What is spin-magnetic moment of electron?

We investigate the problem about what the spin-magnetic moment is. The magnetic moment of the Dirac electron in the frame along z-axis is evaluated. This is identified with the spin-magnetic moment of the electron, because there is not any z-component of magnetic moment caused by orbital angular momentum in our frame. The correct value of the spin-magnetic moment and the correct ratio of the spin-magnetic moment to the spin (i.e. g=2) are obtained explicitly. In deriving them, the negative energy solutions of the Dirac equation perform essential roles. We find that the transition current from a positive energy state to a negative energy state causes spin-magnetic moment of the electrons in vacuum. This fact implies that the ratio of the spin-magnetic moment to the spin may change depending on the environments. For example, it may have different values in materials.     

Classical Electromagnetic Interaction of a Point Charge and a Magnetic Moment: Considerations Related to the Aharonov–Bohm Phase Shift

A fundamentally new understanding of the classical electromagnetic interaction of a point charge and a magnetic dipole moment through order v ² /c ² is suggested. This relativistic analysis connects together hidden momentum in magnets, Solem's strange polarization of the classical hydrogen atom, and the Aharonov–Bohm phase shift. First we review the predictions following from the traditional particle-on-a-frictionless-rigid-ring model for a magnetic moment. This model, which is not relativistic to order v ² /c ² , does reveal a connection between the electric field of the point charge and hidden momentum in the magnetic moment; however, the electric field back at the point charge due to the Faraday-induced changing magnetic moment is of order 1/c ⁴ and hence is negligible in a 1/c ² analysis. Next we use a relativistic magnetic moment model consisting of many superimposed classical hydrogen atoms (and anti-atoms) interacting through the Darwin Lagrangian with an external charge but not with each other. The analysis of Solem regarding the strange polarization of the classical hydrogen atom is seen to give a fundamentally different mechanism for the electric field of the passing charge to change the magnetic moment. The changing magnetic moment leads to an electric force back at the point charge which (i) is of order 1/c ² , (ii) depends upon the magnetic dipole moment, changing sign with the dipole moment, (iii) is odd in the charge q of the passing charge, and (iv) reverses sign for charges passing on opposite sides of the magnetic moment. Using the insight gained from this relativistic model and the analogy of a point charge outside a conductor, we suggest that a realistic multi-particle magnetic moment involves a changing magnetic moment which keeps the electromagnetic field momentum constant. This means also that the magnetic moment does not allow a significant shift in its internal center of energy. This criterion also implies that the Lorentz forces on the charged particle and on the point charge are equal and opposite and that the center of energy of each moves according to Newton's second law F=Ma where F is exactly the Lorentz force. Finally, we note that the results and suggestion given here are precisely what are needed to explain both the Aharonov–Bohm phase shift and the Aharonov–Casher phase shift as arising from classical electromagnetic forces. Such an explanation reinstates the traditional semiclassical connection between classical and quantum phenomena for magnetic moment systems.     

The structural instabilities in ferronematic based on liquid crystal with negative diamagnetic susceptibility anisotropy

The studied ferronematic is a nematic liquid crystal (ZLI1695) of low negative anisotropy of the diamagnetic susceptibility (χ_a<0) doped with the magnetic particles Fe₃O₄. Structural instabilities are interpreted within Burylov and Raikher's theory. The high magnetic fields were oriented perpendicular (Freedericksz transition) or parallel to the initial director. Using capacitance measurements the Freedericksz threshold magnetic field of the ferronematic B_FN, and the critical magnetic field B_max, at which the initial parallel orientation between the director and the magnetic moment of magnetic particles breaks down, have been determined. The values of these quantities have been used to estimate the surface density of the anchoring energy W of liquid crystal molecules on the surface of the magnetic particles. The obtained values indicate a soft anchoring of the liquid crystal on the magnetic particles with a preferred parallel orientation of the magnetic moment of magnetic particles and the director.     

Uniform spin wave modes in antiferromagnetic nanoparticles with uncompensated moments

In magnetic nanoparticles the uniform precession (q = 0 spin wave) mode gives the predominant contribution to the magnetic excitations. We have calculated the energy of the uniform mode in antiferromagnetic nanoparticles with uncompensated magnetic moments, using the coherent potential approximation. In the presence of uncompensated moments, an antiferromagnetic nanoparticle must be considered as a kind of a ferrimagnet. Two magnetic anisotropy terms are considered, a planar term confining the spins to the basal plane, and an axial term determining an easy axis in this plane. Excitation energies are calculated for various combinations of these two anisotropy terms, ranging from the simple uniaxial case to the planar case with a strong out-of-plane anisotropy. In the simple uniaxial case, the uncompensated moment has a large influence on the excitation energy, but in the planar case it is much less important. The calculations explain recent neutron scattering measurements on nanoparticles of antiferromagnetic α-Fe₂O₃ and NiO.     

