Magnetic Hamiltonians Research Articles

The accurate determination of magnetic hyperfine and Zeeman parameters for 2II diatomic molecules from experimental data

The parameters γ and AD (for the spin-rotation coupling and the centrifugal correction to the spin-orbit coupling) in the effective Hamiltonian of a diatomic molecule in a 2Λ state, Λ ≠ 0, make indistinguishable contributions to the energy, and one or other of these terms can be removed by a unitary transformation. The present work considers the effects of this and other transformations on the terms of the magnetic hyperfine and Zeeman Hamiltonians. It is found that the hyperfine parameter b is particularly affected by the transformations, and that care must be taken in correcting b before interpreting its value in terms of the electronic structure. An application to 15NO gives consistent values of the corrected b between ÃD and fits. The transformation of the Zeeman Hamiltonian produces higher order Zeeman terms that so far have not been included in fits of data in magnetic fields. Neglect of these contributions is equivalent to a constraint on the fit. A re-fit of LMR data for the FO radical shows that this approach is viable, and leads to the determination of separate values for AD and γ. These values and those obtained for b and gl correspond to the unitary transformation that optimizes the chosen form of the Zeeman Hamiltonian.

Calculation of nuclear magnetic shieldings XIV. Relativistic mass—velocity corrected perturbation Hamiltonians

A two-component relativistic SCF perturbation theory, based on the Douglas—Kroll—Hess (DKH) transformation, has been applied to the calculation of nuclear magnetic shielding tensors of hydrogen halides, HX (X = F, Cl, Br, I). Calculations were performed via the unrestricted coupled Hartree—Fock (CHF) scheme using gauge-including atomic orbitals (GIAOs) at four different levels. In the level I calculation, both the scalar relativistic (SR) and spin—orbit (SO) interactions were included in the zero-order Hamiltonian. However, the magnetic pertubation Hamiltonians were treated non-relativistically. The results of these calculations indicated a large interplay between the SR and SO interactions. The level I calculation was found to be insufficient to explain the full relativistic effect on the halogen atom shieldings. In order to reproduce the full relativistic effect, the mass-velocity effect on the magnetic perturbation Hamiltonians was introduced in the levels II—IV calculations. Inclusion of the mass-velocity effects into all of the perturbation Hamiltonians made in levels III and IV improved the results greatly. The cross term between the nuclear attraction potential and the magnetic vector potential was introduced approximately in level IV. The level III calculation agreed most closely with the four-component relativistic random phase approximation (RPA) calculation.

Aspects of spin dynamics and magnetic interactions

Non-collinear magnetic alignment is somewhat unusual for equilibrium, and those systems exhibiting such ground states are frequently `victims’ of competing forces. For non-equilibrium, or dynamical systems (e.g. T>0) non-collinear alignment is universal. We discuss such systems and present some basic formalism for evaluating from first principles the equation of motion and related relevant properties. Considerable discussion is also devoted to obtaining from first principles, parameters for model magnetic Hamiltonians. These models represent a convenient way to gain insight and to approximately evaluate magnetic interactions for very complex systems.

<I>Review</I>/<I>Synthèse</I>: Triangular antiferromagnets

In this article we review the effects of magnetic frustation in the stacked triangular lattice. Frustration increases the degeneracy of the ground state, giving rise to different physics. In particular it leads to unique phase diagrams with multicritical points and novel critical phenomena. We describe the confrontation of theory and experiment for a number of systems with differing magnetic Hamiltonians; Heisenberg, Heisenberg with easy-axis anisotropy, Heisenberg with easy-plane anisotropy, Ising and singlet ground state. Interestingly each leads to different magnetic properties and phase diagrams. We also describe the effects of ferromagnetic, rather than antiferromagnetic, stacking and of small distortions of the triangular lattice.

