The single-ion anisotropy effects in the mixed-spin ternary-alloy

The effect of single-ion anisotropy on the thermal properties of the ternary-alloy in the form of $A{B}_p{C}_{1?p}$ is investigated on the Bethe lattice (BL) in terms of exact recursion relations. The simulation on the BL consists of placing A atoms (spin-1/2) on the odd shells and randomly placing B (spin-3/2) or C (spin-5/2) atoms with concentrations p and $1?p$, respectively, on the even shells. The phase diagrams are calculated in possible planes spanned by the system parameters: temperature, single-ion anisotropy, concentration and ratio of the bilinear interaction parameters for $z=3$ corresponding to the honeycomb lattice. It is found that the crystal field drives the system to the lowest possible state therefore reducing the temperatures of the critical lines in agreement with the literature.     

The spin-1 Blume-Capel model with random crystal field on the Bethe lattice

The dependence of the phase diagrams on the random crystal field (RCF) is investigated for the spin-1 Blume-Capel (BC) model on the Bethe lattice. The calculations are carried out in terms of the recursion relations for the coordination number z=4 which corresponds to the square lattice. The model presents tricritical points which are observed at lower negative crystal fields and higher temperatures for higher probabilities p and which vanish at lower p’s. The effect of randomness is illustrated for p=0.5 and shown that it changes the phase diagrams drastically from random to non-random systems. The reentrant behavior is also observed for appropriate p values.     

Random walks on the Bethe lattice

We obtain random walk statistics for a nearest-neighbor (Pólya) walk on a Bethe lattice (infinite Cayley tree) of coordination numberz, and show how a random walk problem for a particular inhomogeneous Bethe lattice may be solved exactly. We question the common assertion that the Bethe lattice is an infinite-dimensional system.Supported in part by the U.S. Department of Energy.     

Reentrant phase transitions and multicompensation points in the mixed-spin Ising ferrimagnet on a decorated Bethe lattice

A mixed-spin Ising model on a decorated Bethe lattice is rigorously solved by combining the decoration–iteration transformation with the method of exact recursion relations. Exact results for critical lines, compensation temperatures, total and sublattice magnetizations are obtained from a precise mapping relationship with the corresponding spin-1/2 Ising model on a simple (undecorated) Bethe lattice. The effect of next-nearest-neighbour interaction and single-ion anisotropy on magnetic properties of the ferrimagnetic model is investigated in particular. It is shown that the total magnetization may exhibit multicompensation phenomenon and the critical temperature vs. the single-ion anisotropy dependence basically changes with the coordination number of the underlying Bethe lattice. The possibility of observing reentrant phase transitions is related to a high enough coordination number of the underlying Bethe lattice.     

Magnetic phase diagrams of Fe–Mn–Al alloy on the Bethe lattice

The magnetic behaviors of the Fe–Mn–Al alloy are simulated on the Bethe lattice by using a trimodal random bilinear exchange interaction(J) distribution in the Blume–Capel(BC) model. Ferromagnetic(J 0) or antiferromagnetic(J 0)bonds or dilution of the bonds(J = 0) are assumed between the atoms with some probabilities. It is found that the secondor the first-order phase boundaries separate the ferromagnetic(F), antiferromagnetic(AF), paramagnetic(P), or spin-glass(SG) phases from the possible other one. In addition to the tricritical points, the special points at which the second- and the first-order and the spin-glass phase lines meet are also found. Very rich phase diagrams in agreement with the literature are obtained.     

The hysteresis loops of FM/AFM two-layer Bethe lattice

The distinct hysteresis loops (HLs) of ferromagnetic/antiferromagnetic (FM/AFM) two-layer Bethe lattice with the Ising spins of the top layer having only FM interactions and the bottom ones having only AFM interactions with the interlayer coupling is either FM or AFM type are studied by using a pairwise approach. The sublattice magnetizations are studied by increasing and decreasing the external magnetic field (H) to obtain the HLs. The shapes of the HLs are strongly dependent on the competitions among the system parameters and on the phase configurations. The HLs are formed only when the AFM-type interactions are involved. The small loops of hysteresis are also formed because of the reentrant behavior in the FM region.     

