Study of the Insulating Magnetic Field in an Accelerating Ion Diode

The results of examination of the insulating magnetic field in an accelerating ion diode are presented. This field is produced in order to suppress the electron current and thus enhance the neutron yield of the D(d, n)³He nuclear reaction. The following two designs are discussed: a gas-filled diode with inertial electrostatic confinement of ions and a vacuum diode with a laser-plasma ion source and pulsed magnetic insulation. Although the insulating field of permanent magnets is highly nonuniform, it made it possible to extend the range of accelerating voltages to U = 200 kV and raise the neutron yield to Q = 10⁷ in the first design. The nonuniform field structure is less prominent in the device with pulsed magnetic insulation, which demonstrated efficient deuteron acceleration with currents up to 1 kA at U = 400 kV. The predicted neutron yield is as high as 109 neutrons/pulse.     

Photoconductivity of 2<Emphasis Type="Italic">D</Emphasis> electrons over helium in the presence of cyclotron pumping

Recent measurements of photoconductivity for 2D electrons at the helium surface in the presence of a magnetic field orthogonal to the 2D plane require a qualitative explanation, because of the very fact of its existence. Various scenarios of the effect are discussed, and arguments in favor of one of these—that which is associated with the emergence of thermoelectric power along a 2D charged system in a magnetic field under the effect of a spatially nonuniform external pumping—are presented. The corresponding nonuniform electron distribution δn_s (against the background of the uniform distribution) leads to the effect that is observed with the aid of Corbino disks and which consists in a change in the conductivity of the 2D system.     

Entanglement in Mixed-Spin (1/2, 3/2) Heisenberg XXZ Model with Dzyaloshinskii-Moriya Interaction

In this paper, the entanglement in a mixed-spin (1/2, 3/2) Heisenberg XXZ model with Dzyaloshinskii-Moriya (DM) interaction in an inhomogeneous external magnetic field is studied. We not only calculate the ground-state entanglement but also investigate the behaviors of quantum phase transition following the changes of DM interaction and nonuniform magnetic field. More importantly, we note that the DM interaction improves the critical magnetic field B _c , the critical temperature T _c and broadens the region of entanglement.     

Effect of the magnetic anisotropy energy distribution of MnSb clusters on spontaneous magnetization reversal of GaMnSb thin films

Temperature m(T) and time m(t) dependences of the magnetic moment of GaMnSb thin films with MnSb clusters have been measured. The m(t) dependences are straightened in semilogarithmic coordinates m(lnt). The temperature dependences of magnetic viscosity S(T) corresponding to the slope of straight lines m(lnt) have been studied. It have been demonstrated that the behavior of dependences S(T) is governed by the lognormal distribution of the magnetic anisotropy energy of MnSb clusters. It have been found that the behavior of dependences m(T) measured after the films were cooled in zero magnetic field and in magnetic field H = 10 kOe is also governed by the lognormal distribution of the magnetic anisotropy energy of MnSb clusters.     

Quantum Dense Coding About a Two-Qubit Heisenberg XYZ Model

By taking into account the nonuniform magnetic field, the quantum dense coding with thermal entangled states of a two-qubit anisotropic Heisenberg XYZ chain are investigated in detail. We mainly show the different properties about the dense coding capacity (χ) with the changes of different parameters. It is found that dense coding capacity χ can be enhanced by decreasing the magnetic field B, the degree of inhomogeneity b and temperature T, or increasing the coupling constant along z-axis J _z . In addition, we also find χ remains the stable value as the change of the anisotropy of the XY plane Δ in a certain temperature condition. Through studying different parameters effect on χ, it presents that we can properly turn the values of B, b, J _z , Δ or adjust the temperature T to obtain a valid dense coding capacity (χ satisfies χ > 1). Moreover, the temperature plays a key role in adjusting the value of dense coding capacity χ. The valid dense coding capacity could be always obtained in the lower temperature-limit case.     

Entanglement of Two Coupled Atoms in the Presence of a Time-Dependent External Magnetic Field

We study the problem of a time-dependent nonuniform magnetic field in the Heisenberg chain. We consider two cases: a single two-level atom and N-level atoms affecting by the magnetic field. We obtain the wave function and use it for calculating the expectation values of the dynamical operators, more precisely, the atomic inversion, in order to study the phenomena of revivals and collapses. Furthermore, we obtain the expectation value of other operators of the SU(2) group and discuss the phenomenon of squeezing. We show that the phase angle η and the detuning parameter δ are the most substantial parameters of the model under consideration.     

