Many-body Green's function theory for the magnetic reorientation of thin ferromagnetic films

The field-induced reorientation of the magnetization of ferromagnetic films is treated within the framework of many-body Green's function theory by considering all components of the magnetization. We present a new method for the calculation of expectation values in terms of the eigenvalues and eigenvectors of the equations of motion matrix for the set of Green's functions. This formulation allows a straightforward extension of the monolayer case to thin films with many layers and for arbitrary spin and moreover provides a practicable procedure for numerical computation. The model Hamiltonian includes a Heisenberg term, an external magnetic field, a second-order uniaxial single-ion anisotropy, and the magnetic dipole-dipole coupling. We utilize the Tyablikov (RPA) decoupling for the exchange interaction terms and the Anderson-Callen decoupling for the anisotropy terms. The dipole coupling is treated in the mean-field approximation, a procedure which we demonstrate to be a sufficiently good approximation for realistic coupling strengths. We apply the new method to monolayers with spin and to multilayer systems with S=1. We compare some of our results to those where mean-field theory (MFT) is applied to all interactions, pointing out some significant differences. Received 19 June 2000 and Received in final form 2 August 2000     

Field-induced magnetic reorientation and effective anisotropy of a ferromagnetic monolayer within spin wave theory

The reorientation of the magnetization of a ferromagnetic monolayer is calculated with the help of many-body Green's function theory. This allows, in contrast to other spin wave theories, a satisfactory calculation of magnetic properties over the entire temperature range of interest since interactions between spin waves are taken into account. A Heisenberg Hamiltonian plus a second-order uniaxial single-ion anisotropy and an external magnetic field is treated by the Tyablikov (Random Phase Approximation: RPA) decoupling of the exchange interaction term and the Anderson-Callen decoupling of the anisotropy term. The orientation of the magnetization is determined by the spin components (), which are calculated with the help of the spectral theorem. The knowledge of the orientation angle allows a non-perturbative determination of the temperature dependence of the effective second-order anisotropy coefficient. Results for the Green's function theory are compared with those obtained with mean-field theory (MFT). We find significant differences between these approaches. Received 6 April 1999 and Received in final form 9 July 1999     

Many-body Green's function theory for thin ferromagnetic anisotropic Heisenberg films: treatment of the exchange anisotropy

The many-body Green's function theory developed in our previous work for treating the reorientation of the magnetization of thin ferromagnetic films is extended to include the exchange anisotropy. This leads to additional momentum dependencies which require some non-trivial changes in the formalism. The theory is developed for arbitrary spin values S and for multilayers. The effects of the exchange anisotropy and the single-ion anisotropy, which was treated in our earlier work, on the magnetic properties of thin ferromagnetic films are compared. Received 31 October 2002 Published online 7 May 2003     

Magnon scattering by a symmetric atomic well in free standing very thin magnetic films

A theoretical model is presented for the study of the scattering of magnons at an extended symmetric atomic well in very thin magnetic films. The thin film consists of three cubic atomic planes with ordered spins coupled by Heisenberg exchange, and the system is supported on a non-magnetic substrate, and considered otherwise free from magnetic interactions. The coherent transmission and reflection scattering coefficients are derived as elements of a Landauer type scattering matrix. Transmission and reflection scattering cross sections are hence calculated specifically, as a function of the varying local magnetic exchange on the inhomogeneous boundary. Detailed numerical results for the individual incident film magnons, and for the calculated overall magnon conductance, show characteristic transmission properties, with associated Fano resonances, depending on the magnetic boundary conditions and on the magnon incidence.     

Cu cap layer on Ni8/Cu(001): reorientation and TC-shift

Adding a non-magnetic Cu overlayer on Ni₈/Cu(001) is known to induce the reorientation of the magnetic easy axis from in-plane to out-of-plane and to reduce the Curie temperature. In this paper both effects are described on the same footing using an effective Heisenberg trilayer. The model takes into account thermal fluctuations of the magnetization and allows to separate explicitly between two possible mechanisms behind the experimental observations, namely between a reduction of the magnetic moment by hybridization and a lattice relaxation at the Ni/Cu interface. Ferromagnetic resonance data for the reorientation and the decreased Curie temperature due to the Cu cap layer are best reproduced by assuming a reduction of the magnetic moment at the interface by ≈1/3.     

