Compensation temperatures and magnetic susceptibility of a mixed ferro-ferrimagnetic ternary alloy

We study the compensation behaviour and magnetic susceptibility of a mixed ferro-ferrimagnetic ternary alloy of the type ABpC1−p on a cubic lattice by the use of Monte Carlo simulations. We consider that the A and X (X=B or C) ions are alternately connected and have different Ising spins SA=3/2, SB=2, and SC=5/2, respectively. In particular, we find that the magnetic susceptibility may exhibit an outstanding behaviour in a vicinity of the critical and compensation temperatures. The relation of the studied model to ternary Prussian blue analogs is also discussed.     

Mixed spin-1 and spin-3/2 Ising system with two alternative layers of a honeycomb lattice within the effective-field theory

An effective-field theory with correlations is developed for a mixed spin-1 and spin-3/2 Ising system with two alternative layers of a honeycomb lattice. Spin-1 atoms and spin-3/2 atoms are distributed in alternative layers of a honeycomb lattice. We consider that the nearest-neighbor spins of each layer are coupled ferromagnetically and the interaction between the vertically aligned spins and adjacent spins are coupled either ferromagnetically or antiferromagnetically depending on the sign of the bilinear exchange interactions. We investigate the temperature dependence of the total magnetization to find the compensation points and to determine the type of compensation behavior. We present the phase diagrams in different planes for h=0, and the phase diagrams contain the paramagnetic, nonmagnetic and ferrimagnetic phases. The system also presents a tricritical behavior besides multicritical point (A), isolated critical point (C) and double critical end point (B) depending on the interaction parameters.     

Study of a random Heisenberg ferromagnet by the Molecular CPA method

The spin wave Green function of a random dilute Heisenberg ferromagnet is calculated by the Molecular CPA method for the bond model of the f.c.c. lattice. It is found that the ferromagnetic spin order atT=0 becomes unstable, if the concentration of the non-zero bondC _A decreases below the critical valueC _A ⁰ =0.1702, which is some-what larger than the percolation concentrationC _A ^P =0.125. In the regionC _A <C _A ⁰ , aδ function spectrum appears atE=0 corresponding to the free rotations of the total spins of the finite clusters. The peculiar structure of the spin wave state density near the critical concentration is analysed in detail and a speculation is made for the topological structure of the spin clusters.     

Critical parameters near the ferromagnetic-paramagnetic phase transition in La0.7A0.3(Mn1−xbx)O3 (A=Sr; B=Ti and Al; x=0.0 and 0.05) compounds

The critical parameters provide important information concerning the interaction mechanisms near the paramagnetic-to-ferromagnetic transition. In this paper, we present a thorough study for the critical behavior of La_0.7A_0.3(Mn_1−xB_x)O₃ (A=Sr; B=Ti and Al; x=0.0 and 0.05) polycrystalline samples near ferromagnetic-paramagnetic phase transition temperature by analyzing isothermal magnetization data. We have analyzed our dc-magnetization data near the transition temperature with the help of the modified Arrot plot, Kouvel-Fisher method. We have determined the critical temperature T_C and the critical parameters β, γ and δ. With the values of T_C, β and γ, we plot M×(1−T/T_C)^−β vs. H×(1−T/T_C)^−γ. All the data collapse on one of the two curves. This suggests that the data below and above T_C obey scaling, following a single equation of state. Critical parameters for x=0 and x_Ti=0.05 samples are between those predicted for a 3D-Heisenberg model and mean-field theory and for x_Al=0.05 samples the values obtained for the critical parameters are close to those predicted by the mean-field theory.     

Magnetic properties of GdCo12B6 compound under high pressures

The effects of hydrostatic pressure up to 10 kbar on Curie temperature T_C, compensation temperature T_COMP and spontaneous magnetization M_S of ferrimagnetic GdCo₁₂B₆ compound have been studied. Two antiferromagnetically coupled sublattices that are carrying magnetization of typically 0.42 μ_B/Co atom and 7 μ_B/Gd cancel out at compensation temperature at about 50 K and magnetic ordering temperature T_C=163±2 K. The volume dependence of intrinsic magnetic properties of the GdCo₁₂B₆ compound has been determined by studying it under hydrostatic pressure. The observed increase of M_S with pressure (dM_S/dp=+0.005 μ_B kbar^?1 at 5 K) is attributed predominantly to the pressure induced decrease of Co magnetic moments. The crucial role of Co in this behavior is confirmed by the change of sign of the pressure slope at temperatures above T_COMP and by the fact that the estimated decrease of m_Co is also quite comparable with pressure induced decrease of M_S in YCo₁₂B₆ (dM_S/dp=?0.007 μ_B kbar^?1). The decrease of m_Co is also responsible for the increase of T_COMP with pressure (dT_COMP/dp=+0.06 K kbar^?1). The decrease of T_C with pressure (dT_C/dp=?0.55 K kbar^?1) is comparable to the decrease observed on RCo₁₂B₆ compounds with non-magnetic R and can be attributed to the volume dependence of Co–Co exchange interactions. The remarkable role of the hybridization as a consequence of small distances between Co and B atoms could be a background of this rather unexpected volume stability of magnetic properties.     