Multiply-charged magnetoexcitons in low-dimensional structures

The frequencies and intensities of absorption lines of a “hole + Nelectrons” complex in a magnetic field are found. The motion of all particles is assumed to be two-dimensional, and the electron and hole quantum wells are assumed to be spatially separated. It is shown how Kohn’s theorem can be extended to the case of a system with a finite total mass. The energy of a N-electron complex in a quantum ring oscillates as a function of the magnetic flux with a period that depends on N and the ratio of the masses. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 6, 423–427 (25 September 1997)     

Magnetic response of a two-dimensional degenerate electron gas in nanostructures with cylindrical symmetry

An investigation is made of the magnetic response of nanostructures with cylindrical symmetry located in a longitudinal magnetic field. Analytic expressions are obtained for the magnetic moment of the nanostructures, cylinders and bracelets. It is shown that the magnetic moment describes Aharonov-Bohm oscillations. The profile of the oscillations and the position of the oscillation maxima are studied. In the limit T→0 the curves of the magnetic response as a function of the magnetic field flux contain “beak”-shaped kinks, and the positions of the points at which these kinks occur are determined. The temperature dependence of the magnetic response is studied and the influence of the spin-magnetic interaction on the magnetic response of the nanostructures is examined. It is shown that this interaction destroys the periodicity of the magnetic response with respect to flux and gives rise to a monotonic term in the response. Zh. éksp. Teor. Fiz. 115, 1450–1462 (April 1999)     

Neutron diffraction study of the magnetic ordering in the series R 2 BaNiO 5 (R = Rare Earth)

A neutron diffraction study, as a function of temperature, of the title compounds is presented. The whole family (space group Immm, a ≈ 3.8?, b ≈ 5.8?, c ≈ 11.3?) is structurally characterised by the presence of flattened NiO₆ octahedra that form chains along the a-axis, giving rise to a strong Ni-O-Ni antiferromagnetic interaction. Whereas for Y-compound only strong 1D correlations exist above 1.5 K, presenting the Haldane gap characteristic of 1D AF chain with integer spin, 3D AF ordering is established simultaneously for both R and Ni sublattices at temperatures depending on the rare earth size and magnetic moment. The magnetic structures of R₂BaNiO₅ ( R = Nd, Tb, Dy, Ho, Er and Tm) have been determined and refined as a function of temperature. The whole family orders with a magnetic structure characterised by the temperature-independent propagation vector = (1/2, 0, 1/2). At 1.5 K the directions of the magnetic moments differ because of the different anisotropy of the rare earth ions. Except for Tm and Yb (which does not order above 1.5 K), the magnetic moment of the R³⁺ cations are close to the free-ion value. The magnetic moment of Ni²⁺ is around 1.4 , the strong reduction with respect to the free-ion value is probably due to a combination of low-dimensional quantum effects and covalency. The thermal evolution of the magnetic structures from T _N down to 1.5 K is studied in detail. A smooth re-orientation, governed by the magnetic anisotropy of R³⁺, seems to occur below and very close to T _N in some of these compounds: the Ni moment rotates from nearly parallel to the a-axis toward the c-axis following the R moments. We demonstrate that for setting up the 3D magnetic ordering the R-R exchange interactions cannot be neglected. Received 19 July 2001     

Influence of an isolated magnetic impurity on an unconventional superconducting state

The effect of the moment of a magnetic impurity on the order parameter of an unconventional superconductor is examined. The coupling of the magnetic moment to the order parameter induces a locally time-reversal symmetry-breaking state which generates a magnetic field distribution in the vicinity of the impurity. The magnetic field can cause precession of the magnetic moment. The case of a spin polarized muon injected into the superconductor is discussed. Zh. éksp. Teor. Fiz. 112, 304–312 (July 1997) Published in English in the original Russian journal. Reproduced here with stylistic changes by the Translation Editor.     

Effects of magnetic structure distortion near a μ + meson in μSR spectroscopy

Possible effects of strong local anisotropy in the vicinity of a μ meson occupying a rare-earth metal interstitial site are considered. The distortion of the magnetic structure and the corresponding contribution to the dipolar field at the muon are calculated. A threshold-type change of the dipolar field depending on the local anisotropy or external magnetic field is predicted for the case where the direction toward the muon is perpendicular to the magnetic moment of one in the ions. The possibility of existence of two strengths of the dipolar field for the ferromagnetic phases of Dy and Tb, and of its abrupt change depending on the direction of the magnetic moment of the plane is predicted for helical antiferromagnetic structures. Fiz. Tverd. Tela (St. Petersburg) 40, 1298–1304 (July 1998)     

First-principles calculations to investigate half-metallic ferromagnetism in Zn0.50Ti0.50S alloy by using DFT + U calculations

