Features of the magnetic and magnetoelectric properties of HoAl3(BO3)4

The main features of the magnetic and record magnetoelectric properties of a HoAl₃(BO₃)₄ aluminoborate single crystal have been studied experimentally and theoretically. It has been found that the electric polarization that was previously detected in HoAl₃(BO₃)₄ and is record for multiferroics is significantly larger, ΔP _ba (B _a ) ≈ ?5240 μC/m², with an increase in the magnetic field to 9 T at T = 5 K. The measured magnetic properties and revealed features have been interpreted within a united theoretical approach based on the molecular field approximation and on calculations in the crystal field model for a rare-earth ion. The experimental temperature (from 3 to 300 K) and field (up to 9 T) dependences of the magnetization have been described. The parameters of the crystal field of trigonal symmetry for a Ho³⁺ ion in HoAl₃(BO₃)₄ have been determined from the interpretation of the experimental data.     

Exchange charge model and analysis of the microscopic crystal field effects in KAl(MoO4)2:Cr

In the present paper, we report on consistent crystal field calculations of the Cr³⁺ ions energy levels in KAl(MoO₄)₂ using actual D_3d site symmetry of the Cr³⁺ position and employing the exchange charge model (ECM) of the crystal field. In addition to the energy level calculations, the Huang-Rhys factor S=5.7 and effective phonon energy ?ω=268 cm^-1 were evaluated in the single configurational coordinate model. Detailed treatment of the microscopic crystal field effects in the ECM framework allowed to obtain analytical dependence of the crystal field strength 10Dq on the Cr-O interionic distance and extracting from it the values of some parameters of the electron-vibrational interaction (EVI) in the KAl(MoO₄)₂:Cr³⁺ system. All obtained results are compared with experimental data and discussed; agreement between the calculated and experimental parameters is good.     

A numerical estimate of the upper limit for the Higgs boson mass

TheSU (2) Higgs model with a scalar doublet field is studied by Monte Carlo calculations on 12⁴ and 16⁴ lattices. The gauge coupling is chosen to be similar in magnitude to the physical value in the standard model. The numerical results at large scalar self-coupling imply an upper limitm _H /m _W ?9 for the ratio of the Higgs boson mass to the W-mass.     

Etude par effet Mössbauer de Ca2MnO4 dope a l'etain

The antiferromagnetic layer phase Ca₂MnO₄ doped with ¹¹⁹Sn⁴⁺ has been investigated by Mössbauer spectroscopy. Below the Néel temperature a hyperfine magnetic field transfered on the tin nucleus is observed with saturation value H(0)?38 kOe. The low value of the transfered field is attributed to the absence of e_g electrons on the 3d orbitals of Mn⁴⁺. Supposing the field to follow the power law H(T) = H(0)D[1 ? (T/T_N)]^β as the sublattice magnetizations usually do, the study of the temperature dependence of the field yields β = 0.44 ± 0.10. This value for the critical exponent is in rather good agreement with the value deduced from neutron measurements (β = 0.38 ± 0.06) as well as with those calculated from three dimensional Heisenberg and Ising models (0.31?β?0.38). It is anyway very different from the theoretical value for a two dimensional Ising model (β = 0.125) and from the experimental values for various two-dimensional antiferromagnets isostructural with Ca₂MnO₄ such as K₂MnF₄ (β = 0.15) or K₂NiF₄ (β = 0.14).     

Upper bound estimate for the Higgs mass from the lattice regularized Weinberg-Salam model

There are indications that, as a consequence of the trivality of the scalar φ⁴ theory, the Weinberg-Salam model is massive free field theory. However, considering theWS model as an effective field theory, an upper bound for the Higgs mass can exist. We have studied this phenomenon by simulating the SU(2) gauge Higgs model on a lattice. The results indicate that R_max = m_H/m_W|_max = 9.3 ± 1. However, serious finite size effects make it unfeasible to explore the region m_H ⩽ Λ_cutoff with Monte Carlo simulation.     

Hierarchy of interactions and mass relations in asymptotically free E6 model of unified interactions

The hierarchy of gauge interactions within the E₆ model is proved, and the vector and spinor field masses are obtained. The mass spectrum of the charged W-bosons is found, and the mass scale is fixed so that the mass of the lightest of them is about 70 GeV. The lepton spectroscopy is studied and a new charged lepton, with mass of order 4–8 GeV is predicted. For the low-energy phenomenology, the model may be considered as a theory of 6 flavoured quarks and 4 charged leptons, each with its neutrino. Being 4-component the neutrinos are massive except for the ν_e (m_νe = 0, exactly) and ν_μ (m_νμ ≈ 0, approximately) particles. The problem of the “superfluous” particles which as a rule accompanies the asymptotic freedom in such theories is also briefly discussed.     

