Triplet superfluidity in neutron matter with Skyrme forces at subnuclear and supranuclear densities in a strong magnetic field

Within a generalized non-relativistic Fermi-liquid approach we have found general analytical formulae for phase-transition temperatures T _c,1(n, H) and T _c,2(n, H) (which are nonlinear functions of density, n, and linear of magnetic field, H) for phase transitions in spatially uniform, dense, pure neutron matter from normal to superfluid states with spin-triplet p-wave pairing (similar to anisotropic superfluid phases ³He - A₁ and ³He - A₂) in steady and homogeneous sufficiently strong magnetic field (but |μ _n |H ≪ E _c < ɛ _F (n), where μ _n is the magnetic dipole moment of a neutron, E _c is the cutoff energy and ɛ _F (n)is the Fermi energy in neutron matter). General formulae for T _c,1,2(n,H) are valid for arbitrary parameterization of the effective Skyrme forces in neutron matter. We have used for definiteness the so-called SLy2, Gs and RATP parameterizations of the Skyrme forces with different exponents in their power dependence on density n (at sub- and supranuclear densities) from the interval 0.7 n ₀ ≲ n < n _c (Skyrme)< 2 n ₀, where n ₀ =0.17 fm⁻³ is the nuclear density and n _c (Skyrme)is the the critical density of the ferromagnetic instability in superfluid neutron matter. These phase transitions might exist in the liquid outer core of magnetized neutron stars.     

First order spin flop transition in yttrium iron garnet (YIG)

We have studied the field dependence of the sublattice magnetization of ferrimagnetic yttrium iron garnet (YIG) using neutron scattering. In contrast to the macroscopic spontaneous magnetization that shows the normal field dependence of a soft ferromagnet (sudden saturation at the demagnetization field and no hysteresis) in neutron scattering a field induced first order spin flop transition with considerable hysteresis is observed at a critical field of H_c∼580 G (external field). Considering that with neutron scattering the antiferromagnetic component of ∼4/5 of the total moment is detected preferentially while in the macroscopic magnetization samples the ferromagnetic component of ∼1/5 exclusively it becomes clear that ferromagnetic and antiferromagnetic component have a completely independent field (and temperature) dependence. This indicates that the two magnetic structures have to be viewed as two weakly coupled order parameters. In the zero field ground state the moment orientations of the two ordering structures are orthogonal. Only for fields H₀>H_c a nearly collinear ferrimagnetic order is established by the field.     

Thermodynamic functions of degenerate magnetized electron gas

The Fermi energy, pressure, internal energy, entropy, and heat capacity of completely degenerate relativistic electron gas are calculated by numerical methods. It is shown that the maximum admissible magnetic field on the order of 10⁹ G in white dwarfs increases the pressure by a factor of 1.06 in the central region, where the electron concentration is ∼10³³ cm⁻³, while the equilibrium radius increases by approximately a factor of 1.03, which obviously cannot be observed experimentally. A magnetic field of ∼10⁸ G or lower has no effect on the pressure and other thermodynamic functions. It is also shown that the contribution of degenerate electron gas to the total pressure in neutron stars is negligible compared to that of neutron gas even in magnetic fields with a maximum induction ∼10¹⁷ G possible in neutron stars. The neutron beta-decay forbiddeness conditions in a superstrong magnetic field are formulated. It is assumed that small neutron stars have such magnetic fields and that pulsars with small periods are the most probable objects that can have super-strong magnetic fields.     

Phase transition to the state with nonzero average helicity in dense neutron matter

The possibility of the appearance of the states with a nonzero average helicity in neutron matter is studied in the model with the Skyrme effective interaction. By providing the analysis of the self-consistent equations at zero temperature, it is shown that neutron matter with the Skyrme BSk18 effective force undergoes at high densities a phase transition to the state in which the degeneracy with respect to helicity of neutrons is spontaneously removed.     