Elastic constants of solids and fluids with initial pressure via a unified approach based on equations-of-state

The second and third-order Brugger elastic constants are obtained for liquids and ideal gases having an initial hydrostatic pressure p₁. For liquids the second-order elastic constants are C₁₁ = A + p₁, C₁₂ = A − p₁, and the third-order constants are C₁₁₁ = −(B + 5A + 3p₁), C₁₁₂ = −(B + A − p₁), and C₁₂₃ = A − B − p₁, where A and B are the Beyer expansion coefficients in the liquid equation of state. For ideal gases the second-order constants are C₁₁ = p₁γ + p₁, C₁₂ = p₁γ − p₁, and the third-order constants are C₁₁₁ = −p₁(γ² + 4γ + 3), C₁₁₂ = −p₁(γ² − 1), and C₁₂₃ = −p₁ (γ² − 2γ + 1), where γ is the ratio of specific heats. The inequality of C₁₁ and C₁₂ results in a nonzero shear constant C₄₄ = (1/2)(C₁₁ − C₁₂) = p₁ for both liquids and gases. For water at standard temperature and pressure the ratio of terms p₁/A contributing to the second-order constants is approximately 4.3 × 10⁻⁵. For atmospheric gases the ratio of corresponding terms is approximately 0.7. Analytical expressions that include initial stresses are derived for the material ‘nonlinearity parameters’ associated with harmonic generation and acoustoelasticity for fluids and solids of arbitrary crystal symmetry. The expressions are used to validate the relationships for the elastic constants of fluids.     

X-ray diffraction of the smectic phases of N-(p-n-heptyloxybenzylidene)-p′-n-pentylaniline

Using X-ray diffraction the various smectic phases of N-($\text{p}$-$\text{n}$-heptyloxybenzylidene)-$\text{p}$′-$\text{n}$-pentylaniline can be classified (with increasing temperature) as S_H, S_B, S_C and S_A, respectively. The long molecular axes are probably tilted with respect to the normal to the layers in the S_A, S_C and S_H phases, and perpendicular to the layers in the S_B phase.     

Rotational Analysis of the ÃA1-X?A1 Band System of Yttrium Dicarbide, YC2

The 000-000 and 3¹₀ bands of the 775-nm electronic transition of YC₂(òA₁←X?²A₁) have been studied at high resolution, using the laser-induced fluorescence from a supersonic jet expansion. Three types of experiment have been carried out. First, the complete rotational and hyperfine structures of the two bands were recorded. To measure the small asymmetry splittings in the K=2 levels of the X?²A₁ state, portions of the b-type 3¹₀ band were then recorded in the presence of a weak static electric field. Finally, a number of pure rotational transitions between the K=0 levels of the ground state were recorded by pump/probe microwave optical double resonance. A few small rotational perturbations occur in the upper electronic state but, omitting the perturbed lines, the combined data sets could be modeled using an effective Hamiltonian operator appropriate for the rotation, electron spin, and hyperfine structure of a rigid asymmetric top molecule. The molecule is confirmed as being “T-shaped,” where the Y atom is bonded to the side of a C₂ group; the rotational constants determined are for the òA₁, 3¹ level, A=1.76128, B=0.189949, C=0.170056 cm⁻¹, and for the X?²A₁, v=0 level, A=1.742731, B=0.201947, C=0.181285 cm⁻¹. Allowing for electron orbital corrections to the rotational constants, the geometrical structures are found to be òA₁ state, r (Y-C)=2.2795 Å, r (C-C)=1.2630 Å, ∠C-Y-C=32.17°; X?²A₁ state, r (Y-C)=2.1946 Å, r (C-C)=1.2697 Å, ∠C-Y-C=33.63°. A molecular orbital diagram is given for the states of YC₂ and the interpretation of the electron spin and hyperfine parameters is discussed.     