Kac-Moody symmetries of critical ground states

The symmetries of critical ground states of two-dimensional lattice models are investigated. We show how mapping a critical ground state to a model of a rough interface can be used to identify the chiral symmetry algebra of the conformal field theory that describes its scaling limit. This is demonstrated in the case of the six-vertex model, the three-coloring model on the honeycomb lattice, and the four-coloring model on the square lattice. These models are critical and they are described in the continuum by conformal field theories whose symmetry algebras are the su(2)_k=1, su(3)_k=1, and the su(4)_k=1 Kac-Moody algebra, respectively. Our approach is based on the Frenkel-Kac-Segal vertex operator construction of level-one Kac-Moody algebras.     

Quadratic crystal field tensors and spin Hamiltonian tensors of Fe3+ in Li2Ge7O15 above and below the phase transition temperature

Dopant Fe³⁺ ions in tetrahedral and octahedral positions of Ge⁴⁺ in the crystal Li₂Ge₇O₁₅ were studied using EPR. Fe³⁺ substitutes for Ge⁴⁺ with a local charge compensation. The octahedral site and the tetrahedral sites significantly differ by the value of the invariant sumS(B ₄) of theB ₄ tensor of the spin Hamiltonian of Fe³⁺. The irreducible tensor products {V ₄ ? V ₄}₄ and {V ₄?V ₄}₂ theV ₄ tensor of the crystal field calculated using the point-charge model for octahedral and tetrahedral complexes provide the predominant contribution of the crystal field to theB ₄ andB ₂ tensors of the spin Hamiltonian of Fe³⁺, respectively. A comparison of the fourth-rank tensorsB ₄ of the spin Hamiltonian and {V ₄?V ₄}₄ of the crystal field determined at 300 K with those determined at 77 K supports the conclusion that the phase transition is accompanied by combined rotation of the [GeO₄] tetrahedra with the [Ge(1)O₆] octahedron almost unaltered. The spectrum lines are narrow and the variety of point defects in the vicinity of the paramagnetic impurity ions Fe³⁺, Cr³⁺ and Cu²⁺ is not detected. These facts are inconsistent with the statistically distributed model for the Li(2) atom. In specific cases at 300 K, when the wings of the two spectrum lines of theM→M+1 and theM+2 →M+3 transitions of Fe³⁺ ions belonging to one system of translationally equivalent positions overlap an extra line appears in the center between these lines. It is suggested that this effect is due to the soft phonon mode above the phase transition temperature.     

Magnetization,magnetoelectric polarization,and specific heat of HoGa3(BO3)4

A comprehensive experimental and theoretical study of magnetic, magnetoelectric, thermal, and spectroscopic characteristics of HoGa₃(BO₃)₄ gallium borate single crystals has been performed. A large magnetoelectric effect exceeding its values found in all iron and aluminum borates except HoAl₃(BO₃)₄ has been observed. The magnetoelectric polarization of HoGa₃(BO₃)₄ equals ΔP _ba (B _a ) ≈ ?1020 μC/m² at T = 5 K in a magnetic field of 9 T. The theoretical treatment based on the crystal field model for rare-earth ions provides a unified approach for the consistent interpretation of all measured characteristics. The crystal-field parameters are determined. The temperature (in the 3–300 K range) and magnetic field (up to 9 T) dependences of the magnetization, the Schottky anomaly in the temperature dependence of the specific heat, and its shift in the field B ‖ c are described. To compare the thermal properties of HoGa₃(BO₃)₄ with those of HoAl₃(BO₃)₄ exhibiting record values of the polarization, the specific heat of HoAl₃(BO₃)₄ at various B values and the temperature dependence of the polarization ΔP _b (T) in the applied magnetic field of 9 T have been measured.     