Landau Hamiltonians with Unbounded Random Potentials

We prove the almost sure existence of a pure point spectrum for the two-dimensional Landau Hamiltonian with an unbounded Anderson-like random potential, provided that the magnetic field is sufficiently large. For these models, the probability distribution of the coupling constant is assumed to be absolutely continuous. The corresponding densityg has support equal to $$\mathbb{R} $$ , and satisfies $$$$ , for some ∈ > 0. This includes the case of Gaussian distributions. We show that the almost sure spectrum ∑ is $$\mathbb{R} $$ , provided the magnetic field B≠0. We prove that for each positive integer n, there exists a field strength B n , such that for all B>B n , the almost sure spectrum ∑ is pure point at all energies $$E \leqslant (2n + 3)B - \mathcal{O}(B^{ - 1} ) $$ except in intervals of width $$\mathcal{O}(B^{ - 1} ) $$ about each lower Landau level $$E_m (B) \equiv (2m + 1)B $$ , for m < n. We also prove that for any B≠0, the integrated density of states is Lipschitz continuous away from the Landau energiesE n (B). This follows from a new Wegner estimate for the finite-area magnetic Hamiltonians with random potentials.

Landau Hamiltonians with random potentials: Localization and the density of states

We prove the existence of localized states at the edges of the bands for the two-dimensional Landau Hamiltonian with a random potential, of arbitrary disorder, provided that the magnetic field is sufficiently large. The corresponding eigenfunctions decay exponentially with the magnetic field and distance. We also prove that the integrated density of states is Lipschitz continuous away from the Landau energies. The proof relies on a Wegner estimate for the finite-area magnetic Hamiltonians with random potentials and exponential decay estimates for the finitearea Green's functions. The proof of the decay estimates for the Green's functions uses fundamental results from two-dimensional bond percolation theory.

Two-dimensional nuclear magnets

Abstract We review in this paper the experimental results on two-dimensional nuclear magnetic systems obtained by physical adsorption of 3He atoms on solid substrates. Two-dimensional nuclear antiferromagnets and ferromagnets have been observed and studied in recent years, providing useful model systems for spin 1/2 magnetic Hamiltonians and leading to results of general validity on the magnetic ordering of two-dimensional spin systems. Heisenberg, multiple spin and Rudermann-Kittel exchange as well as vacancy-induced magnetism are discussed in the context of the experimental investigations of adsorbed 3He films.

Boundary K-matrices for the XYZ, XXZ and XXX spin chains

The general solutions for the factorization equations of the reflection matrices $K^{\pm}(\theta)$ for the eight vertex and six vertex models (XYZ, XXZ and XXX chains) are found. The associated integrable magnetic Hamiltonians are explicitly derived, finding families dependig on several continuous as well as discrete parameters.

Spin dynamics in CuO and Cu1-xLixO from 63Cu and 7Li nuclear relaxation.

$^{63}\mathrm{Cu}$ nuclear quadrupole resonance (NQR), nuclear antiferromagnetic resonance (AFNMR), and spin-lattice relaxation, as well as $^{7}\mathrm{Li}$ NMR and relaxation measurements in CuO and in ${\mathrm{Cu}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Li}}_{\mathit{x}}$O, are used to study the spin dynamics in the paramagnetic and in the antiferromagnetic (AF) phase, and in particular the effects induced by lithium doping. It is argued that Li enters in CuO lattice up to a doping x around 4%; from a comparison of the electric-field gradient (EFG) and of the dipolar field at the nucleus with theoretical estimates, it appears that ${\mathrm{Li}}^{+}$ is slightly displaced from the Cu lattice site. From NQR, NMR, and AFNMR spectra, information on the Cu hyperfine interaction and the EFG are derived. The N\'eel temperature ${\mathit{T}}_{\mathit{N}}$ is affected by Li doping to a moderate extent, decreasing from 226 K in CuO to ${\mathit{T}}_{\mathit{N}}$=183 K for x=3.7%. The relaxation rates, driven by the time-dependent part of the magnetic electron-nucleus Hamiltonians, indicate that the ${\mathrm{Cu}}^{2+}$ spin dynamics is almost unaffected by Li doping for T\ensuremath{\gg}${\mathit{T}}_{\mathit{N}}$ and possibly controlled by valence fluctuations. The Li doping modifies in a dramatic way the spin fluctuations in the AF phase.The relaxation rates in ${\mathrm{Cu}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Li}}_{\mathit{x}}$O, in fact, increase by orders of magnitude (similarly to the case of copper-oxide precursors of high-${\mathit{T}}_{\mathit{c}}$ superconductors) and display temperature behaviors quite different from those in CuO. These effects are associated with an effective low-frequency spectral density of the spin fluctuations negligible in CuO, which strongly increases upon Li doping. This increase is related to the fluctuations induced in the local ${\mathrm{Cu}}^{2+}$ spin configuration as a consequence of the diffusionlike motion of the holes in the AF matrix, implying the insurgence of low-frequency spin excitations. The orders of magnitude of the relaxation rates, their dependences on x and on T, as well as on the measuring frequency, are satisfactorily explained by a picture in which the correlation time ${\mathrm{\ensuremath{\tau}}}_{\mathit{h}}$ for the hole-hopping motion is controlled by an energy gap E(x) between localized and itinerant states. Quantitative information on ${\mathrm{\ensuremath{\tau}}}_{\mathit{h}}$ and E(x) is thus derived.