On evaluation of transverse spin fluctuations in quantum magnets

A numerical method is described for evaluating transverse spin correlations in the random phase approximation. Quantum spin-fluctuation corrections to sublattice magnetization are evaluated for the antiferromagnetic ground state of the half-filled Hubbard model in two and three dimensions in the whole U/t range. Extension to the case of defects in the AF is also discussed for spin vacancies and low-U impurities. In the limit, the vacancy-induced enhancement in the spin fluctuation correction is obtained for the spin-vacancy problem in two dimensions, for vacancy concentration up to the percolation threshold. For low-U impurities, the overall spin fluctuation correction is found to be strongly suppressed, although surprisingly spin fluctuations are locally enhanced at the low-U sites. Received 27 April 1998 and Received in final form 13 August 1998     

Quantum fluctuations and ground state of weakly interacting helix spin chains in a magnetic field

Ferromagnetic spin chains of a hexagonal lattice coupled by a weak antiferromagnetic interaction J₁ develop a helix arrangement if the intrachain antiferromagnetic NNN exchange J₂ is sufficiently large. We show that the classical minimum energy spin configuration is an umbrella when an external magnetic field is applied. The scenario is dramatically changed by quantum fluctuations. Indeed we find that the zero point motion forces the spins in a plane containing the magnetic field so that classical expectation is deceptive for our model. Our result is obtained by controlled expansion in the low field-long wavelength modulation limit. Received: 9 September 1997 / Revised: 15 October 1997 / Accepted: 17 November 1997     

Modified spin-wave theory for the S = 1 frustrated antiferromagnetic Heisenberg chain

We study the one-dimensional isotropic spin-1 Heisenberg magnet with antiferromagnetic nearest-neighbor (nn) and next-nearest-neighbor (nnn) interactions by using the modified spin wave theory (MSWT). The ground state energy and the singlet-triplet energy gap are obtained for several values of j, defined as the ratio of the nnn interaction constant to the nn one. We also compare two different ways of implementing the MSWT currently found in the literature, and show that, despite the remarkable differences between the equations to be solved in each procedure, the results given by both are equivalent, except for the predicted value of the j_max, the maximum value of j accessible in each treatment. Here, we suggest that j_max is related to the disorder point of the first kind. Our results show that the ground state and the gap energies increase with j, for j ≤j_max, in accordance to previous numerical results.     

Optical properties of multilayer structures

This paper describes the magneto-optical effects of metallic multilayers under the condition of total internal reflection. In the framework of the Green's dyadic technique, we present numerical simulations which account for the variation of the magneto-optical signal with the angle of incidence. The Attenuated Total Reflection (ATR) has become a new technique of characterization for thin films. We show, in this paper, optical effects due to a slight variation of the indice of refraction for thin dielectric films in reflection by the reflectivity and the Kerr rotation spectra of an optimized system. In transmission, this variation is brought to the fore by the near-field intensity spectra. Received 29 March 2000     

Heisenberg-type ferromagnetic films with a sandwich structure

Green’s function theory is applied to an alternating two-element multilayer ferromagnetic film. The Hamiltonian is based on the Heisenberg model with a second-order uniaxial single-ion anisotropy and with the interaction between the layer in the interfaces. Magnetization and the phase transition in such system are derived for several sets of material parameters.     

Spin-wave interaction in two-dimensional ferromagnets with dipolar forces

We discuss the spin-wave interaction in two-dimensional (2D) Heisenberg ferromagnet (FM) with dipolar forces at T_C?T?0 using 1/S expansion. A comprehensive analysis is carried out of the first 1/S corrections to the spin-wave spectrum. In particular, we obtain that the spin-wave interaction leads to the gap in the spectrum ε_k renormalizing greatly the bare gapless spectrum at small momenta k. Expressions for the spin-wave damping Γ_k are derived self-consistently and it is concluded that magnons are well-defined quasi-particles in both quantum and classical 2D FMs at small T. We observe thermal enhancement of both Γ_k and Γ_k/ε_k at small momenta. In particular, a peak appears in Γ_k and Γ_k/ε_k at small k and at any given direction of k. If S∼1 the height of the peak in Γ_k/ε_k is not larger than a value proportional to T/D?1, where D is the spin-wave stiffness. In the case of large spins S?1 the peak in Γ_k/ε_k cannot be greater than that of the classical 2D FM found at k=0 whose height is small only numerically: Γ₀/ε₀≈0.16 for the simple square lattice.     

Quantum corrections of the Dzyaloshinskii-Moriya interaction on the spin-$\frac{1}{2}$ AF-Heisenberg chain in an uniform magnetic field

We have investigated the ground state phase diagram of the 1D AF spin- Heisenberg model with the staggered Dzyaloshinskii-Moriya (DM) interaction in an external uniform magnetic field H. We have used the exact diagonalization technique. In the absence of the uniform magnetic field (H=0), we have shown that the DM interaction induces a staggered chiral phase. The staggered chiral phase remains stable even in the presence of the uniform magnetic field. We have identified that the ground state phase diagram consists of four Luttinger liquid, staggered chiral, spin-flop, and ferromagnetic phases.     