Spectroscopic studies of the two-dimensional magnetic insulators chromium trichloride and chromium tribromide—I

The general aspects of the crystal field spectra of the two-dimensional magnetic insulators CrCl₃ and CrBr₃ are considered in detail, with special emphasis on the broad, spin-allowed ⁴T₂ and ⁴T₁ bands. A fit of the point-charge model Hamiltonian to the spectra is presented, with attention to the magnitude of the trigonal field effects. The temperature dependence of the ⁴T₂ and ⁴T₁ dipole strengths in the range 4.2< T < 300°K is analyzed in terms of single-ion (odd-parity trigonal field and odd-parity vibronic) and exchange mechanisms. A moment analysis of the M.C.D. spectra is performed, which (together with dipole strength temperature dependence data) yields a reasonable interpretation of the spin-allowed transition mechanism. The odd-parity crystal field is found to be the most important parity-breaking mechanism in both the ⁴T₂ and ⁴T₁ bands. Both also receive some contribution from the vibronic mechanism. This process is more significant for the ⁴T₂ state than for the ⁴T₁, and may involve a slightly anharmonic low-energy vibration. Evidence for a small exchange contribution is found in the ⁴T₂ band of both systems. Factors influencing the bandshapes are examined quantitatively. The antiresonance formalism of Sturge et al. is applied to the anomalous lineshapes of certain transitions in absorption and M.C.D. and one particularly complex bandshape (that for ⁴A₂ → ⁴T₂ - ²E - ²T₁ in CrCl₃) is analyzed through a computation.     

Mössbauer spectroscopy of Np3As4. Interpretation of the spectra and of the magnetic behaviour in a crystal field model

Np₃As₄ (Th₃P₄-type structure) is ferromagnetic below T_c=81 K. In this work, we present results of Mössbauer experiments performed between 4.2 and 150 K. The isomer shift with respect to NpAl₂ is 5.9 mm/s, suggesting a Np⁴⁺ valence state. The hyperfine field at 4.2 K is 377 T, corresponding to an ordered moment μ_ord=1.75μ_B. The quadrupolar interaction is very small both in the ferromagnetic and in the paramagnetic state (e²qQ<3 mm/s).The low value of μ_ord (free ion value 3.2μ_B) as well as the absence of a significant quadrupolar component are discussed in terms of crystal field effects.In particular, the contributions to the electric field gradient of both the lattice and the 5f electrons have been considered, taking into account the distortion of the 5f charge cloud in presence of a molecular field below T_c.We show that the reduction of μ_ord is linked to a rotation of the moment towards the [111] direction as in the case of the isostructural compound U₃P₄.The crystal field ground state which accounts for this effect leads to a vanishingly small quadrupolar interaction both in the ordered and in the paramagnetic states.As a consequence, the lattice contribution to the electric field gradient, itself, is likely to be very small. Two mechanisms are proposed for this lattice term reduction: either a compensation by the conduction electrons or a reduction of B⁰₂ due to the competing effects of the ligands surrounding Np⁴⁺.Lastly, the model gives a good agreement with the temperature variation of the hyperfine field.     

Non-Darcy free convection of Fe3O4-water nanoliquid in a complex shaped enclosure under impact of uniform Lorentz force

Effect of Lorentz forces on natural convection in a complex shaped cavity filled with nanoliquid immersed in porous medium is investigated by means of Control volume based finite element method (CVFEM). Non Darcy model is taken into account for porous media. The working fluid is Fe₃O₄ –water and its viscosity considered as function of magnetic field. Figures are illustrated for different values of Darcy number (Da), Fe₃O₄ -water volume fraction (?), Rayleigh (Ra) and Hartmann (Ha) numbers. Results depict that enhancing in Lorentz forces results in reduce in nanofluid motion and increase the thickness of thermal boundary. Convective heat transfer enhances with rise of Darcy number.     

Specimen geometry effects on the irreversible magnetization in the low field regime for specimens of bulk Nb3Sn

Irreversible magnetization curves in particular in self field conditions were investigated for specimens of bulk Nb₃Sn as an isotropic and non-granular alternative to high T _c materials. The specimens were cut into squares with side length to thickness ratios of about 0.8 to almost 20, leading to diamagnetic slopes |χ _d | ranging from slightly more than 1 (slab in parallel field) to 13 (plate in perpendicular field). The peak in the low field magnetization (caused by the field dependence of j _c ) moves from negative field for specimens with small |χ _d | (where it should be according to the standard Bean model) to zero or even positive fields for specimens with large |χ _d | . Finite element self consistent calculations with field dependent and thus spacially varying j _c were used to fit the measured hysteresis curves. A strong current peak in the center plane of the specimens — caused by the demagnetization field — probably causes the shift of the magnetization peak to positive field. Best agreement between the experimental and calculated magnetizations have been obtained for the extreme geometries: either thin disk in perpendicular (χ _d < ?4) or thin slab in parallel magnetic field (χ _d > ?1.2).     