Boundary K-matrices for the six vertex and the n(2n-1)An-1vertex models

Boundary conditions compatible with integrability are obtained for two dimensional models by solving the factorizability equations for the reflection matrices $K^{\pm}(\theta)$. For the six vertex model the general solution depending on four arbitrary parameters is found. For the $A_{n-1}$ models all diagonal solutions are found. The associated integrable magnetic Hamiltonians are explicitly derived.

The behaviour of the Landé factor and effective exchange parameter in a group of Pr intermetallics observed through reduced level scheme models

The present work constitutes a portion of a continuing series of studies dealing with models, in which we retain only the two lowest levels of the crystal field splitting scheme of rare-earth ion in rare-earth intermetallics. In these reduced level scheme models, the crystal field and the magnetic Hamiltonians are represented in matrix notation. These two matrices constitute the model Hamiltonian proposed in this paper, from which we derive the magnetic state equations of interest for this work. Putting into these equations a group of adequate experimental data found in the literature for a particular rare-earth intermetallic we obtain the Landé factor and effective exchange parameter related to this rare-earth intermetallic. This study will be applied to a group of Pr intermetallics, in cubic symmetry, in which the ground level may be a non-magnetic singlet level or a non-magnetic doublet level. In both cases, the first excited level is a triplet one.

Nonadiabatic geometric spinor phase in rotating magnetic fields

We describe exact cyclic spinor evolutions in cyclic and noncyclic magnetic Hamiltonians, each resulting in a pure geometric phase. These evolutions are realisable in neutron interferometric and polarimetric experiments.

Study of crystal field splitting of PrAl 2 through reduced level scheme models

Under the action of the crystal field, the 4 f-shell of the light rare-earth intermetallics is split into a series of levels that may be degenerate or not. The location of these levels in the overall crystal field splitting scheme is not well determined in the literature for several light rare-earth intermetallics, including PrAl 2. For many authors, the ground level of PrAl 2 is a singlet while for others it is a doublet. In this work, we will try to determine the level scheme of the ground multiplet of PrAl 2 using two models in which the crystal field and magnetic Hamiltonians are simplified, i.e. we keep in both models only the two lowest levels of the ground multiplet of PrAl 2. In the first model, the ground and the first excited levels are, respectively, singlet and triplet (singlet-triplet model) and in the second one they are, respectively, doublet and triplet (doublet-triplet model). The exchange, of the Heisenberg-type between the rare-earth ions, is treated in mean field approximation. Using these approaches, we construct, in matrix notation, the model Hamiltonians corresponding to the models mentioned above and from them we derive the magnetic state equations of interest. The theoretical curves of magnetic entropy temperature of PrAl 2 are compared with the corresponding experimental curves given in the literature and we conclude that the ground level of this compound is a doublet.

