Separable interactions and liquid 3He: II. Extrema of Landau expansion and phase diagram in the weak-coupling limit

In a previous paper we derived a Landau expansion starting from an exactly solvable model for a system of fermions with an l = 1 pairing interaction in the presence of a magnetic field. The Landau expansion, which can be used to study the phases of liquid ³He, is a complicated function of 9 complex variables, in which it is not obvious a priori that the field dependence of the coefficients of the fourth-order terms can be neglected. In the present paper the extrema of the Landau expansion are analyzed in some detail with the weak-coupling values of the coefficients. The absolute minimum of the Landau expansion can be found by minimizing a three-parameter function Φ_BW, the minimalization of which leads to three possible phases, the A1-phase, the ABM-phase (or two-dimensional 2D-phase) and the proper generalization of the BW-phase in the presence of a magnetic field. The phase diagram is compared with the one given by Ambegaokar and Mermin.     

Anomalous thermal expansion of high-temperature superconductors Bi2Sr2−x LaxCuO6 at low temperatures

The low-temperature thermal expansion of Bi₂Sr_2?x La_xCuO₆ single crystals with different doping levels is measured. The effect of a magnetic field on the thermal expansion of Bi₂Sr_2?x La_xCuO₆ is studied. Anomalous (negative) thermal expansion whose characteristics depend on the doping level of the sample is revealed at T ≤ 10–20 K. It is found that these characteristics are significantly affected by moderately strong magnetic fields (2–4 T). The experimental results can be interpreted within a model relating the anomalous thermal expansion in high-temperature superconductors at low temperatures and the strong effect of the magnetic field on this expansion to the change in the stabilizing role of the charge-density waves in the oxygen sublattice.     

Low temperature thermal expansion of praseodymium between 0.5 and 25 K

The linear thermal expansion coefficients parallel and perpendicular to the hexagonal axis of single crystal Praseodymium have been measured between 0.5 and 25 K and in external magnetic fields up to 12 kOe. α₆ ? α_⊥ is found to be of the order of 10^?4 at 20 K, decreasing with decreasing temperatures. Below 1 K we found evidence of a nuclear hyperfine contribution to the thermal expansion. A separation of the electronic term allows a determination of the electronic Grüneisenparameter.     

Advection of passive magnetic field by the Gaussian velocity field with finite correlations in time and spatial parity violation

Using the field theoretic renormalization group technique the model of passively advected weak magnetic field by an incompressible isotropic helical turbulent flow is investigated up to the second order of the perturbation theory (two-loop approximation) in the framework of an extended Kazantsev-Kraichnan model of kinematic magnetohydrodynamics. Statistical fluctuations of the velocity field are taken in the form of a Gaussian distribution with zero mean and defined noise with finite correlations in time. The two-loop analysis of all possible scaling regimes is done and the influence of helicity on the stability of scaling regimes is discussed and shown in the plane of exponents ? ? η, where ? characterizes the energy spectrum of the velocity field in the inertial range E ∞ k ^{1 ? 2ε}, and η is related to the correlation time at the wave number k which is scaled as k ^{?2 + η}. It is shown that in non-helical case the scaling regimes of the present vector model are completely identical and have also the same properties as those obtained in the corresponding model of passively advected scalar field. Besides, it is also shown that when the turbulent environment under consideration is helical then the properties of the scaling regimes in models of passively advected scalar and vector (magnetic) fields are essentially different. The results demonstrate the importance of the presence of a symmetry breaking in a given turbulent environment for investigation of the influence of an internal tensor structure of the advected field on the inertial range scaling properties of the model under consideration and will be used in the analysis of the influence of helicity on the anomalous scaling of correlation functions of passively advected magnetic field.     

A convergent expansion about mean field theory: I. The expansion

We give a convergent expansion for nearly Gaussian quantum field theory in the multiphase region. The expansion combines (1) an expansion in phase boundaries, (2) a cluster expansion, and (3) a perturbation expansion to isolate dominant behavior. We study in detail the ground state of the $\text{P}$(φ)₂ = (λφ⁴ ? φ² ? μφ)₂ model, with ∥ μ ∥ ? λ² ? 1. The ground state is close to the classical free field, obtained by replacing $\text{P}$(φ) by the quadratic mean field polynomial $\text{P}$_c(φ), tangent to $\text{P}$ at a global minimum. Selecting one minimum gives a pure phase (ergodic ground state) satisfying the Wightman-Osterwalder-Schrader axioms with a positive mass. We also establish analyticity in λ for μ = 0 in the sector ∥ Im λ ∥ < ? Re λ ? 1, for ? ? 1.     