Anti-Invar properties and magnetic order in fcc Fe-Ni-C alloy

Anti-Invar effect was revealed in the fcc Fe-25.3%Ni-0.73%C (wt%) alloy, which demonstrates high values of thermal expansion coefficient (TEC) (15-21)×10⁻⁶ K⁻¹ accompanied by almost temperature-insensitive behavior in temperature range of 122-525 K. Alloying with carbon considerably expanded the low temperature range of anti-Invar behavior in fcc Fe-Ni-based alloy. The Curie temperature of the alloy T_C=195 K was determined on measurements of temperature dependences of magnetic susceptibility and saturation magnetization. The Mössbauer and small-angle neutron scattering (SANS) experiments on the fcc Fe-25.3%Ni-(0.73-0.78)%C alloys with the varying temperatures below and above the Curie point and in external magnetic field of 1.5-5 T were conducted. Low value of the Debye temperature Θ_D=180 K was estimated using the temperature dependence of the integral intensity of Mössbauer spectra for specified temperature range. The inequality B_eff=(0.7-0.9)B_ext was obtained in external field Mössbauer measurement that points to antiferromagnetically coupled Fe atoms, which have a tendency to align their spins perpendicular to B_ext. Nano length scale magnetic inhomogeneities nearby and far above T_C were revealed, which assumed that it is caused by mixed antiferromagnetically and ferromagnetically coupled Fe atom spins. The anti-Invar behavior of Fe-Ni-C alloy is explained in terms of evolution of magnetic order with changing temperature resulting from thermally varied interspin interaction and decreasing stiffness of interatomic bond.     

Precision measurement of the hyperfine structure of Lu175 with the atomic beam magnetic resonance method

The hyperfine structure separations of both doublet states² D _3/2 and² D _5/2 of the ground state configuration 6s ² 5d of Lu¹⁷⁵ have been remeasured with high precision using the atomic beam magnetic resonance method. Magnetic dipole transitions between Zeeman components of the hfs levels were induced applying Ramsey's technique of separated oscillatory fields whenever the field dependence of the resonances was small enough. The hfs intervals at zero field and hfs interaction constants were derived from the measurements. The constants were then corrected for hfs perturbations between the two levels of the doublet. Configuration interaction has been taken into account for the calculation of the dipole matrix elements. The corrected hfs constants are:J=3/2:A=194.332921 (300) MHzB=1511.396 267 (320) MHzC=?70 (19) HzJ=5/2:A=146.776 472 (138) MHzB=1860.656132 (840) MHzC=913 (162) HzD=?16 (24) Hz A quadrupole hfs anomaly between Lu¹⁷⁵ and Lu^176m was not found when comparing the following two ratios: Lu¹⁷⁵:B(5/2)/B(3/2)=1.2310850 (16) Lu^176m :B(5/2)/B(3/2)=1.2310818 (30). So far we have not succeeded in computing an octopole moment from the twoC-factors for the terms² D _3/2,5/2 because the influence of higher configurations could not sufficiently be considered.     

Conventional and inverse magnetocaloric effects,and critical behaviors in Ni43Mn46Sn8In3 alloy

A systematic study of the conventional and inverse magnetocaloric effects, and critical behaviors in an alloy ingot of Ni₄₃Mn₄₆Sn₈In₃ has been performed. Our results reveal the sample exhibiting structural and magnetic phase transitions at temperatures T_C^M = 166 K (T_C of the martensitic phase), T_M–A = 260 K (the martensitic-to-austenitic phase transformation) and T_C^A = 296 K (T_C of the austenitic phase). The large values of refrigerant capacity (RC) around T_M–A and T_C^A are found to be RC_M–A = 172.6 and RC_A = 155.9 J kg⁻¹, respectively, under an applied field change of 30 kOe. Our critical analyses near the T_C^M and T_C^A reveal that a coexistence of the long- and short-range ferromagnetic order in the martensitic phase, while the long-range ferromagnetic order exists in the austenitic phase. Interestingly, at around T_C^A, the maximum magnetic entropy change (|ΔS_max|) versus magnetic field H obeys a power law, |ΔS_max| = a·Hⁿ, where the exponent n is found to be about 0.66.     