In plane to out of plane magnetic reorientation transition in partially ordered FePd thin films

It is demonstrated that perpendicular magnetic anisotropy may be obtained with a room temperature growth process in ordered (FePd) alloys. Indeed, using atomic layer by atomic layer epitaxy, a partial chemical ordering into the L1₀ structure is obtained, with a corresponding intermediate perpendicular anisotropy (). These samples provide an appropriate template for the study of the magnetic reorientation from in plane to out of plane magnetization upon layer's thickness increase. VSM, transverse Kerr measurements and magnetic force microscopy have been used in order to determine the relevant magnetic parameters and the occurrence of the reorientation transition. Received 13 October 1998 and Received in final form 5 February 1999     

Quantum spin model of a cubic ferromagnet in a magnetic field

The zero temperature phase diagram of a one-dimensional ferromagnet with cubic single ion anisotropy in an external magnetic field is studied. The mean-field approximation and the density-matrix renormalization group method are applied. Two phases at finite magnetic fields are identified: a canted phase with spontaneously broken symmetry and a phase with magnetization along the magnetic field. Both methods predict that the canted phase exists even for the single-ion anisotropy strong enough to destroy the magnetic order at zero magnetic field. In contrast to the mean-field theory, the density-matrix renormalization group predicts a reentrant behavior for the model. The character of the phase transition at finite magnetic field has also been considered and the critical index has been found. Received 9 May 2000 and Received in final form 5 July 2000     

The analytical treatment of magnetic properties of three-layer ferrimagnetic superlattice

The Hamiltonian of the magnetic superlattice with three-layer unit cell was treated within the Boson formalism. The Boson Green’s functions (BGFs) were derived and it was shown that the system for BGFs splits into two sets which lead to the energies with opposite signs, although the energies of elementary excitations are strictly only the positive ones. However, when corresponding energies are used, the correlation functions calculated from both sets are the same. All the physically relevant quantities: total energy of the system, ground state energy, layer magnetization and zero-point (quantum) fluctuations are derived analytically by using both sets, showing that they lead to the same expressions. The Hamiltonian was also diagonalized by the so-called “u-v” transformation of the operators. It is shown that in spite of formal independence of the approaches, there exists a close relationship between BGF and “u-v” transformations.     

Magnetism of alloyed models of Cr(Mn) V and Mn Cr overlayers on V (001) substrates

The magnetism is calculated for substitutional alloyed of Cr_x(Mn_x)V_1-x monolayers (MLs) and Cr_xMn_1-x on V (001) surface with a variety of concentrations (x = 0.25, 0.50 and 0.75). The substitutional surface alloys were treated by an artificial super cell construction. Parallel magnetic ordering is obtained for all the considered structures. The surface net magnetization increases in terms of Cr (Mn) concentration in Cr_x(Mn_x)V_1-x/V (001) system, while no serious variations occur in Cr_xMn_1-x/V (001). Vanadium atoms at the interfacial layers acquire appreciable magnetic moments antiferromagneticlly (AF) coupled with the surface moments. Received 25 February 2002 / Received in final form 13 May 2002 Published online 14 October 2002 RID="a" ID="a"e-mail: jkalifa@sci.ju.edu.jo     

Scaling behaviour of the energy gap of spin-1/2 AF-Heisenberg chains in both uniform and staggered fields

The energy gap of the 1D AF-Heisenberg model in the presence of both uniform (H) and staggered (h) magnetic fields is investigated using the exact diagonalization technique. The opening of the gap in the presence of a staggered field is found to scale with h^ν, where ν=ν(H) is the critical exponent, and depends on the uniform field. With respect to the range of the staggered magnetic field, two regimes are identified through which the dependence of the real critical exponent ν(H) on H can be calculated numerically. Our numerical results are in good agreement with the results obtained by other theoretical approaches.     

Second- to first-order transition in two coupled antiferromagnetic rings

We numerically investigate an S=1/2 spin model, in which two dimerized antiferromagnetic rings interact with each other ferromagnetically. It is shown that the order of the magnetoelastic transition is strongly affected by the interring coupling J_⊥ and there may exist a critical J_⊥^* dividing the first-order transition and the continuous transition.     

Order by thermal disorder in 2D planar rotator model with dipolar interactions

The energy of a square planar rotator model of spins interacting via dipolar forces is minimized by infinite inequivalent configurations corresponding to spins arranged on four interpenetrating sublattices making angles , , , with a reference axis, being arbitrary. This infinite degeneracy of the ground state is accidental in nature and one expects that it is removed by thermal fluctuations in agreement with Monte Carlo simulation. Indeed we find that the elementary excitation energies which depend on lead to a free energy which is a function of with minima at and corresponding to columnar configurations. This selection of columnar configurations out of the infinite ground state manifold is an example of order by thermal disorder. Received 4 August 1998     

Low temperature thermodynamics of inverse square spin models in one dimension

We present a field-theoretic renormalization group calculation in two loop order for classical O(N)-models with an inverse square interaction in the vicinity of their lower critical dimensionality one. The magnetic susceptibility at low temperatures is shown to diverge like with a=(N-2)/(N-1) and . From a comparison with the exactly solvable Haldane-Shastry model we find that the same temperature dependence applies also to ferromagnetic quantum spin chains. Received: 20 February 1998 / Revised: 27 April 1998 / Accepted: 30 April 1998