Ferromagnetic Ordering of Energy Levels

We study a natural conjecture regarding ferromagnetic ordering of energy levels in the Heisenberg model which complements the Lieb–Mattis Theorem of 1962 for antiferromagnets: for ferromagnetic Heisenberg models the lowest energies in each subspace of fixed total spin are strictly ordered according to the total spin, with the lowest, i.e., the ground state, belonging to the maximal total spin subspace. Our main result is a proof of this conjecture for the spin-1/2 Heisenberg XXX and XXZ ferromagnets in one dimension. Our proof has two main ingredients. The first is an extension of a result of Koma and Nachtergaele which shows that monotonicity as a function of the total spin follows from the monotonicity of the ground state energy in each total spin subspace as a function of the length of the chain. For the second part of the proof we use the Temperley–Lieb algebra to calculate, in a suitable basis, the matrix elements of the Hamiltonian restricted to each subspace of the highest weight vectors with a given total spin. We then show that the positivity properties of these matrix elements imply the necessary monotonicity in the volume. Our method also shows that the first excited state of the XXX ferromagnet on any finite tree has one less than maximal total spin.     

Nuclear spin nanomagnet in an optically excited quantum dot

Linearly polarized light tuned slightly below the optical transition of the negatively charged exciton (trion) in a single quantum dot causes the spontaneous nuclear spin polarization (self-polarization) at a level close to 100%. The effective magnetic field of spin-polarized nuclei shifts the optical transition energy close to resonance with photon energy. The resonantly enhanced Overhauser effect sustains the stability of the nuclear self-polarization even in the absence of spin polarization of the quantum dot electron. As a result the optically selected single quantum dot represents a tiny magnet with the ferromagnetic ordering of nuclear spins-the nuclear spin nanomagnet.     

Electronic and magnetic properties of basic nanosystems of early 3d transition metals (Sc,Ti, V,Cr, and Mn)

This detailed and systematic theoretical study on the behavior of basic low dimensional (one- and two-dimensional) systems of early 3d transition metals should serve as a guideline to experimentalists as well as to theoreticians. We find that, lowering of dimensionality is favorable for emergence of magnetic ordering in all the systems studied, except Ti monolayers (MLs). For Ti MLs, both nonmagnetic and ferromagnetic states are degenerate within the numerical limits. For such a case, the interactions with substrate would play a decisive role in the magnetic ordering of the atoms in the ML. The total energy calculations show that the nonmagnetic and ferromagnetic states are almost degenerate for Cr and V MLs too; however, anti-ferromagnetic ordering is favored in these. The ferromagnetic ordering in Sc linear chains and anti-ferromagnetic ordering in MLs of Mn and Cr are found to be favored by a relatively larger margin showing good stability. Some low dimensional systems, showing electrons with only one kind of spin available at Fermi energy, may be suitable for spintronics related applications. The linear chains of Cr and Mn, and MLs of Sc are likely to form stable magnetic nanosystems as these exhibit almost saturated magnetic moment per atom around the equilibrium separation. The magnetic moment strengthens considerably as one goes from two- to one-dimension. Our results are supported qualitatively by available experimental results and offer a good insight into these nanosystems.     

Magnetic ordering in hexagonally bonded sheets with first-row elements

We report first-principles total-energy electronic-structure calculations in the density-functional theory performed for hexagonally bonded honeycomb sheets consisting of B, N, and C atoms. We find that the ground state of BNC sheets with particular stoichiometry is ferromagnetic. Detailed analyses of energy bands and spin densities unequivocally reveal the nature of the ferromagnetic ordering, leading to an argument that the BNC sheet is a manifestation of the flat-band ferromagnetism.     

Ferromagnetismus in schmalen Energiebändern

The method of spectral moments is applied to the Hubbard-model for six various densities of states. We find for each density of states a criterion for ferromagnetism as a function of the electron concentrationn. The most surprising result may be that sometimes there are two distinct ferromagnetic solutions, a fact which was pointed out also by Meyer and Schweitzer using the Roth-method. Looking for the reason of the possibility of magnetic ordering we discuss the behaviour of some important physical quantities (energy, magnetization, spin dependent band shift, band width and Fermi-energy).     

Absence of an equilibrium ferromagnetic spin-glass phase in three dimensions

Using ground state computations, we study the transition from a spin glass to a ferromagnet in 3D spin glasses when changing the mean value of the spin-spin interaction. We find good evidence for replica symmetry breaking up until the critical value where ferromagnetic ordering sets in, and no ferromagnetic spin glass phase. This phase diagram is in conflict with the droplet/scaling and mean field theories of spin glasses. We also find that the exponents of the second order ferromagnetic transition do not depend on the microscopic Hamiltonian, suggesting universality of this transition.     

On the theory of ferromagnetism of hexagonal diborides

The electronic structure and the magnetic properties of the MnB₂ and CrB₂ compounds with hexagonal AlB₂-type lattices were studied. The problem was treated in terms of the generalized Hubbard model with an infinite electron-electron repulsion energy in the same atom. Equations for spin magnetic susceptibility were derived and used to determine the conditions of ferromagnetic instability and construct the phase diagram of the existence of ferromagnetic ordering.     

