Contribution of spin-orbit interaction to the magnetic susceptibility of interacting electrons in metals

The effect of spin-orbit interaction on the magnetic susceptibility of metals has been investigated using a pseudopotential formalism. The orbital spin and spin-orbit contributions to the magnetic susceptibility of Zn and Cd have been calculated. An important feature is that the spin-orbit contribution is diamagnetic and is of the same order of magnitude as orbital contribution in the case of Zn and Cd.     

Electronic structure and magnetic susceptibility of monoclinic α-plutonium

The electronic structure of the α-phase of plutonium has been calculated by the band methods with allowance for the spin-orbit interaction and Coulomb correlations in the complete matrix form (the LDA + U + SO method). The strong spin-orbit interaction of the 5 f electrons is manifested in the splitting of the calculated density of the 5f states, which makes a small contribution at the Fermi level on the order of the contribution from the 6d states. Using the results of the ab initio calculations, the spin and orbit contributions to the magnetic susceptibility of α-plutonium have been determined. Along with the impurity contribution, they describe well the experimental data on the susceptibility of this plutonium phase to a temperature of 300 K.     

Effect of spin-orbit scattering on the magnetic and superconducting properties of nearly ferromagnetic metals: application to granular Pt

We calculate the effect of scattering on the static, exchange enhanced, spin susceptibility and show that, in particular, spin-orbit scattering leads to a reduction of the giant moments and spin glass freezing temperature due to dilute magnetic impurities. The harmful spin fluctuation contribution to the intragrain pairing interaction is strongly reduced opening the way for BCS superconductivity. We are thus able to explain the superconducting and magnetic properties recently observed in granular Pt as being due to scattering effects in single small grains.     

Theory of anisotropic diamagnetism, local moment magnetization and carrier spin-polarization in Pb1−x Eu x Te

We present theoretical analyses of anisotropic lattice diamagnetism, magnetization due to magnetic ions and carrier spin-polarization in the diluted magnetic semiconductor, Pb_1-x Eu _x Te. The lattice diamagnetism results from orbital susceptibility due to inter band effects and spin-orbit contributions. The spin-orbit contribution is found to be dominant. However, both the contributions show pronounced anisotropy. With increase in x, the diamagnetism decreases. We consider contributions from randomly distributed isolated magnetic ions and clusters of pairs and triads for the local moment magnetization. The isolated magnetic-ion contribution is the dominant one.We calculate the magnetization for two typical magnetic ion concentrations: x=0.03 and x=0.06. Temperature dependence of the magnetization is also considered. Apart from lattice and localized magnetic ions, the carrier contribution to the spin-density is also calculated for a carrier density of p=10¹⁸ cm⁻³. the relative spin-density of carriers increases with increase in the magnetic field strength and magnetic ion concentration. The agreement with experiment where available is reasonably good.     

Einfluß einer Quasiteilchen-Spinbahnwechselwirkung auf die magnetischen Momente leichter Atomkerne

Using Migdal's theory of interacting quasiparticles, the influence of a two-body spin-orbit interaction in addition to the spin-spin interaction on magnetic moments of nuclei was investigated in the mass regionA=11 toA=65. The coupling constants of the spin-orbit interaction were determined from spin-orbit splittings of single particle energies, and those of the spin-spin interaction were adjusted by fitting magnetic moments. The constants of the spin-spin interaction were found to be dependent on the mass value. The inclusion of the spin-orbit interaction led to a better agreement of theoretical and experimental magnetic moments of light nuclei. The spin-orbit contribution was averaged 7% over all nuclei, but reached 20–30% for some of them.     

Transport and thermodynamic properties of a 2DEG in the presence of tilted magnetic field: the influence of Dresselhauss interaction

The effect of Dresselhauss spin-orbit coupling on transport and thermodynamic properties of a non-interacting two-dimensional electron gas (2DEG) is investigated. The Hamiltonian used also includes a tilted magnetic field and a Rashba spin-orbit interaction. The Dresselhauss spin-orbit interaction, likewise the Rashba spin-orbit interaction, introduces a beating pattern in the conductivity tensor and in the magnetization along the field direction. A method to estimate the contribution of the Rashba and Dresselhauss interactions to the beating pattern is given using the periodicity of the beating patterns.     