Commensurability effects in a Josephson tunnel junction in the field of an array of magnetic particles

Commensurability effects have been theoretically studied in a hybrid system consisting of a Josephson junction located in a nonuniform field induced by an array of magnetic particles. A periodic phase-difference distribution in the junction that is caused by the formation of a regular lattice of Abrikosov vortices generated by the magnetic field of the particles in superconducting electrodes is calculated. The dependence of the critical current through the junction I _c on the applied magnetic field H is shown to differ strongly from the conventional Fraunhofer diffraction pattern because of the periodic modulation of the Josephson phase difference created by the vortices. More specifically, the I _c(H) pattern contains additional resonance peaks, whose positions and heights depend on the parameters and magnetic state of the particles in the array. These specific features of the I _c(H) dependence are observed when the period of the Josephson current modulation by the field of the magnetic particles and the characteristic scale of the change in the phase difference by the applied magnetic field are commensurable. The conditions that determine the positions of the commensurability peaks are obtained, and they are found to agree well with experimental results.     

Magnetic field buoyancy in accretion disks of young stars

Buoyancy of the fossil magnetic field in the accretion disks of young stars is investigated. It is assumed that the Parker instability leads to the formation of slender flux tubes of toroidal magnetic field in the regions of effective magnetic field generation. Stationary solution of the induction equation is written in the form in which the buoyancy is treated as the additional mechanism of the magnetic flux escape. We calculate the fossil magnetic field intensity in the accretion disks of young T Tauri stars for the cases when radius of the magnetic flux tubes a _mft = 0.1H,0.5H or 1H, where H is the accretion disk height scale. Calculations show that the buoyancy limits toroidal magnetic field growth, so that its strength is comparable with the vertical magnetic field strength for the case a _mft = 0.1H.     

Self-similar distribution in “giant” magnetic flux creep

The problem of magnetic field penetration into the half-space is considered in parallel geometry in an external magnetic field increasing with time in accordance with the law B(0, t, τ₀ = B _{c 1} (1 + t/τ₀) ^m , m ≥ 0, t ≥ 0 (τ ₀ is the time of magnetic flux redistribution and B _{c 1} is the lower critical field). It is assumed that the flow of vortices is thermally activated in the “giant” creep mode (i.e., for weak pinning creep and high temperatures). A model equation is derived for describing the magnetic flux evolution. Analytic formulas are obtained for the depth and velocity of magnetic field penetration. It is shown that the giant creep regime is stable for 0 ≤ m ≤ 1/2.     

Nonperturbative phenomena in QCD at finite temperature in a magnetic field

The norperturbative QCD vacuum at finite temperature in a external magnetic field is studied. Equations that relate nonperturbative QCD condensates at finite temperature to the thermodynamic pressure at T ≠ 0 and H ≠ 0 are obtained, and low-energy theorems are derived. The free energy of the QCD vacuum in the hadronic phase at H ≠ 0 is calculated, and expressions for the quark and gluon condensates are obtained. Various limiting cases for the behavior of the condensates at low and high temperatures and in weak and strong magnetic fields are investigated. A new interesting phenomenon that consists in the freezing of the quark condensate by a magnetic field is found. The character of spontaneous chiral-symmetry breaking in finite-temperature QCD in a magnetic field is studied. For this purpose, the Gell-Mann-Oakes-Renner formula relating the pion mass M _π and the axial-vector coupling constant F _π to the quark condensate is derived at T ≠ 0 and H ≠ 0. It is shown that this formula preserves its form at finite temperature after taking into account a magnetic field—that is, no additional terms independent of T and H appear. Thus, the scheme of soft chiral-symmetry breaking remains unchanged. The quark-hadron phase transition in QCD in a magnetic field is studied. It is shown that the phase-transition temperature becomes lower than that in the case of zero magnetic field.     

The Langevin formula for describing the magnetization curve of a magnetic liquid

It has been shown that, at the initial stage of the magnetization curve, the magnetic susceptibility of magnetic liquid determined as χ = Mμ₀/B (M is the magnetization, B is the magnetic induction in a sample) obeys the Curie law, and the magnetic susceptibility determined as χ = M/H (H is the magnetic field intensity in a sample) obeys the Curie–Weiss law. Since the Curie law is a particular case of the Langevin dependence, it is assumed that an experimental magnetization curve is described by the Langevin formula with a Langevin parameter ξ = PB/kT, where P is the magnetic moment of a particle and T is the temperature. Experimental verification has shown that, at parameter ξ, the mean relative deviation between the values of M measured and calculated by the Langevin formula is 5%. This deviation can be accounted for by the influence of dispersion of the magnetic moments of nanoparticles.     