Luminescence characteristics of Ca1−xSrxS:Ce nanophosphors

Luminescence characteristics of Ca_1−xSr_xS:Ce (x = 0, 0.25, 0.50, 1) nanophosphors have been investigated. XRD of all the samples show a single cubic phase of Ca_1−xSr_xS:Ce. TEM micrographs exhibit the rod like structure of the samples with a decrease in diameter with decreasing amount of Ca. The results of TEM were found to be in good agreement with the XRD results. The photoluminescence spectrum comprises of a main peak in the range 480-510 nm with a shoulder in the range 530-565 nm, which may be ascribed to transitions from 5d-4f levels of cerium in the mixed host lattice. The red shift in the emission wavelength with increasing Ca content may be correlated with the change in crystal field of mixed host lattice for different Ca and Sr concentrations. We have also investigated TL response of Ca_1−xSr_x:Ce to ⁶⁰Co-γ rays. All the samples with different Sr and Ca contents show different TL response. TL response for the sample with x = 0.75 shows the simplest TL glow curve with the maximum TL intensity, for which we have calculated the activation energy using glow curve deconvolution functions.     

Specific heat measurements on the site-diluted dipolar ising ferromagnet LiTbpY1−pF4

Specific heat measurements on the diluted dipolar ferromagnet LiTb_pY_1?pF₄ are presented for 0.2?p?1.0. The measured critical temperatures T_c(p) agree with those obtained from previous susceptibility and magnetization measurement. The shape of the specific heat curve is found to be largely influenced by the singlet-singlet separation in the ground state pseudo-doublet, which may explain why below p ≈ 0.325 a λ-anomaly in the specific heat curve can no longer be discerned. For a sample with p = 0.20 we find no evidence of an enhanced nuclear spin ordering, as was suggested by Folkins et al.     

Phase diagrams of the mixed spin-1 and spin-1/2 Ising-Heisenberg model on the diamond-like decorated Bethe lattice

The ground-state and finite-temperature behavior of the mixed spin-1 and spin-1/2 Ising-Heisenberg model on the diamond-like decorated Bethe lattice is investigated within the framework of two rigorous methods: the decoration-iteration transformation and exact recursion relations. The model under consideration describes a hybrid classical-quantum system consisting of the Ising and Heisenberg spins, which interact among themselves either through the Ising or XXZ Heisenberg nearest-neighbor interaction. Both sublattice magnetizations of the Ising and Heisenberg spins are exactly calculated with the aim to examine phase diagrams, thermal variations of the total and sublattice magnetizations. The finite-temperature phase diagrams form continuous (second-order) phase transition lines only, which exhibit a small reentrant region if the diamond-like decorated Bethe lattice with a sufficiently high coordination number is considered.     

The statistical mechanics of spin-1 Ising model with AFM/AFM interactions on a bilayer Bethe lattice

The spin-1 Ising model is studied for the case of antiferromagnetic (AFM)/AFM interactions on the bilayer Bethe lattice by using the pairwise approach for several values of the coordination numbers q=3, 4 and 6 when the layers are linked with the external magnetic fields. The ground state (GS) phase diagrams, thermal variations of the order-parameters and the response functions are studied in detail to obtain the phase diagrams of the model. It was found that the system gives only one Néel temperature, T_N, for q=3. Two T_N's and first-order phase transition temperature, T_t, thus tricritical point, are found and the existence of two T_N's leads to the reentrant behavior when q=4 and 6 for some given system parameters.     

Thermodynamics of a model wih interacting annealed bond impurities on the Bethe lattice

A magnetic model is considered consisting of annealed, mutually repelling ferromagnetic bond impurities in an antiferromagnetic host lattice. Using recurrence relation techniques, the grand-canonical version of this model is solved on the three-coordinated Bethe lattice. A generic phase diagram is obtained containing, apart from the usual ferro- and antiferromagnetic regimes, two distinct incommensurate phases as well as a period-four modulated phase. Evidence is obtained that in one of the two incommensurate phases impurity pairing occurs.     

Dynamic phase transitions in the kinetic spin-1 Blume-Capel model on the Bethe lattice

The stationary states of the kinetic spin-1 Blume-Capel (BC) model on the Bethe lattice are analyzed in detail in terms of recursion relations. The model is described using a Glauber-type stochastic dynamics in the presence of a time-dependent oscillating external magnetic field (h) and crystal field (D) interactions. The dynamic order parameter, the hysteresis loop area and the dynamic correlation are calculated. It is found that the magnetization oscillates around nonzero values at low temperatures (T) for the ferromagnetic (F) phase while it only oscillates around zero values at high temperatures for the paramagnetic (P) phase. There are regions of the phase space where the two solutions coexist. The dynamic phase diagrams are obtained on the (kT/J,h/J) and (kT/J,D/J) planes for the coordination number q=4. In addition to second-order and first-order phase transitions, dynamical tricritical points and triple points are also observed.     