Spin and charge ordering in three-leg ladders in oxyborates

We study the spin ordering within the three-leg ladders present in the oxyborate Fe3O2BO3 consisting of localized classical spins interacting with conduction electrons (one electron per rung). We also consider the competition with antiferromagnetic superexchange interactions to determine the magnetic phase diagram. Besides a ferromagnetic phase we find (i) a phase with ferromagnetic rungs ordered antiferromagnetically and (ii) a zigzag canted spin ordering along the legs. We also determine the induced charge ordering within the different phases and the interplay with lattice instability. Our model is discussed in connection with the lattice dimerization transition observed in this system, emphasizing the role of the magnetic structure.     

A study of the effective magnetic anisotropy and the corresponding spin configurations in two dimensional ferromagnetic/antiferromagnetic system

The spin configurations of two dimensional ferromagnetic/antiferromagnetic system were investigated using model calculations and Monte-Carlo simulation methods. The lowest energy state was obtained under various coupling conditions to investigate the role of interfacial interaction on anisotropy. We found that the total ferromagnetic layer anisotropy is contributed not only from its own crystalline anisotropy but also from the antiferromagnetic layer spin flop effect. The overall ferromagnetic layer effective anisotropy is calculated as a function of the exchange energy of antiferromagnetic layer and the interfacial interaction energy. If the effective anisotropy from the spin flop effect is comparable with the crystalline anisotropy, the asymmetric spin configuration is generated. In this configuration, the magnetization direction of the ferromagnetic layer is neither perpendicular nor parallel to the antiferromagnetic spin direction. Temperature effect on the perpendicular-to-collinear coupling transition was also investigated using Monte-Carlo simulation, and the relationship between the effective anisotropy and the temperature was obtained.     

DMRG Studies on Properties of Undoped and Doped Molecule-Based Ferromagnetic Chain

By using density matrix renormalization group （DMRG） method a model for organic molecule-based ferromagnetic chain is proposed. It is found that the ground states of Undoped and doped systems both exhibit ferrimagnetic ordering. The e-e repulsion plays an important role in the stability of the ferromagnetic state either in doped system or undoped system. For the undoped system, each unit cell coatains half of the total spins, which is consistent with Lieb＇s theorem. It is convinced that when the system is doped with one electron, a charge density wave is excited, which decreases the amplitude of spin density wave,therefore acting against the stability of ferromagnetic state.     

Spin waves of a layered ferromagnetic electron gas

Using a first-order Green's function technique, the spin wave spectrum of a layered ferromagnetic electron system is determined in the long-wave length limit. It is shown that the spin wave stiffness is a highly anisotropic quantity. A discussion of the Stoner-Overhauser-Wohlfarth condition shows that both electron tunneling processes and a more sophisticated expression of the Coulomb interaction matrix element than the usual Hubbard form are important for the existence of ferromagnetic ordering.     

Berezinskii–Kosterlitz–Thouless Order in Two-Dimensional O(2)-Ferrofluid

We study a two-dimensional ferrofluid of hard-core particles with internal degrees of freedom (plane rotators) and O(2)-invariant ferromagnetic spin interaction. By reducing the continuous system to an approximating reference lattice system, a lower bound for the two-spin correlation function is obtained. This bound, together with the Fröhlich–Spencer result about the Berezinskii–Kosterlitz–Thouless transition in the two-dimension lattice system of plane rotators, shows that our model also exhibits the same kind of ordering. Namely for a short-range ferromagnetic interaction the two-spin correlation function does not decay faster than some power of the inverse distance between particles, for small temperatures and high densities of the ferrofluid. For a long-range ferromagnetic interaction the model manifests a non-zero order parameter (magnetization) in this domain, whereas for high temperatures spin correlations decay exponentially.     

过渡金属与碳共掺ZnO磁光学性质的第一性原理研究

采用密度泛函理论第一性原理超软赝势的方法,计算了过渡金属与C共掺杂ZnO的磁学和光学性质. 计算结果表明,共掺杂均导致费米能级发生移动,掺杂体系共价性强弱发生变化,且共掺杂更有利于高居里温度铁磁性半导体的实现;为了进一步分析掺杂体系的磁学性质,研究了其铁磁态与反铁磁态的能量差、空间电荷和自旋密度分布．各种类型掺杂体系在高能区的光学性质与纯净ZnO几乎一致,而在低能区却存在较大差异,结合电子结构定性解释了光学性质的变化.     

DMRG Studies on Properties of Undoped and Doped Molecule-Based Ferromagnetic Chain

By using density matrix renormalization group (DMRG) method a model for organic molecule-based ferromagnetic chain is proposed. It is found that the ground states of undoped and doped systems both exhibit ferrimagnetic ordering. The e-e repulsion plays an important role in the stability of the ferromagnetic state either in doped system or undoped system. For the undoped system, each unit cell contains half of the total spins, which is consistent with Lieb‘s theorem. It is convinced that when the system is doped with one electron, a charge density wave is excited, which decreases the amplitude of spin density wave, therefore acting against the stability of ferromagnetic state.     