Hyperfeinstruktur und Lebensdauer des 82 P 3/2-Terms von Rubidium

The hyperfine structure splitting of the 8² P _3/2 state of Rb⁸⁵ and Rb⁸⁷ has been investigated with optical double resonance. The following interaction constants have been obtained:A _8p ⁸⁵ =1.99(2) MHz,B _8p ⁸⁵ =1.98(12) MHzA _8p ⁸⁷ =6.75(3) MHz,B _8p ⁸⁷ =0.96(6) MHz. The lifetime of the 8² P _3/2 state is: τ=4.0(8) · 10^?7 sec.     

Frustrated model to describe reentrant behavior in copper oxide superconductors

The quenched decorated Ising model with competitive interactions is used here to described the magnetic properties of the copper oxide superconductors compounds in the insulating phase (antiferromagnetic). The model consists of planes in which the nodal spins interact antiferromagnetically (J_A<0) with their nearest-neighbors, and ferromagnetically (J_F>0) with the spins that decorate the bonds, which are quenched and distributed randomly over the two-dimensional lattice. The planes interact antiferromagnetically with weak-exchange interaction (i.e., , λ=10^-5). By using the framework of an effective-field theory, based on the differential operator technique, we discuss the antiferromagnetic-phase stability limit in the temperature-decorated bond concentration space (T-p), for λ=10^-5 and various values of frustration parameter α=J_A/J_F. For certain region range of the parameter α we observe a reentrant behavior at low-temperature. We also discuss the critical behavior of T_N versus α for some values of decorated bond concentrations and reentrant phenomena is observed. We calculate the dependence of the staggered magnetization as a function of the temperature to analyze the reentrant behavior observed in the phase diagrams.     

Systematic trends in the line strengths of E1 transitions in the oxygen isoelectronic sequence

Line strengthsS for the dipole allowed transitions within then=2 complex of the oxygen isoelectronic sequence have been fitted in the formZ ² S=A+B/(Z −C), whereZ is the nuclear charge of a particular ion. The constantsA, B andC are determined by using a non-linear least square method. The data forS are taken from the configuration interaction calculations which included internal, semi-internal and all external type correlations for ions in the rangeZ=8 − 25. It is shown that the values ofA obtained from the fit for all the transitions are in excellent accord with the ab-initio values obtained in the hydrogenic limitZ → ∞ provided near degeneracy effects are included in the ground state multiplet 1s²2s²2p^{4 1}S.     

Spin-glass-like behaviour and magnetic order in Mn[Cr0.5Ga1.5]S4 spinels

Magnetization and susceptibility were investigated as a function of temperature and magnetic field in polycrystalline Mn[Cr_0.5Ga_1.5]S₄ spinel. The dc susceptibility measurements at 919 Oe showed a disordered ferrimagnetic behaviour with a Curie-Weiss temperature θ_CW=−55 K and an effective magnetic moment of 5.96 μ_B close to the spin-only value of 6.52 μ_B for Cr³⁺ and Mn²⁺ ions in the 3d³ and 3d⁵ configurations, respectively. The magnetization measured at 100 Oe revealed the multiple magnetic transitions with a sharp maximum at the Néel temperature T_N=3.9 K, a minimum at the Yafet-Kittel temperature T_YK=5 K, a broad maximum at the freezing temperature T_f=7.9 K, and an inflection point at the Curie temperature T_C=48 K indicating a transition to paramagnetic phase. A large splitting between the zero-field-cooled (ZFC) and field-cooled (FC) magnetizations at a temperature smaller than T_C suggests the presence of spin-glass-like behaviour. This behaviour is considered in a framework of competing interactions between the antiferromagnetic ordering of the A(Mn) sublattice and the ferromagnetic ordering of the B(Cr) sublattice.     

Discrimination of measurement contexts in quantum mechanics

We demonstrate that it is possible to discern the way that has been followed to measure a quantum observable that can be expressed in terms of different products of observables, whereas no such discrimination is possible by assigning predetermined values. Specifically we show how to distinguish different routes (contexts) to measure C=AB=A^′B^′, when C,A,B and C,A^′,B^′ commute with each other, but A and B do not commute with A^′ and B^′.     

