Zeeman Term Research Articles

Coexistence of antiferromagnetism and superconductivity withint-Jmodel with strong correlations and nonzero spin polarization

The coexistence of antiferromagnetism with superconductivity is studied theoretically within the t-J model with the Zeeman term included. The strong electron correlations are accounted for by means of the extended Gutzwiller projection method within a statistically-consistent approach proposed recently. The phase diagram on the band filling - magnetic field plane is shown, and subsequently the system properties are analyzed for the fixed band filling n=0.97. In this regime, the results reflect principal qualitative features observed recently in selected heavy fermion systems. Namely, (i) with the increasing magnetic field the system evolves from coexisting antiferromagnetic-superconducting phase, through antiferromagnetic phase, towards polarized paramagnetic state, and (ii) the onset of superconducting order suppresses partly the staggered moment. The superconducting gap has both the spin-singlet and the staggered-triplet components, a direct consequence of a coexistence of the superconducting state with antiferromagnetism.

Mechanisms of Cr and H incorporation in stishovite determined by single-crystal EPR spectroscopy and DFT calculations

Synthetic stishovite before and after electron- and γ-ray irradiation has been investigated by single-crystal electron paramagnetic resonance (EPR) spectroscopy for the first time. Room-temperature single-crystal EPR spectra of as-is stishovite reveal two high-spin (S = 3/2) Cr 3+ centers: one with D 2 h symmetry and another of triclinic symmetry. Quantitatively determined spin Hamiltonian parameters, including matrices g , D , and A ( 53 Cr) and high-spin Zeeman term BS 3 , suggest that the D 2 h center represents a substitutional Cr 3+ ion at the Si site without an immediate charge compensator. The triclinic center, which is characterized by a well-resolved 1 H superhyperfine structure, also arises from a substitutional Cr 3+ ion at the Si site but has an H + charge compensator bonded to one of the four equatorial oxygen atoms. The magnitude and orientation of the 1 H superhyperfine structure yield the location of the H atom at (0.46, 0.12, 0). These structural models for Cr and H in stishovite also have been corroborated by periodic density functional theory (DFT) calculations using the Vienna ab initio simulation package (VASP), with 2 × 2 × 4 supercells, plane-wave basis sets and the projector augmented wave (PAW) potentials. In addition, 85 K EPR spectra of irradiated stishovite show that the two Cr 3+ centers are both converted to an S = 1/2 Cr 5+ center characterized by two 29 Si superhyperfine structures arising from interactions with two nearest and eight second-nearest Si atoms, respectively. The spin Hamiltonian parameters of this Cr 5+ center provide further support for the location of the two Cr 3+ centers at the Si site.

Magnetic properties of 2D nano-islands II: Ising spin model with out-of-plane magnetic field

An Ising effective field theory model is presented to calculate the magnetic properties of 2D nano-islands on a nonmagnetic substrate, subject to an externally out-of-plane applied magnetic field. The system Hamiltonian contains nearest neighbor exchange interactions, single-atom magnetic anisotropies, and the Zeeman term. The calculations yield, in particular, the single site spin correlations, the magnetizations, and the isothermal susceptibilities, for the core and periphery domains of the nano-island. The choice of a spin S=1 for the atoms of the system permits the analysis of local spin fluctuations via the single site spin correlations. We investigate in this respect the effects due to the different magnetocrystalline anisotropies and reduced dimensionalities, for the core and periphery domains, and in particular the critical influence of the applied magnetic field. Detailed theoretical results are presented for the square and hexagonal lattice symmetries, with numerical applications for the 2D monolayer Co nano-islands on a Pt substrate. It is shown that the remarkable differences between the magnetic properties of the core and periphery domains in zero field are washed out when an out-of-plane field is applied. The applied field also provokes critical discontinuities for the spin correlations and magnetization reversals, for the core and periphery domains, which are especially evident for the hexagonal lattice nano-island in the range of fields of interest. The discontinuities and magnetization reversals occur over elementary temperature widths, and shift to lower temperatures with increasing field. The field-dependant isothermal susceptibilities show new features very different from those for the susceptibilities in zero field. The present Ising model does not show any blocking temperature transition to superparamagnetism.