Magnetic transitions in LaFe13−x−yCoySix compounds

The magnetic properties of a set of LaFe_13?x?yCo_ySi_x compounds (x = 1.6 ? 2.6; y = 0, y = 1.0) have been investigated using magnetic measurements, thermal expansion, ⁵⁷Fe Mössbauer spectroscopy and high resolution neutron powder diffraction methods over the temperature range 10–300 K. The natures of the magnetic transitions in these LaFe_13?x?yCo_ySi_x compounds have been determined. The Curie temperatures of LaFe_13?xSi_x were found to increase with Si content from T_C = 219(5) K for Si content x = 1.6 to T_C = 250(5) K for x = 2.6. Substitution of Co for Fe in LaFe_10.4Si_2.6 resulted in a further enhancement of the magnetic ordering temperature to T_C = 281(5) K for the LaFe_9.4CoSi_2.6 compound. The nature of the magnetic transition at the Curie temperature changes from first order for LaFe_11.4Si_1.6 to second order for LaFe_10.4Si_2.6 and LaFe_9.4CoSi_2.6. The temperature dependences of the mean magnetic hyperfine field values lead to T_C values in good agreement with analyses of the magnetic measurements. The magnetic entropy change, ?ΔS_M, has been determined from the magnetization curves as functions of temperature and magnetic field (ΔB = 0 ? 5 T) by applying the standard Maxwell relation. In the case of LaFe_12.4Si_1.6 for example, the magnetic entropy change around T_C is determined to be -ΔS_M ～ 14.5 J kg^?1 K^?1 for a magnetic field change Δ B = 0 ? 5 T.     

Features of low-temperature thermal expansion of n-type Bi<Subscript>2</Subscript>Se<Subscript>3</Subscript> single crystals in magnetic field

Tensometric study of n-type Bi₂Se₃ single crystals in dc magnetic fields to 6 T in a temperature range of 7–23 K detected a weak negative thermal expansion (NTE) in the basal plane. The NTE increases with the field strength and depends on its orientation with respect to the trigonal c axis. In a magnetic field of 6 T, parallel to the c axis, the linear NTE coefficient reaches ?7 · 10^?7 K^?1, and a minimum sample length is reached at a temperature of 13 K, where a Hall carrier concentration maximum is also detected. The found magnetoelastic anomaly can be associated with the topological insulator state.     

Thermodynamics of the quantum and classical Ising models with skew magnetic field

The thermodynamics of the unitary (normalized spin) quantum and classical Ising models with skew magnetic field, for |J|β?0.9, is derived for the ferromagnetic and antiferromagnetic cases. The high-temperature expansion (β-expansion) of the Helmholtz free energy is calculated up to order β⁷ for the quantum version (spin S≥1/2) and up to order β¹⁹ for the classical version. In contrast to the S=1/2 case, the thermodynamics of the transverse Ising and that of the XY model for S>1/2 are not equivalent. Moreover, the critical line of the T=0 classical antiferromagnetic Ising model with skew magnetic field is absent from this classical model, at least in the temperature range of |J|β?0.9.     

Langmuir Probe Diagnostics of a Low Temperature Non-Isothermal Plasma in a Weak Magnetic Field