Mixed spin-1/2 and spin-1 Ising model with uniaxial and biaxial single-ion anisotropy on the Bethe lattice

The mixed spin-1/2 and spin-1 Ising model on the Bethe lattice with both uniaxial as well as biaxial single-ion anisotropy terms is solved exactly by combining star-triangle and triangle-star mapping transformations with exact recursion relations. Magnetic properties (magnetization, phase diagrams, and compensation phenomenon) are investigated in detail. Particular attention is focused on the effect of uniaxial and biaxial single-ion anisotropies that basically influence the magnetic behavior of the spin-1 atoms.      

Sandwiched trilayer of Bethe lattices in the form of spin-(1/2,1,1/2)

The sandwiched trilayer of Bethe lattices in the form of the spins with spin-(1/2,1,1/2) Ising model is studied in terms of the recursion relations with either ferromagnetic or antiferromagnetic type bilinear interactions between the nearest-neighbor (NN) spins. The ground-state (GS) phase diagrams are obtained and it was found that the model presents six different GS phase configurations. In order to obtain the phase diagrams, the thermal variations of the order-parameter, spin-spin correlation functions and free energy are analyzed and different topological phase diagrams are obtained. It was found that the system exhibits different critical behaviors such as, second- and first-order phase transitions, tricritical and bicritical points for the values of the coordination numbers q=3,4 and 6.     

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.     

Trilayer Bethe lattices in the form of spin-(1/2,3/2,1/2)

The critical behaviors of the trilayer Bethe lattice in the form of spin-(1/2,3/2,1/2) with the exterior two layers consisting of spin-1/2 and the interior one having only spin-3/2 Ising spins are studied in terms of the recursion relations with either ferromagnetic or antiferromagnetic bilinear exchange interactions between the nearest-neighbor spins. The ground-state phase diagrams are calculated and it is found that the model presents six different ground state phase configurations. The thermal variations of the order-parameter and free energy are investigated, therefore, topologically different phase diagrams of the model are obtained. It is found that the model exhibits second- and first-order phase transitions, tricritical and bicritical points for the values of the coordination numbers q=3, 4 and 6 and, the reentrant behavior for q=4 and 6, respectively.     

Composition stability limits for the rocksalt-structure phase (Pb1−ySny)1−xTex from lattice parameter measurements

The lattice parameters at 25°C have been measured on powders with a precision of one part in 3(10⁴) for (Pb_1−ySn_y)_1−xTe_x for y = 1·0, 0·90, 0·80,and0·00 and values of x both without and, for the first threey-values, within the composition stability range. For the first threey-values, the composition stability limits for samples metal-saturated at 400°C is 0·5000 ± 0·0002, while those for samples Te-saturated at 356°C is x = 0·5070fory = 1·0, x = 0·5056fory = 0·90,andx = 0·5038fory = 0·80. The fine powders pick up oxygen quickly in air, which reacts with the Pb and Sn upon heating to deplete the telluride solid-solution of metal and consequently reduce its parameter by 2–3(10⁻³)Å. The metals are substantially all returned to the telluride phase upon H₂-reduction at 500–600°C. The present results for SnTe are used to extend the sources of data used in an analysis of SnTe. This analysis shows that the ratio of the number of valence band holes per Sn-vacancy, c, to the 77°K Hall factor, r, is 3·2 ± 0·3 over the entire range of 3(10¹⁹) to 1·8(10²¹) cm⁻³ in the apparent hole concentration. The results for the solid solutions are extrapolated to give the atomic fraction of Te in the 356°C, Te-saturated solid solution for y < 0·8. Comparison with the electrical measurements of others gives c/r equal to about unity for y = 0·27and0·13.     

Analyticity of the density of states in the anderson model on the Bethe lattice

Let H=1/2+V on l²(B), whereB is the Bethe lattice andV(x),x B, are i.i.d.r.v.'s with common probability distribution. It is shown that for distributions sufficiently close to the Cauchy distribution, the density of states(E) is analytic in a strip about the real axis.