ABSTRACT

The spin-polarized structural, electronic and magnetic properties of the Ti-doped zincblende ZnS compound at x?=?0.50 (Zn_0.50Ti_0.50S alloy) have been investigated by employing the first-principles full-potential linearised augmented plane wave with local orbitals (FP-L/APW?+?lo) method within the frame-work of spin-polarized density functional theory (spin-DFT). For the treating of the structural properties, the electronic exchange and correlation (XC) functional was defined by generalised gradient approximation (GGA), whereas both GGA and GGA?+?U approximations are applied to treat and to compare the electronic and magnetic properties (U is the Coulomb repulsion energy). It has been confirmed that the ferromagnetic (FM) state of this alloy is found the most stable phase; however, all the equilibrium lattice parameters such as; lattice constant (a₀), bulk modulus (B₀), and its first-pressure derivative (B′) are computed in all paramagnetic, ferromagnetic and anti-ferromagnetic phases. The calculations of electronic properties unveil the perfect half-metallic character in the tetragonal Zn_0.50Ti_0.50S system. The computed magnetic properties reveal that the total magnetic moment is mainly originated from the transition element (TM) of Ti. Moreover, we have found that the p-d hybridisation is the paramount responsible for the reduction of the magnetic moment of TM from its free space charge value and for the production of minor magnetic moments on the nonmagnetic Zn and S sites.     

Symmetry analysis of the interplay between local moment anisotropies and propagation vectors in the borocarbides

Representational analysis is used to examine the interplay between Fermi surface nesting and local moment effects in the formation of the magnetically ordered states of the rare-earth nickel borocarbides, RNi₂B₂C. We derive compatibility tables for the propagation wavevector k, the local moment anisotropy and the ordered moment direction μ _k for materials with this tetragonal crystal structure. The magnetic structures observed in the rare-earth nickel borocarbides are discussed in this context.     

Energy Losses of a Charged Particle due to Excitation of Helicons in Plasma-Like Media

We study the energy lost by a particle moving along the helical line in a static magnetic field due to Vavilov–Cherenkov radiation of volume and surface helicons. It is found that the energy losses related to excitation of volume helicons are equivalent to the energy losses of a magnetic moment created due to the charge rotation. The magnetic moment moves at a constant velocity along the magnetic field. It is shown that collisionless damping of volume helicons in plasmas is based on the Cherenkov radiation of magnetic moment. Radiation of surface helicons by a particle does not correspond to the energy losses of a moving magnetic moment. This is related to the fact that not only magnetic (H) waves but also electric (E) waves contribute to the excitation of surface helicons, which leads to an increase in the energy losses of a particle.     

Anisotropy of a hole magnetic polaron in a semimagnetic semiconductor

It is shown that the shape of a hole magnetic polaron in a semimagnetic semiconductor with the sphalerite structure is anisotropic: The polaron is strongly oblate in the direction of its magnetic moment. When the anisotropy of the hole spectrum is taken into account, the properties of the polaron depend on the orientation of its spin with respect to the crystallographic axes. Specifically, the binding energy of the polaron is maximum when the spin is oriented along the [111] axis. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 3, 209–213 (10 February 1996)     

Local Thermodynamical Stability of Fermion Lattice Systems

We study the magnetic moment of neutral atoms in large magnetic fields. Asymptotic formulas for the energy exist with high precision in different regions depending on how large the nuclear charge Z is compared to the magnetic field strength B. All these formulas take the splitting of the kinetic energy into Landau levels as the principal feature and then treat the electric potential as a perturbation. We prove that these approximate formulas predict correctly'(to highest order) the total magnetic moment of the atom. The proof of this fact relies on a 'virial theorem' for Coulomb systems in a constant magnetic field.     

High-order perturbation theory for the hydrogen atom in a magnetic field

The states of a hydrogen atom with principal quantum numbers n⩽3 in a constant uniform magnetic field ℋ are studied. Coefficients in the expansion of the energy of these states in powers of ℋ² up to the 75th order are obtained. Series for the energies of the states and the wave functions are summed to values of ℋ on the order of the atomic magnetic field. A generalization of the moment method upon which these calculations are based can be used in other cases in which a hydrogen atom is perturbed by a potential with a polynomial dependence on the coordinates. Zh. éksp. Teor. Fiz. 113, 550–562 (February 1998)     

Structural and magnetic properties of Fe<Subscript>m</Subscript>Y<Subscript>n</Subscript> (m + n = 7, Y = Ru,Rh, Pd,and Pt) nanoalloys