This article presents measurements by a cylindrical Langmuir probe in the plasma of a DC cylindrical magnetron discharge át the pressure 1.5 Pa that aim at the experimental assessment of the influence of a weak magnetic field to the estimation of the electron density when using conventional methods of probe data interpretation. The probe data was obtained under the presence of a weak magnetic field in the range 1.10^?2?5.10^?2 T. The influence of the magnetic field on the electron probe current is experimentally assessed for two cylindrical probes with different radii, 50 μm and 21 μm. This assessment is based on comparison of the values of the electron density estimated from the electron current part with the values of the positive ion density estimated from the positive ion current part of the probe characteristic respectively by assuming that at the magnetic field strengths used in the present study the probe positive ion currents are possible to be assumed as uninfluenced by the magnetic field. For interpretation of the probe positive ion current two theories are used and compared to each other: the radial motion model by Allen, Boyd and Reynolds [10] and Chen [11] and the model that accounts for the collisions of positive ions with neutrals in the probe space charge sheath that we call Chen-Talbot model [8]. At lower magnetic field 3 · 10^?2 T the positive ion density values interpreted by using the Chen-Talbot model [8] are in better agreement with the values of electron density compared to those obtained by using the theory [10,11]; therefore the model [8] is used for calculation of the positive ion density from the probe data at higher magnetic fields. The comparison of the positive ion and electron density values calculated from the same probe data at higher magnetic fields shows that up to the magnetic field strength 4 . 10^?2 T with the probe 100 μm and up to 5 . 10^?2 T with the probe 42 μm in diameter respectively the decrease of the magnitude of the electron current at the space potential due to the magnetic field does not exceed the error limits that are usual for Langmuir probe measurements (absolute error ±20%).     

The one-dimensional Hubbard model for large or infiniteU

The magnetic properties of the one-dimensional Hubbard model with a hardcore interaction on a ring (periodic boundary conditions) are investigated. At finite temperatures it is shown to behave up to exponentially small corrections as a pure paramagnet. An explicit expression for the ground-state degeneracies is derived. The eigenstates of this model are used to perform a perlurbational treatment for large but finite interactions. In first order inU ¹ an effective Hamiltonian for the one-dimensional Hubbard model is derived. It is the Hamiltonian of the one-dimensional Hcisenberg model with antiferromagnetic couplings between nearest neighbor spins. An asymptotic expansion for the ground-state energy is given. The results are valid for arbitrary densities of electrons.     

Bianchi Type I Magnetized Barotropic Perfect Fluid Cosmological Model in General Relativity

Bianchi Type I barotropic perfect fluid cosmological model in presence of magnetic field, is investigated. To get the deterministic model, we have also assumed that σ ₁¹ α θ where σ ₁¹ is the eigen-value of shear tensor σ _i ^j and θ the expansion in the model. The behavior of the model in presence and absence of magnetic field and singularities in the model are also discussed.     

Design of a highly sensitive photonic crystal refractive index sensor incorporating ring-shaped GaAs cavity

Two highly sensitive optical sensor topologies are proposed and simulated in this paper. The proposed structures are optimized to provide better performance characteristics such as sensitivity, detection limit, and quality factor. They are based on two-dimensional photonic crystals consisting of rectangular arrays of GaAs rods in SiO₂ substrates. Such lattices have bandgaps for transverse magnetic modes. Two-dimensional finite difference time domain and plane wave expansion methods are used for the simulation and analysis of the refractive index sensors and particle swarm optimization method is used to optimize the structural parameters. The designed structures show a high sensitivity to refractive index variations. They are able to detect refractive indices from 1.33 to 1.5. An excellent figure of merit equal to 737 RIU^?1 is observed for the proposed structure and a significant improvement is observed compared to the structures reported in the literature.     

Consistent asymptotic expansion of the partial wave sum of the scattering amplitude

A consistent asymptotic expansion of the partial wave sum for the quantal scattering amplitude is given to arbitrary order of large ?^?1, the Sommerfeld parameter n or the grazing angular momentum Λ. It is explicitly shown that the leading term of this expansion is the familiar semiclassical expression, and how in the sharp cut-off model the Fraunhofer diffraction pattern arises from the second-order term.     

Controlling magnetic properties of iron oxide nanoparticles using post-synthesis thermal treatment

Changes in morphological and magnetic properties of Fe₃O₄ nanoparticles before and after annealing are investigated in the present work. The nanoparticles are synthesized in a standard capacitively coupled plasma enhanced chemical vapour deposition system with two electrodes using ferrocene as the source compound. Post annealing, due to the sintering process, the particles fuse along with recrystallization. This results in increased size of the nanoparticles and the interparticle interaction, which play a major role in deciding the magnetic properties. X-ray diffraction patterns of the samples before and after annealing indicate a phase change from Fe₃O₄ to Fe₂O₃. Annealing at 200 ^°C causes the apparent saturation magnetization to increase from 6 emu?g^?1 to 15 emu?g^?1. When annealed at 500 ^°C, the magnetic properties of the nanoparticles resemble those of the bulk material. The evidence for the transition from a superparamagnetic state to a collective state is also observed when annealed at 500 ^°C. Variation of the magnetic relaxation data with annealing also reflects the change in the magnetic state brought about by the annealing. The correlation between annealing temperature and the magnetic properties can be used to obtain nanocrystallites of iron oxide with different sizes and magnetic properties.     

