxMNO3 manganites

Multiferroic ground states with a spatially modulated antiferromagnetic structure and electric polarization have been revealed in Eu_1−xY_xMnO₃ (0.2?x?0.5$0.2?x?0.5$) single crystals. While the slightly substituted (x?0.1$x?0.1$) compounds exhibited a transition from the incommensurate (IC) to the canted antiferromagnetic (CAF) state at _TCA<_TN$T_{\mathrm{CA}}<T_{\mathrm{N}}$, the transitions from IC to commensurate ferroelectric (C/FE) phase were observed at _Tlock<_TN$T_{\mathrm{lock}}<T_{\mathrm{N}}$ for x>0.2$x>0.2$. Various phase transitions were observed in the magnetic fields up to 250 kOe along a, b, c axes by magnetization, magnetostriction and electric polarization measurements which show an existence of a spontaneous electric polarization below T_lock.     

Berezinskii–Kosterlitz–Thouless transition close to the percolation threshold

We use Monte Carlo to investigate the Berezinskii–Kosterlitz–Thouless transition close to the site percolation threshold in a square lattice. Several thermodynamic quantities are calculated for lattice sizes L×L$L\times L$, from 16<L<640$16<L<640$. Our results are consistent with an infinite order transition for any value of the concentration of magnetic sites. We found that close to the critical percolation concentration, _pc$p_c$ (0.592746), the Berezinskii–Kosterlitz–Thouless transition temperature goes to zero as _TBKT∝(p−_pc)^0.908$T_{\mathit{BKT}}\propto {(p-p_c)}^{0.908}$ and the specific heat behaves as _Tsh∝p^1.133$T_{sh}\propto p^{1.133}$.     

Phase diagrams of a spin-1 Ising superlattice

The three-dimensional spin-1 Ising superlattice consisting of two different ferromagnetic materials with two different crystal fields _Δ1${\Delta }_1$ and _Δ2${\Delta }_2$ is considered in the mean field approximation. The phase diagrams are considered in the (t,_d2$t,d_2$) plane for different ranges of variation of _d1(t=T/J,_d1=_Δ1/J$d_1(t=T/J,d_1={\Delta }_1/J$, _d2=_Δ2/J$d_2={\Delta }_2/J$ are the reduced temperature and crystal fields respectively). The phase diagrams exhibit a variety of multicritical points and reentrant and double reentrant behaviours. They are found to depend qualitatively and/or quantitatively on the thicknesses of the materials in a supercell. This has direct consequences on the nature of the magnetic states of superlattices with different thicknesses.     

Spreading of periodic diseases and synchronization phenomena on networks

In this paper, we investigate numerically the Susceptible–Infected–Recovered–Susceptible (SIRS) epidemic model on an exponential network generated by a preferential attachment procedure. The discrete SIRS model considers two main parameters: the duration _τ0${\tau }_0$ of the complete infection–recovery cycle and the duration _τI${\tau }_I$ of infection. A permanent source of infection _I0$I_0$ has also been introduced in order to avoid the vanishing of the disease in the SIRS model. The fraction of infected agents is found to oscillate with a period T≥_τ0$T\ge {\tau }_0$. Simulations reveal that the average fraction of infected agents depends on _I0$I_0$ and _τI/_τ0${\tau }_I/{\tau }_0$. A maximum of synchronization of infected agents, i.e. a maximum amplitude of periodic spreading oscillations, is found to occur when the ratio _τI/_τ0${\tau }_I/{\tau }_0$ is slightly smaller than 1/2$1/2$. The model is in agreement with the general observation that an outbreak corresponds to high _τI/_τ0${\tau }_I/{\tau }_0$ values.     

Constant angle surfaces in product spaces

We classify all the surfaces in M²(_c1)×M²(_c2)$M^2\left(c_1\right)\times M^2\left(c_2\right)$ for which the tangent space _TpM²$T_p{M}^2$ makes constant angles with _Tp(M²(_c1)×{_p2})$T_p(M^2\left(c_1\right)\times \left\{p_2\right\})$ (or equivalently with _Tp({_p1}×M²(_c2))$T_p(\left\{p_1\right\}\times M^2\left(c_2\right))$ for every point p=(_p1,_p2)$p=(p_1,p_2)$ of M²$M^2$. Here M²(_c1)$M^2\left(c_1\right)$ and M²(_c2)$M^2\left(c_2\right)$ are 2$2$-dimensional space forms, not both flat. As a corollary we give a classification of all the totally geodesic surfaces in M²(_c1)×M²(_c2)$M^2\left(c_1\right)\times M^2\left(c_2\right)$.