A Theoretical Study on the Spin-Hamiltonian Parameters for Samarium(III) Ion in Potassium Yttrium Tungstate Crystal

The nine spin-Hamiltonian (SH) parameters (g-factors gi and hyperfine structure constants 147Ai and 149Ai for 147Sm3+ and 149Sm3+ isotopes, where i = x, y, z) for the Samarium(III) ion in monoclinic potassium yttrium tungstate [KY(WO4)2] crystal are calculated within the rhombic symmetry approximation from a diagonalization of energy matrix method. Differing from the conventional diagonalization method used in the calculation of crystal-field levels, in the present method, we attach the Zeeman (or magnetic) and hyperfine interaction terms to the conventional Hamiltonian and construct the 66×66 energy matrix for 4f5 ions in rhombic crystal field and under an external magnetic field by considering all the ground-term multiplets 4HJ. The calculated results are in reasonable agreement with the experimental values

Defect model and spin-Hamiltonian parameters for the tetragonal Nd 3+ center in the tetragonal phase of SrTiO 3 crystal

The spin-Hamiltonian parameters ( g factors g ∥, g ⊥ and hyperfine structure constants 143A ∥, 143A ⊥, 145A ∥ and 145A ⊥) of the tetragonal Nd 3+ center in the low-temperature ( T≈4.2 K) tetragonal phase of SrTiO 3 are calculated from a diagonalization (of energy matrix) method. In the method, the Zeeman and hyperfine interaction terms are attached to the conventional Hamiltonian and a 52×52 energy matrix concerning the ground term 4 H J ( J=9/2, 11/2, 13/2, 15/2) is constructed. The Nd 3+ center is attributed to Nd 3+ occupying the 12-fold coordinated Sr 2+ site in SrTiO 3. Differing from the defect model assumed in the previous paper that the tetragonal distortion of this Nd 3+ center is due to the association of one interstitial oxygen ion at a nearest neighborhood of Nd 3+ and the Nd 3+ displacement Δ z along C 4 axis, we suggest that it is due to the distortion of SrTiO 3 lattice in the tetragonal phase. The calculated g factors g ∥ and g ⊥ show good agreement with the experimental values, suggesting that our defect model of Nd 3+ center in SrTiO 3 is reasonable. The experimental hyperfine structure constants were not reported and so our calculated results remain to be checked by EPR experiment.

Parametric properties of the electron spin relaxation due to spin-orbit interaction in InAs quantum dots

To deal with the Hamiltonian model in InAs QDs with a single electron, we’ve taken the SO interaction as a perturbation term, calculated the SO matrix elements under Fock-Darwin eigenfunction which are used for second order corrections on the energies and wave functions, and considered the influence of new energy levels on g factor and effective mass m*. The expression of phonon-assisted electron spin relaxation rate Γ in InAs QDs is deduced, which shows different dependences on confined potential frequency ω0, temperature T, vertical height z0 and magnetic field B. Among them, temperature for the electron spin relaxation plays a dominant role, followed by lateral confinement potential frequency, magnetic field and the vertical height, in order of importance. (1) Growth of ω0, which corresponds to the decrease of the effective transverse size d in InAs QDs, suppresses the increase of the rate Γ. (2) The temperature T affects the rate Γ evidently, which will reduce the inhibition of ω0 on Γ. With increase of the temperature from 1 K to 7 K, the spin inversion relaxation rate grows explosively from 103 s－1 to 108 s－1. (3) The rate Γ decreases with the growth of the vertical height z0 and have the order of magnitude 100－103 s-1 at T=1 K, whereas the influence of the temperature increase (at T=6 K) on the rate will gradually exceed that of the height growth. (4) At different frequencies ω0 all curves of the rate Γ versus magnetic field B have a peak that almost appears at the same field, which is attributed to the contribution of the Zeeman term H ^ Z exceeding that of H ^ SO since there is a considerable g factor in InAs material.