Neutron Matter Properties Using Skyrme Interaction

The purpose of the present work is to extend earlier nuclear matter calculations to study the properties of neutron matter. The binding energy per particle, symmetry energy, single particle potential, effective mass, and magnetic susceptibility are calculated using a modified Skyrme interaction. These are calculated as a function of the Fermi momentum k_f in the range 0 < k_f < 2 fm^?1. Two sets of the interaction parameters are obtained by fitting the interaction parameters using the available information on neutron matter. Relativistic corrections to the order 1/c² are also calculated. The relativistic corrections are very small and they increase as k_f is increased.     

Magneto-optical studies on ferromagnetic stripe domains in K2CuF4

Ferromagnetic stripe domains are observed in K₂CuF₄ below T_c=6.19 K by use of Faraday rotation (FR). They are about 4 μm wide and lie parallel to the c-planes. They are due to a very small intraplanar anisotropy field as a result of the minute orthorhombic lattice distortion observed by Hidaka and Walker. A stripe domain model, including closure domains for complete demagnetization, is in accordance with the experimental observations if the anisotropy fields H^out_A=1.4kOe and Hⁱⁿ_A=0.1 Oe are introduced. Long-range order, presumably induced by interplanar exchange, is a accompanied by 3d Ising critical behavior as verified by critical exponents obtained from different magneto-optical measurements (α=0.07, β=0.33 and δ=4.6). Changes of the domain structure, of the ac-plane FR, and of the ac-plane linear birefringence due to a transverse magnetic field H 6 a are discussed. A non-vanishing internal field is preceded by a domain instability. The compatibility of the domain structure with neutron scattering results of Hirakawa and Yoshizawa is discussed.     

Effect of an external magnetic field and a trapped magnetic flux on the current-voltage characteristics of a granular high-temperature superconductor YBa2Cu3O7−δ

A comparative study of the current-voltage characteristics of the high-temperature ceramic superconductor YBa₂Cu₃O_～6.95 at T = 77.3 K is performed over wide ranges of external magnetic fields H _ext and “treatment” fields H _treat. It is found that the field dependences of the parameters a and j _c involved in the exponential equation E = a(j ? j _c)^v describing the current-voltage characteristics depend substantially on the method used for applying the magnetic field, whereas the exponent v ～ 2 depends on neither the method of application nor on the magnetic field strength. The field dependence of the trapped magnetic field H _trap is determined.     

High-frequency absorption of the dynamic mixed state in the surface superconductivity region

We analyze the absorption of a high-frequency electromagnetic field in the type II superconductor Pb_0.8In_0.2 in magnetic fields H _c2 < H < H _c3. The absorption component proportional to the rate of variation of the external magnetic field is detected. We assume that this absorption component is associated with the dynamic mixed state of the superconducting shell containing 2D magnetic flux vortices (Kulik vortices). The motion of these vortices under the action of the critical current ensures the required difference between the external and internal magnetic inductions of the superconducting shell upon a change in the external magnetic field. This model correctly describes the observed behavior of absorption of rf electromagnetic radiation.     

Hydrogen-like atom in a superstrong magnetic field: Photon emission and relativistic energy level shift

Following our previous work, additional arguments are presented that in superstrong magnetic fields B ? (Zα)² B ₀, B ₀ = m ² c ³/e? ≈ 4.41 × 10¹³ G, the Dirac equation and the Schrödinger equation for an electron in the nucleus field following from it become spatially one-dimensional with the only z coordinate along the magnetic field, “Dirac” spinors become two-component, while the 2 × 2 matrices operate in the {0; 3} subspace. Based on the obtained solution of the Dirac equation and the known solution of the “onedimensional” Schrödinger equation by ordinary QED methods extrapolated to the {0; 3} subspace, the probability of photon emission by a “one-dimensional” hydrogen-like atom is calculated, which, for example, for the Lyman-alpha line differs almost twice from the probability in the “three-dimensional” case. Similarly, despite the coincidence of nonrelativistic energy levels, the calculated relativistic corrections of the order of (Zα)⁴ substantially differ from corrections in the absence of a magnetic field. A conclusion is made that, by analyzing the hydrogen emission spectrum and emission spectra at all, we can judge in principle about the presence or absence of superstrong magnetic fields in the vicinity of magnetars (neutron stars and probably brown dwarfs). Possible prospects of applying the proposed method for calculations of multielectron atoms are pointed out and the possibility of a more reliable determination of the presence of superstrong magnetic fields in magnetars by this method is considered.     