Effect of nonuniform mechanical stresses on the domain structure of iron borate

A magnetooptic method is used to study the effect of nonuniform radial mechanical stresses on the domain structure, magnetic susceptibility, and magnetic hysteresis loops of a FeBO₃ single crystal. When a magnetic field is applied in the basal plane of FeBO₃ along the stress vector, a system of tapered domains appears in the crystal during magnetization. These domains exist in a certain temperature-dependent field range H₀ ≤ H ≤ H _c . The appearance of a system of tapered domains is found to substantially affect the technical magnetization of a stressed crystal. The results obtained are discussed within the thermodynamic theory of a domain structure. A theoretical model used is shown to adequately describe the experimental temperature and field dependences of the ratio \({D \mathord{\left/ {\vphantom {D {\sqrt L }}} \right. \kern-\nulldelimiterspace} {\sqrt L }}\) (where D and L are the average width and length of a tapered domain, respectively). The calculated value of D is approximately 1.3 times smaller than the experimentally observed domain width.     

Magnetic catalysis of stability of quark matter in the Nambu-Jona-Lasinio model

The effect of an external magnetic field H on the stability of quark matter is studied on the basis of the Nambu-Jona-Lasinio model. It is shown that, at H = 0, droplets of quark matter are stable only in the case where the coupling constant G is greater than some value G_bag. If H ≠ 0, stable multiquark formations may exist even for G ≤ G_bag (magnetic catalysis of stability). For G > G_bag, a magnetic field facilitates the formation of stable quark matter.     

Anomalies in the Magnetic Susceptibility in the Second-Order Phase Transitions beyond the Curie Point

Taking into account the inexhaustible interest in studying the peculiarities of physical properties in the neighborhood of phase transitions and the growth of experimental investigations of cobalt fluoride, we have studied the peculiarities of magnetic susceptibility in the vicinity of the critical field H_C at which cobalt fluoride performs the second-order phase transition from the antiferromagnetic phase to the angular phase. It is discovered that in the magnetic field H ‖ C₄, the magnetic susceptibility becomes infinite at H → H_C. It is shown that as the magnetic field direction deviates from the C₄ axis, the magnetic susceptibility in the critical field H_C proves to be finite. It is also shown that the change in the magnetic susceptibility with the change in the magnetic field considerably decreases at extremely insignificant deviations of the field H from the C₄ axis. Since the calculations are performed in terms of the Landau theory of phase transitions, we pay attention to the similarity and difference between the obtained results and those in the vicinity of the Curie point obtained by using the Landau theory of phase transitions.     

Equilibrium and stability of the charged particles’ fluxes drifting crosswise to the strong magnetic field at the expense of the Hall charge separation

The current equilibrium is investigated, where the generation of the Hall electric field on the magnetic Debye radius r _B = B ₀/(4πen _e) is considered by the drifting of the relativistic electrons crosswise to the strong magnetic field. In this case, the electron propagation is possible at the distance d that is essentially larger than the electron radius of the backward reflection in the magnetic field r ₀ ? m _e v _z c/(eB ₀). The instability of the joint drift motion of ions and electrons is investigated for the frequency oscillation w much higher than the ion cyclotron frequency w _Bi and by 4π n _i m _i c ² ? B ₀ ² and (k · B ₀) = 0. It is shown that the resonance effects by the ion beam’s plasma frequency w ? kv ₀ = w _pi leads to the generation of the nonpotential perturbations with the characteristic increment Imw ～ 10^?1 ÷ 10^{? 2} w _pi. Estimates show that the instability, associated with the propagation of the high-energy ion beam through the strong magnetic field, can essentially be like the edge-localized mode in tokamaks.     

Composition-induced transition of spin-modulated structure into a uniform antiferromagnetic state in a Bi<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>La<Subscript>x</Subscript>FeO<Subscript>3</Subscript> system studied using <Superscript>57</Superscript>Fe NMR

By analyzing the NMR line shape, the transformation of a spatially spin-modulated magnetic structure in BiFeO₃ into an ordinary spatially uniform structure of the LaFeO₃ orthoferrite in Bi_1?xLa_xFeO₃ solid solutions is studied. The measurements are made using a spin-echo technique at temperatures of 77 and 4.2 K on ceramics with compositions x=0, 0.1, 0.2, 0.61, 0.9, and 1.0 enriched by the ⁵⁷Fe isotope. It is shown that the spin-modulated structure disappears near the concentration x=0.2, which corresponds, according to the published data, to the phase transition with a change in the unit-cell symmetry R3c → C222. A formula is obtained describing the NMR absorption line shape for the spin-modulated structure with account of local line-width. Theoretical spectra adequately describe the evolution of the experimental spectrum in the concentration range 0≤x≤0.2. Highly nonuniform local magnetic fields in the intermediate compositions make it impossible to detect NMR signals in a sample with x=0.61. A uniform magnetic structure characterized by a single narrow line arises in the range of existence of a phase with the symmetry Pnma typical of the pure orthoferrite LaFeO₃.     