First-principles theory of magnetically induced ferroelectricity in TbMnO<Subscript>3</Subscript>

We study the polarization induced via spin-orbit interaction by a magnetic cycloidal order in orthorhombic TbMnO₃ using first-principle methods. The case of magnetic spiral lying in the b-c plane is analyzed, in which the pure electronic contribution to the polarization is shown to be small. We focus our attention on the lattice-mediated contribution, and study it’s dependence on the Coulomb interaction parameter U in the LDA+U method and on the wave-vector of the spin spiral. The role of the spin-orbit interaction on different sites is also analyzed.     

Magnetic instability in superconductivity

Possible magnetic ordering in the magnetic superconductors is investigated by calculating the wave number dependent susceptibility χ(q) in the superconducting state for (i) clean superconductor, (ii-1) dirty superconductor with weak spin-orbit scattering and (ii-2) dirty superconductor with strong spin-orbit scattering. The wave vector q_max which maximizes χ(q) is estimated for each cases and it is pointed out that the possible magnetic ordering in superconducting state is the spin density wave with the wave number q_max.     

三角对称晶场中6 S(3d5)态离子零场分裂参量的微观起源

基于完全对角化方法(complete diagonalization method, CDM), 研究了⁶ S(3d⁵)态离子在三角晶场(包括C_3v,D₃,D_3d点群对称晶场)中零场分裂(zero-field splitting, ZFS)参量D和(a-F)的微观起源.研究中除了考虑研究者通常考虑的SO(spin-orbit)磁相互作用外,同 关键词： 6 S(3d⁵)态离子')" href="#">⁶ S(3d⁵)态离子 零场分裂参量 磁相互作用 完全对角化方法     

耦合电磁场对石墨烯量子磁振荡的影响

我们研究了包含自旋轨道耦合与杂质散射在内的石墨烯量子磁振荡对外加电磁场的响应.我们发现,石墨烯中自旋轨道耦合、电磁场以及边界共同修正了朗道能谱,且当电场与磁场比值超过某一临界值时,量子磁振荡会突然消失,这与非相对论二维电子气的情况显著不同.这种现象可以通过朗道量子化轨道由封闭转化为开放的半经典理论来解释.此外,我们还发现杂质散射和温度的共同作用会使得磁振荡振幅衰减.我们的结果可用于分析石墨烯及其类似结构(硅烯、锗烯、锡烯等)的费米能级与朗道能谱的相互作用,进而探测自旋轨道耦合引起的能隙.     

Effect of spin-flip processes on the Pauli susceptibility

The reduction of the Pauli susceptibility due to a perturbing Hamiltonian which allows for spin-flip processes is calculated. The results are applied to the spin-orbit coupling in liquid metals, and the exchange interaction in magnetic metals at high temperatures and near the Curie point. The corrections are small.     

Thermodynamic behaviour of Rashba quantum dot in the presence of magnetic field

The thermodynamic properties of an In Sb quantum dot have been investigated in the presence of Rashba spin–orbit interaction and a static magnetic field. The energy spectrum and wave-functions for the system are obtained by solving the Schrodinger wave-equation analytically. These energy levels are employed to calculate the specific heat, entropy,magnetization and susceptibility of the quantum dot system using canonical formalism. It is observed that the system is susceptible to maximum heat absorption at a particular value of magnetic field which depends on the Rashba coupling parameter as well as the temperature. The variation of specific heat shows a Schottky-like anomaly in the low temperature limit and rapidly converges to the value of 2kB with the further increase in temperature. The entropy of the quantum dot is found to be inversely proportional to the magnetic field but has a direct variation with temperature. The substantial effect of Rashba spin–orbit interaction on the magnetic properties of quantum dot is observed at low values of magnetic field and temperature.     

自旋轨道耦合和磁场对准一维铁磁/半导体/铁磁系统中电子输运性质的影响

利用传递矩阵方法，我们计算了自旋轨道耦合和磁场对准一维铁磁/半导体/铁磁系统中电子输运性质的影响。计算结果发现，透射系数的振幅随磁场增加而增大。在反铁磁排列时，即使在磁场作用下，上、下自旋电子具有相同的透射系数。与不加磁场时的情况相反，在一定的磁场和耦合强度时，铁磁排列中，上自旋电子的透射系数大于下自旋电子的，而且出现了自旋反转。     

Many-body theory of magnetization of Bloch electrons in the presence of spin-orbit interactions

We derive a theory of magnetization of an interacting electron system in the presence of a periodic potential, spin-orbit interaction and an applied magnetic field in the paramagnetic limits. Starting from a thermodynamic potential, which includes both the quasi-particle and correlation contributions, we show that modifications brought about by the electron-electron interactions for the magnetization in the quasi-particle approximation is precisely cancelled by the contributions due to electron correlations.This is in contrast to the explicit many-body effects seen in case of the magnetic susceptibility and the Knight-shift. The magnetization is expressed as a product of the spin-density and the effective g-factor, mainly due to the spin-orbit interaction. We show the importance of self-energy corrections on the single-particle energy spectrum by considering a variant of the Hubbard Hamiltonian in momentum space.     