Magnetoresistance of single Co nanowires

Polycrystalline single Co nanowires are prepared by electron beam lithography on GaAs substrates at room temperature. The width of the Co nanowires is varied between 150 and 4000 nm. Magnetoresistance measurements are carried out in a temperature range between 1.5 and 45 K applying magnetic fields μ₀H up to 4.5 T parallel and perpendicular to the current direction. The in plane (longitudinal) magnetoresistance (MR) shows pronounced features at magnetic fields H_c (coercive fields) indicating the magnetization reversal process. From the MR-curves we determined H_c as a function of the angle α between current and field direction (from in plane to out of plane) and of the width w of the Co nanowires. The H_c=H_c(α,w) behavior allows to discuss the reversal process in more detail.     

Relativistic theory of inverse beta-decay of polarized neutron in strong magnetic field

The relativistic theory of the inverse beta-decay of polarized neutron,ν _e +n → > p +e ^-, in strong magnetic field is developed. For the proton wave function we use the exact solution of the Dirac equation in the magnetic filed that enables us to account exactly for effects of the proton momentum quantization in the magnetic field and also for the proton recoil motion. The effect of nucleons anomalous magnetic moments in strong magnetic fields is also discussed. We examine the cross-section for different energies and directions of propagation of the initial neutrino accounting for neutron polarization. It is shown that in the super-strong magnetic field the totally polarized neutron matter is transparent for neutrinos propagating antiparallel to the direction of polarization. The developed relativistic approach can be used for calculations of cross-sections of the other URCA processes in strong magnetic fields.     

Isoscalar and isovector nuclear matter properties and neutron skin thickness

Isoscalar and isovector nuclear matter properties are investigated in the Skyrme Hartree-Fock (SHF) and the relativistic mean field (RMF) models. The Skyrme parameters are related analytically to the isoscalar and the isovector nuclear matter properties of the Hamiltonian density. Linear correlations are found among the isovector nuclear matter properties of the Hamiltonian density in both the SHF and the RMF models. We also discovered that the correlations between the isovector properties and the incompressibility K show a singularity at the critical incompressibility K_c=306 MeV. It is shown that the neutron skin thickness gives crucial information about not only for the neutron EOS but also about the isovector nuclear matter properties and about the parameterization of Skyrme interaction. Charge exchange spin-dipole (SD) excitations are proposed to determine the neutron skin thickness model independently.     

Magnetoresistance hysteresis of granular YBa2Cu3O7−δ high-temperature superconductor in weak magnetic fields

The variation of the transverse magnetoresistance of YBa₂Cu₃O_～6.95 high-temperature superconducting ceramic with external magnetic field intensity H _ext first increasing from zero to ～500 Oe (Δρ⁺ / ρ_{273 K}) and then decreasing from about 500 Oe to zero (Δρ^? / ρ_{273 K}) is studied for transport current densities varying from j/j _c ≈ 0.01 to ≈0.99 (where j _c is the critical current density in the absence of the magnetic field) at 77.3 K. It is found that the field dependence of the magnetoresistance of YBa₂Cu₃O_～6.95 high-temperature superconductor is characterized by pronounced hysteresis, the difference Δρ⁺ / ρ_{273 K} ? Δρ^? / ρ_{273 K} increasing with j/j _c. As j/j _c grows, the effective critical fields of Josephson weak links, H _c2J , and the lower critical fields of superconducting grains, H _c1A , decline. When field H _ext rises, the critical fields are lower than when H _ext diminishes: H _c2J ⁺ < H _c2J ^? and H _c1A ⁺ < H _c1A ^? .     