The structural and magnetic properties of the small binary clusters Fe _m Y _n (with m + n = 7, Y = Ru, Rh, Pd, Pt) were studied through extensive ab initio calculations, by means of the fully unconstrained version of the density-functional method, as implemented in the SIESTA code, within the generalized gradient approximation. The lowest energy state geometries, the chemical ordering, and the electronic and the magnetic structures were calculated. We found that the lowest energy geometrical structures for the pure Ru, Rh, Pd, Pt, and Fe heptamers, are a cube without an apex, a triangular prism capped on a square face, a decahedron, a side capped double square, and a decahedron, respectively. Starting from these geometries of the pure element heptamers, we followed the changes in the geometric structure as a function of the chemical composition. We analyzed all the different chemical arrangements, which depend on the particular geometry, and magnetic moment orientations, in the whole range of compositions. In general, there are important modifications to the magnetic moment of the Y atoms as soon as one of them is substituted by an Fe atom in the cluster. In contrast, under the same circumstances, the Fe magnetic moment takes values larger than 3 μ _B and keeps almost this value, insensitive to the structure, composition and chemical order of the system.     

Structural phase transition in FeBO under pressure

Using the density functional theory the structural and magnetic properties of iron borate under high pressure have been studied. At about P = 22.7 GPa a first order phase transition to the phase described by the same space group Rc has been found. The phase transition is accompanied by a 9% volume change of the unit cell, a four times decrease of the magnetic moment on Fe, an increase of the charge density at Fe, and a disappearance of the energy gap in the electronic density of states. Received 21 September 2001 and Received in final form 6 January 2002 Published online 6 June 2002     

Helical instability of a straight Abrikosov vortex in an anisotropic superconductor

Because of attraction of the parallel currents forming an Abrikosov vortex, the vortex energy per unit length decreases, under bending of the vortex, by a quantity proportional to the square of the curvature. Solving the London equation in an approximation allowing for this effect makes it possible to calculate the energy of an Abrikosov vortex in the form of a helix whose length and pitch are much larger than the correlation length, whose curvature is small compared to the reciprocal London length, and whose slope in relation to an axis coinciding with the direction in which the vortex energy is the highest is also small. When the anisotropy is large, which is characteristic of high-T _c superconductors, the energy of such an Abrikosov vortex is lower than that of a straight Abrikosov vortex. Certain consequences of the fact that the Abrikosov vortices in a high-T _c superconductor are helical are discussed. Among these is a phase transition that breaks the symmetry between Abrikosov vortices shaped like right-and left-hand helixes in relation to the magnetic field. Zh. éksp. Teor. Fiz. 111, 1869–1878 (May 1997)     

Calculation of nuclear magnetic shieldings: infinite-order Foldy–Wouthuysen transformation

A scheme for calculating nuclear magnetic shieldings using the infinite-order Foldy–Wouthuysen (FW) transformation proposed by Barysz and Sadlej (BS) is presented. The nuclear magnetic shieldings of hydrogen halides are calculated by three variant BS schemes; a double finite perturbation method for the external magnetic flux density (B ₀) and the nuclear magnetic dipole moment (? μ _M ) (BS/FPT-2), a single finite perturbation method for B ₀ with analytical differentiation of energy with respect to (? μ _M ) (BS/FPT-1), and an approximate analytical differentiation method with respect to both B ₀ and μ _M (BS/CHF). Although the BS/FPT-2 method is exact theoretically, the actual computation for heavy nuclei includes large error due to reduction of the number of significant figures. The BS/FPT-1 and BS/CHF approaches, on the other hand, yield reasonable values for all of the shieldings. Although several results could not be obtained by the BS/FPT-2 method, no serious contradictions were recognized among these three results. From a comparison of our results with values in the literature, our shieldings for the halogen nuclei are lower than those determined by the four-component relativistic random phase approximation (4-RPA), but the reason for this is not obvious.     

A quantitative determination of magnetic fluctuations in CuGeO3

A polarised neutron scattering investigation has been carried out on a powder sample of CuGeO₃ within the temperature range of 1.5 K to 600 K. The magnetic scattering has been separated from all other contributions by using polarised neutrons and polarisation analysis and placed onto an absolute scale. At low temperatures the long wavelength components of the paramagnetic response are suppressed consistent with the formation of Cu dimers in which the magnetic moments are correlated antiferromagnetically. This form of the scattering persists to temperatures well above the dimerisation temperature T _sp ∼ 14 K. However as the temperature is raised the intensity of the long wavelength spin fluctuations increases and above ∼150 K they are the dominant feature in the wave vector dependence of the response. At all temperatures the observed scattering extrapolates smoothly to the Q = 0 value given by the uniform susceptibility. Consequently the thermal variation of the uniform susceptibility arises from the evolution of the long wavelength magnetic fluctuations. At large wave vectors the energy dependence of the scattering revealed that the response occurs below 16 meV in agreement with the reported maximum magnetic excitation energy at the zone boundary in the ground state. However the total magnetic scattering is significantly less than that expected for a local moment system suggesting that the spectrum of thermal and quantum fluctuations overlap. Received 30 May 2000 and Received in final form 22 March 2001