Spin-Hamiltonian parameters and defect structure for the rhombic Dy 3+ center in AgCl crystal

Based on the defect model that the rhombic Dy 3+ center in AgCl crystal is formed by substitutional Dy 3+ ion associated with two nearest Ag + vacancies ( V Ag) along the 〈1 1 0〉 and 〈 1 ¯ 1 ¯ 0 〉 axes owing to charge compensation, the spin-Hamiltonian parameters ( g factors g i and hyperfine structure constants 161 A i and 163 A i , where i = x, y, z) of this rhombic Dy 3+ center are calculated from a diagonalization (of energy matrix) method. In the method, the Zeeman (or magnetic) and hyperfine interaction terms are attached to the classical Hamiltonian used in the calculation of crystal-field energy levels and a 66 × 66 energy matrix concerning this Hamiltonian is constructed by taking all the ground-term multiplets 6 H J ( J = 15/2, 13/2, 11/2, 9/2, 7/2, 5/2) into account. The calculated results ( g factors g i and average | A ¯ ( 161 D y 3 + ) | and | A ¯ ( 163 D y 3 + ) | ) are in reasonable agreement with the experimental values. From the calculations, the above defect model of rhombic Dy 3+ center is confirmed, the defect structure of this Dy 3+ center (characterized by the displacement of Cl − ligand caused by V Ag) is obtained and the components of hyperfine structure constants A i ( 161Dy 3+) and A i ( 163Dy 3+) are predicted. The results are discussed.

A study of the spin-Hamiltonian parameters for the trigonal Sm 3+ center in La 2Mg 3(NO 3) 12·24H 2O crystal

This paper reports a theoretical calculation of spin-Hamiltonian parameters ( g factors g //, g ⊥ and hyperfine structure constants 147 A //, 147 A ⊥, 149 A //, 149 A ⊥) for 147Sm 3+ and 149Sm 3+ isotopes in the trigonal La 3+ site of La 2Mg 3(NO 3) 12·24H 2O crystal from a diagonalization (of energy matrix) method. In the method, the Hamiltonian concerning the energy matrix includes the Zeeman and hyperfine interaction terms and so there is no perturbation calculation in it. The crystal-field parameters in the energy matrix are calculated using the superposition model, in which the structural data of 12-fold coordinated site rather than those of the incorrect 6-fold coordinated site given in the previous paper are applied. The calculated results are in reasonable agreement with the experimental results. The results are discussed.

Enhancement of the spin gap in fully occupied two-dimensional Landau levels

Polarization-resolved magnetoluminescence, together with simultaneous magnetotransport measurements, have been performed on a two-dimensional electron gas (2DEG) confined in CdTe quantum well in order to determine the spin splitting of fully occupied electronic Landau levels, as a function of the magnetic field (arbitrary Landau-level filling factors) and temperature. The spin splitting, extracted from the energy separation of the ${\ensuremath{\sigma}}^{+}$ and ${\ensuremath{\sigma}}^{\ensuremath{-}}$ transitions, is composed of the ordinary Zeeman term and a many-body contribution which is shown to be driven by the spin polarization of the 2DEG. It is argued that both these contributions result in a simple, rigid shift of Landau-level ladders with opposite spins.

Antilinear spectral symmetry and the vortex zero modes in topological insulators and graphene

We construct the general extension of the four-dimensional Jackiw-Rossi-Dirac Hamiltonian that preserves the antilinear reflection symmetry between the positive- and negative-energy eigenstates. Among other systems, the resulting Hamiltonian describes the $s$-wave superconducting vortex at the surface of the topological insulator, at a finite chemical potential, and in the presence of both Zeeman and orbital couplings to the external magnetic field. Here we find that the bound zero mode exists only when the Zeeman term is below a critical value. Other physical realizations pertaining to graphene are considered, and some novel zero-energy wave functions are analytically computed.

Interface roughness influence on exchange bias effect in La2/3Ca1/3MnO3/La1/3Ca2/3MnO3 bilayers

A Monte Carlo simulation study of La2/3Ca1/3MnO3/La1/3Ca2/3MnO3 bilayers exchange bias (EB) properties by using a classical Heisenberg model and Monte Carlo method with Metropolis algorithm is addressed. Samples were built atom-by-atom in order to resemble the real roughness. In this model, several contributions included nearest neighbors exchange interactions; two different interface couplings, magnetocrystalline anisotropy and Zeeman term, were considered. Here, an influence of the relaxation steps on the interface roughness is present. Our study focuses on the influence of interface roughness on hysteresis loops, particularly EB field (Hex) and coercive force (Hc). Results reveal that Hex and Hc decrease as the interface roughness increases.