A model for establishing the ultimate enhancements (A∞) in the low to high magnetic field transfer dynamic nuclear polarization experiment

In a preliminary report, we have demonstrated transfer of a flowing bolus enhanced in low magnetic fields (e.g., 0.33 T) with dynamic nuclear polarization (DNP), but monitored in a high magnetic field (4.7 T). The advantages of the high magnetic field monitoring approach include: 1) greater chemical shift dispersion, and 2) improved signal strength in comparison with static low field DNP experiments. In the present study, a model is developed to predict ultimate DNP enhancements (A_∞) in this experiment for flow liquid/liquid intermolecular transfer (L²IT). L²IT¹H and¹³C data is obtained for benzene and chloroform in order to test the validity of the model. The ultimate¹H and¹³C DNP enhancements obtained for benzene/TEMPO are ?150 and ?220, respectively. For a chloroform/TEMPO (L²IT) sample, the ultimate enhancements are close to the¹H dipolar (?330) and the¹³C scalar (+2660) limit, respectively. In the latter case, the observed¹³C DNP enhancement exceeds the thermal Boltzmann magnetization at 4.7 T by a factor of 21. For a 1-chlorobutane/TEMPO sample selective enhancements were observed at different sites in the molecule. For example, the C-1 carbon exhibits a large scalar enhancement, whereas, the other carbons exhibit dipolar enhancements. Data illustrating the importance of three-spin effects in¹³C DNP studies is also presented. Alternative methods of sample transfer from the low to high magnetic field are also discussed.     

Magnetized cosmological model

The object of this paper is to investigate the behavior of the magnetic field in a cosmological model for perfect fluid distribution. The magnetic field is due to an electric current produced along thex axis. It is assumed that expansion () in the model is proportional to ₁ ¹ , the eigenvalue of the shear tensor _i ^j . The behavior of the model when the magnetic field tends to zero and other physical properties are also discussed.     

Creation of ferromagnetic properties of V–Fe and Zr–Fe alloys by hydrogen absorption

The results of investigations of V_1?y Fe _y H _x and Zr_1?y Fe _y H _x alloys by ⁵⁷Fe Mössbauer spectroscopy are presented and discussed in view of hydrogen ability to create ferromagnetic properties of the alloy. The results indicate two different possibilities of hydrogen influence on the hyperfine magnetic field. Hydrogen absorption causes the ferromagnetic behaviour of the alloys at significant lower iron concentration compared to the concentration of magnetic transition in binary alloys. The main reason for such behaviour is the anisotropic lattice expansion in hydrogenated V–Fe and Zr–Fe alloys as well as the decomposition of paramagnetic Zr-rich intermetallic compounds in the aftermath of the strong electron affinity of hydrogen for zirconium. These trends give rise to growth of magnetic clusters of Fe atoms so strong that they can participate in the overall magnetic properties of the system under investigation.     

Low temperature thermal expansion and magnetostriction of TmCd

Thermal expansion measurements in various external magnetic fields confirm the recently found Jahn-Teller transition in TmCd at 3.16 K. The tetragonal strain ?₃ at T = 0 K is found to be 0.62 × 10^?3. From magnetostriction data we determine a coupling constant g₀² = 0.4 × 10^?3 K which is in good agreement with the value found from ultrasonic experiments. In order to explain our magnetostriction results in the cubic phase, g₀ has to be taken negative.     

Weak correction to the muon magnetic moment in a gauge model

The weak correction, a_μ^w, to the anomalous magnetic moment of the muon is calculated in an SU(2) ? U(1) ? U(1) gauge model of weak and electromagnetic interactions. The R_ξ gauge is used and Ward-Takahashi indentities are utilized eliminating all ξ-dependence before the loop integration is performed. a_μ^w,expt places no constraint on the mass of one of the neutral vector mesons, which may be arbitrarily small.