Angular dependence of the upper critical field in Bi2Sr2CuO6+δ

The angular dependence of the upper critical magnetic field was investigated in a wide range of temperatures in very high-quality Bi₂Sr₂CuO_6+δ single crystals with critical temperature T _c (midpoint) ? 9 K in magnetic fields up to 28 T. Although the typical value of the normal state resistivity ratio ρ_c/ρ_ab≈10⁴, the anisotropy ratio H _c2∥ab/H _c2⊥ab of the upper critical fields is much smaller and shows an unexpected temperature dependence. A model based on strong anisotropy and small transparency between superconducting layers is proposed.     

Dense quark matter conductivity in ultra-intense magnetic field

Heavy-ion collisions generate a huge magnetic field of the order of 10¹⁸ G for a duration of about 0.2 fm/c. This time may become an order of magnitude longer if the electrical conductivity of quark matter is large. We calculate the conductivity in the regime of high density and show that contrary to naive expectations it only weakly depends on the magnetic field.     

NDMAP: the best material to study the Haldane's prediction

As predicted by Haldane, spin, S=1 one-dimensional (1D) Heisenberg antiferromagnet (HAF) has an energy gap between the singlet ground state and first excited triplet. On application of magnetic field, the triplet state Zeeman splits and the energy of one of the triplet state becomes zero at a critical field, H_c. Above H_c the system recovers magnetism. Then, we expect that a quasi-1D HAF will show a magnetic long-range ordering (LRO) at low temperatures due to the inter-chain coupling. This field-induced LRO has not been observed before due to complication of the crystal structure in the materials studied so far and/or technical difficulty.From a heat capacity measurement on a single crystal of an S=1 quasi-Q1D HAF, Ni(C₅H₁₄N₂)₂N₃(PF₆), we found an anomaly at a temperature in finite fields indicating a field-induced phase transition. A magnetic LRO is confirmed by a neutron diffraction measurement on the same sample. The temperature versus magnetic field phase diagram of this compound is constructed and discussed.     

Non-planar spin texture driven dissipation in a ferromagnet-superconductor bilayer

We report the observation of a pronounced dip in the in-plane magnetic field (H_∥) dependence of the critical current density J_c(H) and a peak in resistance R(H) of a NbN-HoNi₅ bilayer at temperatures below the magnetic ordering temperature (T_Curie ≈ 3.5 K) of HoNi₅, which is lower than the onset temperature (≈9 K) of superconductivity in the NbN layer. The extrema in J_c(H) and R(H) appear at fields much below the upper critical field of NbN. We attribute these features to a coupling between localized out-of-plane moments present in the magnetic film and Pearl vortices of the superconducting layer. A spin re-orientation transition of the localized moments by H_∥ breaks this coupling, leading to the observed excess dissipation.     

Energy values for the H+2 ion in superstrong magnetic fields using the adiabatic approximation

Energy values, equilibrium internuclear separations, and zero-point energies of nuclear vibrations parallel to the magnetic field are calculated for the lowest states of the H⁺₂ ion in magnetic fields B?10⁶ T (characteristic of neutron stars) using numerical wave functions that are products of Landau states and arbitrary z-dependent functions, thus improving on previous estimates of variational or LCAO type, which have been obtained in the high-field regime.     

Neutron skin thickness and nuclear matter properties

Linear correlations are found among the isovector nuclear matter properties in both the Skyrme-Hartree-Fock (SHF) and the relativistic mean-field (RMF) models. In addition, we found a kind of correlation between the isovector nuclear matter properties and the incompressibility in the SHF model. The Skyrme parameters are related analytically to nuclear matter properties with the Thomas—Fermi approximation. By using a linear correlation between the neutron skin thickness and the pressure of the neutron matter in the SHF model, we show that the neutron skin thickness of ²⁰⁸Pb gives crucial information about not only the neutron equation of state but also the isovector nuclear matter properties and the parametrization of Skyrme interaction. The text was submitted by the authors in English.