Investigations of the spin-Hamiltonian parameters for Yb3+ in the tetragonal phase of SrTiO3 crystal

The spin-Hamiltonian parameters (g factors, , , and hyperfine structure constants, , ) for Yb3+ at the 12-fold coordinated Sr2+ site of tetragonal SrTiO3 crystal at T ≈ 2 and 50 K were calculated using the completed diagonalization (of the energy matrix) method (CDM). Differing from the conventional CDM, the Hamiltonian concerning the energy matrix in this CDM contains the Zeeman and hyperfine interaction terms and so the spin-Hamiltonian parameters can be calculated directly from CDM. The crystal parameters used in the energy matrix are calculated from the superposition model, in which the tetragonal distortions and hence the order parameters φ at both temperatures are applied. From the calculations, the spin-Hamiltonian parameters at both temperatures are explained reasonably and the signs of hyperfine structure constants for the 171Yb3+ and 173Yb3+ isotopes in SrTiO3 are suggested. The results are discussed.

Spin edge states in two-dimensional electron systems in the presence of Zeeman effect

We study the spin edge states, induced by the combined effect of Bychkov-Rashba spinorbit and Zeeman interactions or of Dresselhaus spin-orbit and Zeeman interactions in a twodimensional electron system, exposed to a perpendicular quantizing magnetic field and restricted by a hard-wall confining potential. We derive an exact analytical formula for the dispersion relations of spin edge states and analyze their energy spectrum versus the momentum and the magnetic field. We calculate the average spin components and the average transverse position of electron. It is shown that by removing the spin degeneracy, spin-orbit interaction splits the spin edge states not only in the energy but also induces their spatial separation. Depending on the type of spin-orbit coupling and the principal quantum number, the Zeeman term in the combination with spin-orbit interaction increases or decreases essentially the splitting of bulk Landau levels while it has a weak influence on the spin edge states.

Spin‐Hamiltonian parameters for Dy3+ ion at the trigonal 12‐fold coordinated La3+ site of La2Mg3(NO3)12·24H2O

AbstractThe spin‐Hamiltonian parameters (g factors g‖, g⊥ and hyperfine structure constants 161A‖, 161A⊥, 163A‖, 163A⊥) for 161Dy3+ and 161Dy3+ isotopes in the trigonal 12‐fold coordinated La3+ site of La2Mg3(NO3)12·24H2O crystal are calculated from a diagonalization (of energy matrix) method. In the method, the Zeeman and hyperfine interaction terms are added to the conventional Hamiltonian used in the studies of crystal‐field energy levels, and a 66×66 energy matrix concerning the ground multiplet 6H15/2 and the first to fifth excited multiplets 6H13/2, 6H11/2, 6H9/2, 6H7/2 and 6H5/2 are applied. The calculated results are discussed. (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

A theoretical investigation of the spin-Hamiltonian parameters for Dy 3+ ion in CaWO 4 crystal

The spin-Hamiltonian parameters, g factors g ∥ and g ⊥ and hyperfine structure constants 161 A ∥, 161 A ⊥, 163 A ∥ and 163 A ⊥, for Dy 3+ ion at the tetragonal (S 4) Ca 2+ site of CaWO 4 crystal are calculated from a diagonalization (of energy matrix) method. In the method, the Zeeman (or magnetic) and hyperfine interaction terms are included in the Hamiltonian, and the 66×66 energy matrix (note: the crystal-field energy levels can also be obtained by diagonalizing the matrix) corresponding to the ground-term states 6 H J (where J=15/2, 13/2, 11/2, 9/2, 7/2 and 5/2) for 4f 9 ion in tetragonal crystal field and under an external magnetic field is established. In the matrix, the free-ion parameters are taken as the mean values obtained for Dy 3+ ions in many crystals and the crystal-field parameters B kq are those obtained from the optical spectra of CaWO 4:Dy 3+. The calculated results are close to the experimental values.