Spin polarization and magnetoresistance through a ferromagnetic barrier in bilayer graphene

We study spin dependent transport through a magnetic bilayer graphene nanojunction configured as a two-dimensional normal/ferromagnetic/normal structure where the gate voltage is applied on the layers of ferromagnetic graphene. Based on the four-band Hamiltonian, conductance is calculated by using the Landauer-Buttiker formula at zero temperature. For a parallel configuration of the ferromagnetic layers of bilayer graphene, the energy band structure is metallic and spin polarization reaches its maximum value close to the resonant states, while for an antiparallel configuration the nanojunction behaves as a semiconductor and there is no spin filtering. As a result, a huge magnetoresistance is achievable by altering the configurations of ferromagnetic graphene around the band gap.     

Magneto-optical resonance in ferromagnetic gadolinium

The optical constants n and k of ferromagnetic and paramagnetic gadolinium have been measured, at various temperatures, from polarimetric measurements, in the low energy range 0.5 to 1.5 eV. For the ferromagnetic state, evidence of extra-optical conductivity is found near 0.69 eV and attributed to magnetic ordering. It confirms Miwa and Mackintosh predictions, assuming that new energy gaps are introduced in the conduction band through the s-f exchange interaction. From the experimental determination of the energy gap resulting from a splitting of the conduction band between spin up and spin down bands, we have deduced the effective s-f exchange energy J(q) = 1.58 × 10^-13 erg.     

Zero-magnetization ferromagnet proven by helicity-switching Compton scattering

A single crystal of gadolinium-doped SmAl(2) has zero magnetization in the midst of the ordered temperature region, despite the probable ferromagnetic spin ordering. The asymmetry in Compton-scattering intensity when switching between right- and left-handed polarization of incident 150-keV synchrotron radiation provides decisive proof that ferromagnetic order is really there, and that spin and orbital magnetic contributions cancel. The experiments also show that the spin direction at this zero-magnetization state is rather stable against the external magnetic field and, nevertheless, reversible by a preceding control of temperature and an external field.     

Spin order in paired quantum Hall states

We consider quantum Hall states at even-denominator filling fractions, especially nu=5/2, in the limit of small Zeeman energy. Assuming that a paired quantum Hall state forms, we study spin ordering and its interplay with pairing. We give numerical evidence that at nu=5/2 an incompressible ground state will exhibit spontaneous ferromagnetism. The Ginzburg-Landau (GL) theory for the spin degrees of freedom of paired Hall states is a perturbed CP2 model. We compute the coefficients in the GL theory by a BCS Stoner mean-field theory for coexisting order parameters, and show that even if repulsion is smaller than that required for a Stoner instability, ferromagnetic fluctuations can induce a partially or fully polarized superconducting state.     

The first principle study on the electronic structure and spin ordering of the rare earth palladium sulfide, EuPd3S4

We have performed relativistic first-principles full-potential linearized augmented plane wave (FLAPW) calculation for rare earth palladium sulfide EuPd₃S₄ in the ferromagnetic and antiferromagnetic states. The density of 4f electrons of Eu is taken from a local-spin-density approximation self-interaction correction (LSDA-SIC) atomic calculation. EuPd₃S₄ is found to exhibit antiferromagnetic ordering in its ground state. The charge, orbital, magnetic moment and spin ordering are explained with the electronic structure, the orbital-projected density of states and the total energy study. EuPd₃S₄ is found to be stable in the body-centered Type-I antiferromagnetic state, in agreement with experimental results. Different Eu states are found in antiferromagnetic ordering. The magnetic moments of different states obtained through spin-polarized calculation are also in good agreement with experimental results. The phenomena observed are explained by the orbital hybridization of Eu and Pd ions as compared with the free ions.     

Antiferromagnetism of nuclear matter in the model with effective Gogny interaction

The possibility of ferromagnetic (FM) and antiferromagnetic (AFM) phase transitions in symmetric nuclear matter is analyzed within the framework of a Fermi liquid theory with effective Gogny interaction. It is shown that, at some critical density, nuclear matter with the D1S effective force undergoes a phase transition to the AFM spin state (opposite directions of neutron and proton spins). The self-consistent equations of spin-polarized nuclear matter with the D1S force have no solutions corresponding to FM spin ordering (the same direction of neutron and proton spins) and, hence, the FM transition does not appear. The AFM spin polarization parameter is found for zero and finite temperature. It is shown that the AFM spin polarization parameter of partially polarized nuclear matter at low enough temperatures increases with temperature. The entropy of the AFM spin state for some temperature range is larger than the entropy of the normal state. Nevertheless, the free energy of the AFM spin state is always less than the free energy of the normal state, and the AFM spin-polarized state is preferable for all temperatures below the critical temperature. The text was submitted by the authors in English.