Ground state hyperfine structure of95Mo and97Mo

The hyperfine structure of the ground state 4d ⁵ 5s ⁷ S ₃ of⁹⁵Mo and⁹⁷Mo has been measured by the atomic beam magnetic resonance technique with the following results:⁹⁵Mo:A=?208.582060(10)MHz,B=37.050 (100) kHzC=?30 (10) Hz,D=?3 (3) Hz⁹⁷Mo:A=? 212.980930 (10) MHz,B?69.990(140)kHzC=?5 (10) Hz,D=0 (3) Hz. After application of corrections calculated according to second order perturbation theory, the hyperfine structure constants became:⁹⁵Mo: A_c=?208.582560(290)MHz,B _c =16.920(4300)kHzC _c=?30(270) Hz,D _c =? 3 (50) Hz⁹⁷Mo: A_c=212.981450(300) MHz,B _c =?90.780(4400)kHzC _c=?6(270) Hz,D _c =0 (50) Hz. With the known ratio ofg _I(⁹⁵Mo)/g _I(⁹⁷Mo) [1] a calculation of the hyperfine anomaly yields:₉₅ Δ ₉₇=?0.01009(17)%. The ratio of the uncorrectedB factors isB(⁹⁷Mo)/B(⁹⁵Mo)=?1.8890(47). Because of the relatively large effects of second order hyperfine structure, the ratio of the correctedBfactors differs considerably from the ratio of the uncorrectedB factors. From the correctedB factors the electric quadrupole moments may be evaluated by means of calculated radial integrals [2]. The results are:Q (⁹⁵Mo)=?0.019(12)barns,Q(⁹⁷Mo)=0.102(39)barns.     

Levelcrossing experiments in the first excited1 P 1 states of the alkaline earths

The hyperfine structure of the lowest¹P₁ state of²⁵Mg,⁴³Ca,⁸⁷Sr,¹³⁵Ba and¹³⁷Ba have been measured by the level-crossing and anticrossing technique. The magnetic dipole and electric quadrupole coupling constants determined by these measurements are²⁵Mg(3s3p¹P₁):A=? 7.7(5) MHz; 16 MHz>B>0 MHz,⁴³Ca(4s4p¹P₁):A=? 15.3(4) MHz; ¦B¦<12 MHz,⁸⁷Sr (5s5p¹P₁:A=? 3.4(4) MHz;B=39(4) MHz,¹³⁵Ba(6s6p¹P₁):A=? 97.5(1.0) MHz;B=31(9)MHz,¹³⁷Ba(6s6p¹P₁):A=?109.2(1.2) MHz;B=51(12)MHz. The results have been compared with the predictions of the Breit-Wills theory of the two-electron hyperfine structure using the experimental data on the³P states. Large discrepancies have been observed which are due to different radial wave functions of thes andp electron in the triplet and singlet system. This effect has been taken into account by fitting the data with the aid of two additional parameters. That this procedure is justified is shown by an analysis of the fine structure splitting, the life times, and the isotopic shifts in thesp configurations of group II elements.     

Inequalities for the Schattenp-norm. IV

We prove some inequalities for the Schattenp-norm of operators on a Hilbert space. It is shown, among other things, that ifA,B, andX are operators such thatA +B ≧ |X| andA +B ≧ |X*|, then ∥AX +XB∥ _p ^p + ∥AX* +X*B∥ _p ^p ≧2 ∥X∥ _2p ^2p for 1 ≦p<∞, and max (∥AX +XB∥, ∥AX* +X*B∥) ≧ ∥X∥². Also, for any three operatorsA,B, andX, $$|| |A|X - X|B| ||_2^2 + || |A*|X - X|B*| ||_2^2 \leqq ||AX - XB||_2^2 + ||A*X - XB*||_2^2 .$$      

Effect of carbon doping on thermodynamic behavior of MgB2

The thermodynamic behavior of carbon doped MgB₂ has been studied using a rigid ion model (RIM). The model potential consists of the long-range Coulomb, the short-range repulsive and the van der Waals interactions. This model has successfully explained the cohesive and thermodynamic properties of Mg(B_1−xC_x)₂ (x=0.0, 0.02, 0.05, 0.075, 0.1, 0.2). The properties studied are the cohesive energy, molecular force constant, Restrahlen frequency, compressibility, Debye temperature and Gruneisen parameter. Our results on Restrahlen frequency and Debye temperature are in reasonably good agreement with the available experimental data. In addition, we have computed the specific heat C_p for Mg(B_1−xC_x)₂ (x=0.2) as a function of temperature T in the range 16 K?T?1000 K. We have also shown the variation of specific heat C_p with doping concentration at room temperature (300 K). The calculated specific heat C_p for Mg(B_1−xC_x)₂ (x=0.2) in the temperature range 16 K?T?22 K for which experimental results are available, agrees pretty well with the experimental data.