Photo‐EPR and magneto‐optical spectroscopy of iron centres in ZnO

AbstractZnO has attracted increasing interest as promising material for optoelectronics and spintronics. Magnetic properties of ZnO can be controlled by doping with transition metal ions among which Fe3+ is one of the interesting candidates. We report on the properties of Fe3+ centres in hydrothermally and chemical vapour transport grown ZnO single crystals investigated by photo‐electron paramagnetic resonance (EPR) and optical spectroscopy. Detailed magneto‐optical studies of Zeeman components of spin‐forbidden electric dipole transitions 4T1(G) → 6A1(6S) of Fe3+ centre in ZnO reveal the trigonal symmetry of fine structure of lowest Γ8 (4T1) excited state. The studies were performed in external magnetic fields up to 10 T and in the temperature range from 2 to 30 K. The energy positions of the Zeeman components at 8 T were measured as a function of the direction of applied magnetic field in $(1\bar {2}10)$ and (0001) planes. The detailed check of the angular variation of Zeeman lines shows two magnetically non‐equivalent Fe3+ centres. These special features were accounted by contribution of higher rank Zeeman terms of dimension BJ3. The photo‐generated EPR spectra of trigonal Fe3+ centres were detected in hydrothermally grown ZnO single crystals in addition to three types of charge compensated iron centres presented in these samples in the dark conditions.

Studies of the EPR parameters and defect models for three Er 3+ impurity centers in ThO 2 crystals

The electron paramagnetic resonance (EPR) parameters ( g factors and hyperfine structure constants of the ground state, and g factors of the first excited state) of three (one cubic and two trigonal) Er 3+ centers in fluoride-type ThO 2 crystal are studied from a diagonalization (of energy matrix) method. In the method, the Zeeman and hyperfine interaction terms are added to the classical Hamiltonian, and a 52 × 52 energy matrix concerning the ground multiplet 4I 15/2 and the first to third excited multiplets 4I 13/2, 4I 11/2 and 4I 9/2 is established for a 4f 11 ion in trigonal crystal field and under an external magnetic field. From the studies, the EPR parameters for three Er 3+ centers in ThO 2 are reasonably explained, the defect models for the two trigonal Er 3+ centers suggested in the previous paper are confirmed and the defect structures of the two trigonal centers are obtained. The results are discussed.

Comparative study of theoretical methods for non-equilibrium quantum transport

We present a detailed comparison of three different methods designed to tackle non-equilibrium quantum transport, namely the functional renormalization group (fRG), the time-dependent density matrix renormalization group (tDMRG) and the iterative summation of real-time path integrals (ISPI). For the non-equilibrium single-impurity Anderson model (including a Zeeman term at the impurity site), we demonstrate that the three methods are in quantitative agreement over a wide range of parameters at the particle–hole symmetric point as well as in the mixed-valence regime. We further compare these techniques with two quantum Monte Carlo approaches and the time-dependent numerical renormalization group method.

Theoretical calculations of the spin-Hamiltonian parameters for the tetragonal Dy3+ center in HfSiO4 crystal

The spin-Hamiltonian parameters (g factors g(parallel to), g(perpendicular to) and hyperfine structure constants (161)A(parallel to), (161)A(perpendicular to), (163)A(parallel to), (163)A(perpendicular to)) for Dy(3+) at the tetragonal H(f)(4+) site of H(f)SiO(4) crystal are calculated from the diagonalization (of energy matrix) method. In the method, we add the Zeeman (or magnetic) and hyperfine interaction terms to the conventional Hamiltonian used in the calculations of crystal-field energy levels. The 66 X 66 energy matrix concerning the new Hamiltonian is established by considering the ground multiplet (6)H(15/2) and the first to fifth excited multiplets (6)H(J) (where J=13/2, 11/2,9/2, 7/2 and 5/2), and the crystal-field parameters in the energy matrix are calculated from the superposition model. From the calculations, the spin-Hamiltonian parameters of H(f)SiO(4):Dy(3+) are explained reasonably and the signs of hyperfine structure constants for (161)Dy(3+) and (161)Dy(3+) isotopes in H(f)SiO(4) are suggested. The results are discussed. (C) 2010 Elsevier B.V. All rights reserved.

Magnetic field effects on the NiO magnon spectra

The effect of an external magnetic field on the eight antiferromagnetic resonance (AFMR) modes of NiO has been studied experimentally using Brillouin light scattering. The results are reproduced by a model that includes the effects of exchange, dipolar coupling, a small cubic anisotropy, and Zeeman terms. Magnetic fields up to 7 T were applied along several NiO crystalline directions. The agreement between theory and experiment provides additional proof that the model, recently introduced to explain the existence of the AFMR multiplet, is indeed valid. Deviations between simulations and experiments, together with a review of previously published results, indicate that large magnetostrictive effects are present in NiO.