Origin of magnetic anisotropy of Gd metal

Using first-principles theory, we have calculated the energy of Gd as a function of spin direction, theta, between the c and a axes and found good agreement with experiment for both the total magnetic anisotropy energy and its angular dependence. The calculated low temperature direction of the magnetic moment lies at an angle of 20 degrees to the c axis. The calculated magnetic anisotropy energy of Gd metal is due to a unique mechanism involving a contribution of 7.5 microeV from the classical dipole-dipole interaction between spins plus a contribution of 16 microeV due to the spin-orbit interaction of the conduction electrons. The 4f spin polarizes the conduction electrons via exchange interaction, which transfers the magnetic anisotropy of the conduction electrons to the 4f spin.     

Study of electronic and magnetic properties of MnS layers

<正>Self-consistent ab initio calculations,based on the density functional theory(DFT) and using the full potential linear augmented plane wave(FLAPW) method,are performed to investigate both electronic and magnetic properties of the MnS layers.Polarized spin and spin-orbit coupling are included in the calculations within the framework of the antiferromagnetic state between two adjacent Mn layers.Magnetic moments considered to lie along axes are computed. Obtained data from ab initio calculations are used as input data for the high temperature series expansion(HTSE) calculations to compute other magnetic parameters.The zero-field high temperature static susceptibility series of the spin-4.39 nearest-neighbour Heisenberg model on centred face cubic(FCC) and lattices is thoroughly analysed by a power series coherent anomaly method(CAM).The exchange interactions between the magnetic atoms,the Neel temperature,and the critical exponent associated with the magnetic susceptibility are obtained for the MnS layer.     

The contribution of the one-pion exchange potential in the frame of a Hartree-method by using one-particle wave functions without definite parity

In order to calculate the spin-orbit splitting and the magnetic moments of nuclei a Hartree-method was carried out with the assumption of parity-mixed one-particle wave functions. Together with a phenomenological determined scalar potential there was used a pseudoscalar potential derived as the contribution of the one-pion exchange potential selfconsistently determined. By using this method of parity-mixing, one obtains a spin-orbit splitting and also magnetic moments, which lie automatically between the Schmidt-lines in good agreement with the experimental values. Only the pion-nucleon coupling constant was used as a parameter in this selfconsistent method. It is shown that we obtain a smaller coupling constant when using the exact solution of this problem than by using perturbation theory. This effective coupling constant is of the same order of magnitude as the one obtained from the scattering data.     

Photoinduced precession of magnetization in ferromagnetic (Ga,Mn)As

Precession of magnetization induced by pulsed optical excitation is observed in a ferromagnetic semiconductor (Ga,Mn)As by time-resolved magneto-optical measurements. It appears as complicated oscillations of a polarization plane of linearly polarized probe pulses, but is reproduced by gyromagnetic theory incorporating an impulsive change in an effective magnetic field due to a change in the magnetic anisotropy. The shape of the impulse suggests a significant nonthermal contribution of photogenerated carriers to the change in anisotropy through spin-orbit interaction.     

Singular temperature dependence of the equation of state of superconductors with spin–orbit interaction in the low-temperature region

The equation of state is investigated for a thin superconducting film in a longitudinal magnetic field and with strong spin-orbit interaction at the critical point. As a first step, the state with the maximal value of the magnetic field for a given value of spin–orbit interaction at T = 0 is chosen. This state is investigated in the low-temperature region. The temperature contribution to the equation of state is weakly singular.     

Effects of applied magnetic field on the infrared transitions between hydrogenic states in a corrugated quantum well

The magnetic field induced transition energies between the ground and excited states of a donor impurity in a Ga_1-xAl_xAs /Ga_1-yAl_yAs corrugated quantum well is reported. The calculations are performed by the variational method based on a two-parametric trial wave function, in the framework of the single band effective mass approximation. The effect of nonparabolicity of the conduction band is considered through the energy dependent effective mass. The effect of magnetic field on the spin-orbit interaction on the electron magnetization and the magnetic susceptibility is discussed. The diamagnetic susceptibility using Hellmann-Feynman theorem is calculated for the ground and excited states of the donor. The transition lines lie in the optical range for a strong magnetic field. The results are compared with the other existing available literature.