Absorption spectrum of Cs2Mg(SO4)2 · 6H2O:Ni2+ single crystals

The absorption spectrum of Ni²⁺ doped in Cs₂Mg(SO₄)₂ · 6H₂O single crystals has been studied at room and liquid nitrogen temperatures in the range 7000–34000 cm^?1. The observed spectrum is satisfactorily interpreted in terms of cubic ligand field model including spin-orbit coulping. The ligand field parameters evaluated to best fit the observed spectrum are B = 955 cm^?1, C = 3572 cm^?1, Dq = 910 cm^?1 and ξ = 550 cm^?1. The non-ligand field band observed at 77K has been interpreted to be the superposition of vabrational mode of SO₄^2? radical on ₃T_1g(F) band.     

Electric field gradients in AFeIIIF4 structures: Calculations for the polarizable point charge model and Mössbauer data

The polarizable point charge model is used to explain Mossbauer data on the EFG at the iron site in AFeF₄ (A = K, Cs, Rb, NH₄). Lattice summations are performed in direct space. The resolution of the self consistent equations involving the electric field is obtained through an iterative method. The major contribution to the EFG is that of “terminal” (non-bridging) fluorines. The fluorine polarizabilities which fit the data are in reasonable agreement with expected values (α_F? 0.9 ų).     

NMR hyperfine spectrum of 143Nd in ferromagnetic cubic intermetallic NdAl2

The hyperfine spectrum of ¹⁴³Nd in NdAl₂ measured at T = 1.4 K provides values of ∣a_t∣ = 786 ± 0.5 MHz and ∣P_t∣ = 3.25 ± 0.03 MHz. The latter value is in agreement with the expected calculated value obtained from the 4f ground state wave function in a crystal field plus molecular field model, which may be deduced from inelastic neutron scattering experiments combined with susceptibility measurements, or from polarized neutron diffraction experiments. It is shown that the 4f electronic moment can be directly obtained from zero field NMR with good accuracy.     

Continuum limit of A Z2 lattice gauge theory

Phase diagrams of lattice gauge theories have in several cases lines of first-order transitions ending at points at which continuous (second-order) transitions take place. In the vicinity of this critical point, a continuum field theory may be defined. We have analyzed here a Z₂ gauge plus matter model (which has no formal continuum limit) and identified the critical point with a usual Ø⁴, globally Z₂ invariant, field theory. The analysis relies on a mean field functional formalism and on a loop-wise expansion around it, which is reviewed.     

Low temperature differential magnetization of Ni(ClO4)26NH3 and Ni(BF4)26NH3

The differential magnetization of Ni(ClO₄)₂6NH₃ and Ni(BF₄)₂6NH₃ was measured as a function of temperature (20 to 0.3 K) and magnetic field (up to 40kOe). An antiferromagnetic transition was found at T_N = 0.45 K for the Ni(ClO₄)₂6NH₃ and T_N = 0.43 K for the Ni(BF₄)₂6NH₃, and a portion of the magnetic phase diagram was determined. The interpretation of the data in terms of a uniaxial model yielded (D/k) ～ 0.2 K for both salts.     

A model for the electrical characteristics of metal-ferroelectric-insulator-semiconductor field-effect transistor

An improved theoretical model on the electrical characteristics of metal-ferroelectric-insulator-semiconductor field-effect transistor (MFIS-FET) has been proposed by considering the history-dependent electric field effect and the mobility model. The capacitance-voltage (C-V) characteristics of MFIS structure is evaluated by combining the switching physics of ferroelectric with the silicon physics, and the drain current-gate voltage (I_D-V_GS) and drain current-drain voltage (I_D-V_DS) characteristics of MFIS-FET are modeled by combining the switching physics of ferroelectric with Pao and Sah’s double integral. For two MFIS-FETs with SrBi₂Ta₂O₉ and (Bi,La)₄Ti₃O₁₂ ferroelectric layers, the C-V, I_D-V_GS and I_D-V_DS characteristics are simulated by using the improved model, and the results are more consistent with the previous experiment than those based on Lue model, indicating that the improved model is suitable for simulating the electrical characteristics of MFIS-FET. This work is expected to provide some guidance to the design and performance improvement of MFIS structure devices.     

Crystal field splitting of 5d states in Ce3+:YPO4

The superposition model is used to obtain a new identification of the 5d levels in Ce³⁺: YPO₄, resulting in a revised parametrization of the 5d crystal field. Electrostatic and pseudo-potential models are employed to relate these parameters to those obtained from 4f crystal field splittings.