On Cluster Properties of Classical Ferromagnets in an External Magnetic Field

Correlation functions of ferromagnetic spin systems satisfying a Lee-Yang property are studied. It is shown that, for classical systems in a non-vanishing uniform external magnetic field h, the connected correlation functions decay exponentially in the distances between the spins, i.e., the inverse correlation length (“mass gap”), m(h), is strictly positive. Our proof is very short and transparent and is valid for complex values of the external magnetic field h, provided that \(\mathrm {Re}\, h \not = 0\). It implies a mean-field lower bound on m(h), as \(h \searrow 0\), first established by Lebowitz and Penrose for the Ising model. Our arguments also apply to some quantum spin systems.     

Self-similar magnetic structures and magnetic flux “Giant” creep

The penetration of a magnetic flux into a type-II high-T _c superconductor occupying the half-space x > 0 is considered. At the superconductor surface, the magnetic field amplitude increases in accordance with the law b(0, t) = b ₀(1 + t)^m (in dimensionless coordinates), where m > 0. The velocity of penetration of vortices is determined in the regime of thermally activated magnetic flux flow: v = v ₀exp?ub;?(U _0/T )(1-b?b/?x)?ub;, where U ₀ is the effective pinning energy and T is the thermal energy of excited vortex filaments (or their bundles). magnetic flux “Giant” creep (for which U ₀/T? 1) is considered. The model Navier-Stokes equation is derived with nonlinear “viscosity” v ∝ U ₀/T and convection velocity v _f ∝ (1 ? U ₀/T). It is shown that motion of vortices is of the diffusion type for j → 0 (j is the current density). For finite current densities 0 < j < j _c, magnetic flux convection takes place, leading to an increase in the amplitude and depth of penetration of the magnetic field into the superconductor. It is shown that the solution to the model equation is finite at each instant (i.e., the magnetic flux penetrates to a finite depth). The penetration depth x _eff ^A (t) ∝ (1 + t)^{(1 + m/2)/2} of the magnetic field in the superconductor and the velocity of the wavefront, which increases linearly in exponent m, exponentially in temperature T, and decreases upon an increase in the effective pinning barrier, are determined. A distinguishing feature of the solutions is their self-similarity; i.e., dissipative magnetic structures emerging in the case of giant creep are invariant to transformations b(x, t) = β^m b(t/β, x/β^{(1 + m/2)/2}), where β > 0.     

Various Quantum Correlations in Two-Qubit Two-Axis Spin Squeezing Model in Thermal Equilibrium under an External Magnetic Field

This paper investigates the influence of the spin squeezing parameter γ, the external magnetic field B and the temperature T on the concurrence (C), the quantum discord (QD), and the geometric quantum discord (GQD) in the two-qubit two-axis spin squeezing model in thermal equilibrium under an external magnetic field. The results show that the spin squeezing parameter γ has a positive effect on all three correlations. When the system is in the ground state, the external magnetic field B has a weakening effect on the three types of quantum correlations. Particularly, the spin squeezing parameter can be used to alleviate the destructive effect of the magnetic field on the geometric quantum discord. At a relatively high temperature, the externally applied magnetic field B helps enhance the quantum discord (QD). Further, the quantum discord is more robust than concurrence, and thus is more suitable for use as a quantum resource in information processing.     

Size Dependences of the Magnetic Properties of Superconducting Lead–Porous Glass Nanostructures

Superconducting structures Pb–PG formed by filling a porous glass matrix with the lead from melt under pressure have been investigated. Samples with characteristic pore structure diameters of d ≈ 7, 3, and 2 nm have been studied. It has been found that the critical temperature of the superconducting transition in the samples under study is similar to the corresponding value T_c ≈ 7.2 K for bulk lead. At the same time, it has been observed that the critical magnetic field of the nanocomposites, which attains H_c(T = 0 K) ≈ 165 kOe for Pb–PG (3 nm), exceeds several times the value H_c(0) = 803 Oe for bulk lead. The low-temperature magnetic- field dependences of magnetic moment M(H) contain quasi-periodic flux jumps, which vanish with a decrease in the lead nanostructure diameter. A qualitative model of the observed effects is considered.