HIGH TEMPERATURE SERIES ANALYSIS OF SUSCEPTIBILITY DATA OF La2CuO4

The zero-field magnetic susceptibility of La 2 CuO 4 is analyzed using high temperature series for five different magnetic Hamiltonians in two-dimensions: spin 1/2 Heisenberg model, spin 1/2 XY model, classical Heisenberg model, classical XY model, and the Ising model. The goodness of fit indicates that the quantum spin 1/2 Heisenberg model is best, with the classical XY model second.

Neutral eigenstates of extended systems: Resonance of neutral VB structures or perturbation of (neel states) spin waves?

For many electronic systems a resonance of covalent valence bond (VB) structures is supposed to give a correct basic description of the wavefunction. Going from this picture to a diatomic-in-molecules (DIM) type Hamiltonian spanned by the neutral eigenstates of the diatom disregards some three-body effects but introduces the energetic effect of hybridization and ionic components on the diatoms. For half-filled bands the magnetic Heisenberg Hamiltonians are identical to DIM-Hamiltonians and therefore quite close to the resonance of neutral VB structures. The present paper claims that the magnetic formulation may be more transparent and more efficient than the original VB resonance picture. When the number of coordination of the atoms in the bond graph increases, Neel states, which we call spin waves, begin to become good zeroth-order descriptions, and give reliable estimates of the binding energy, even for very large or infinite systems, through an asymptotically convergent perturbative expansion. However, all these approaches fail when the ground-state wavefunction is essentially ionic as occurs for metal clusters and tentatively for compact phases of the metals.

Anisotropic Heisenberg chain with composite spin.

A family of one-dimensional magnetic Hamiltonians is introduced, where at each site there are $n$ spin-$S$ operators. It is shown that, for special couplings between spins and for $S=\frac{1}{2}$, the model contains the complete spectrum of the Heisenberg chain with spins \textonehalf{}, 1, frac32;, etc., and the ground state is that of the corresponding Heisenberg chain. By the varying of a single parameter the model allows continuous transitions between chains with different spin. We map the spin-($S+S$) model onto the nonlinear $\ensuremath{\sigma}$ model and discuss the possibility of a finite gap in the spin-(\textonehalf{}+\textonehalf{}) model.

On the relativistic theory of NMR chemical shifts

A relativistic analogue to Ramsey's theory of NMR chemical shifts is formulated. Four-component spinor one-electron wavefunctions and relativistic magnetic hamiltonians are used. In contrast to the third-order Pauli approximation theory of Nakagawa et al., the main relativistic effects are then included in the usual second-order theory.

Quantum Magnetic Hamiltonians with Remarkable Spectral Properties

The Hamiltonian, $H$, of a spinless particle moving in two dimensions in an axially symmetric magnetic field $B(\ensuremath{\rho})$ is considered. If $B(\ensuremath{\rho})\ensuremath{\sim}{\ensuremath{\rho}}^{\ensuremath{-}\ensuremath{\alpha}}$ for $\ensuremath{\rho}$, large with $0&lt;\ensuremath{\alpha}&lt;1$, then it is shown that $H$ has spectrum [$0, \ensuremath{\infty}$) with only eigenvectors and eigenvalues dense in [$0, \ensuremath{\infty}$). If $\ensuremath{\alpha}=1$, then the spectrum is a dense point spectrum in [0, $c$] for suitable $c$ and absolutely continuous in [$c, \ensuremath{\infty}$).

Selfconsistently renormalized spin-wave approximation for some two-dimensional magnetic systems

Some temperature-dependent properties of two-dimensional magnetic hamiltonians with uniaxial anisotropy are studied on the basis of the selfconsistently renormalized (SCR) spin-wave approximation. Due to the importance of anisotropy in two- dimensional systems, particular attention is paid to the kinematical consistency of the theory by considering multiple scattering due to anisotropy. In particular the properties of FeCl2, a layer ferromagnet with large single-ion and exchange anisotropy, and K2NiF4, a layer antiferromagnet with small anisotropy have been studied. In both cases good agreement with experiments is found for temperature renormalization of small k spin-wave energies. Improved results with respect to spin-wave theory are obtained for the order parameter. The large k dependence in the temperature renormalization of spin-wave energies is predicted for antiferromagnets with medium and small anisotropy.