Magnetization and susceptibility of disordered alloy with competitive interactions

A model calculation of magnetization and susceptibility of disordered alloy (A _pB_{1 −p} ) where bothA andB represent the magnetic atoms is presented. It is based on the cluster-variational method where interactions within the clusters of all possible configurations are treated exactly and the rest of the interaction is replaced by an effective variational field. The frustration effect is introduced taking the exchange interactionsJ _AB orJ _BB or both to be antiferromagnetic whereas the exchangeJ _AA is ferromagnetic. The results are qualitatively similar to the observed behaviour of moment and susceptibility in some metallic glasses. The critical concentration for ferromagnetic state is determined in the presence of competitive interactions.     

General Features of the X Part of an ABX Spin System in Isotropic and Liquid Crystalline Phases as Illustrated by theC–{H} Spectra of 2,2′-Difluorobiphenyl

The¹³C–{¹H} NMR spectra of 2,2′-difluorobiphenyl dissolved in isotropic and liquid crystalline solvents have been obtained and analyzed. They are examples of the X part of an ABX spectrum. It is shown that the spectrum of the isotropic solution yieldsJ_AX,J_BX,J_AB, δ_AB, and δ_X, but only if all the transitions are detected, and that intensities as well as frequencies of the transitions are used in the analysis. It is demonstrated that for 2,2′-difluorobiphenyl this requires that for some of the carbons it is necessary to detect very weak transitions. For the spectra of liquid crystalline solutions of ABX systems it is shown that the dipolar couplingsD_AX,D_BX, andD_ABare obtained only if these couplings are in a certain sensitive range of relative values. The sensitive range can be adjusted by using variable angle sample spinning (VASS). It is demonstrated that VASS spectra taken near the magic angle can be used to obtain the absolute signs of the scalar couplings.     

Phase diagrams and magnetic properties of diluted Ising and Heisenberg magnets with competing interactions

Ising and Heisenberg magnets with nearest-neighbor ferromagnetic exchangeJ ₁ and next-nearest antiferromagnetic exchangeJ ₂ and randomly distributed frozen-in nonmagnetic impurities of arbitrary concentration 1–x are studied by several methods: systematic series expansions inx, 1–x and inverse temperature (1/T) as well as Monte Carlo simulation. Depending onRJ ₂/J ₁,T andx the model is in paramagnetic, ferromagnetic, antiferromagnetic or spin glass phases. The microscopic magnetic structures of all these phases are investigated and found to be more complicated than usually (e.g., the ferromagnetic state contains spins and clusters either aligned antiparallel or not aligned at all, when frustration effects make bonds ineffective). We suggest that the concentrationx _c of magnetic ions below which no (anti-)ferromagnetic long range order occurs depends onR continuously, andx _c 1 at the multicritical point (R _m ,T=0) where the order changes from ferromagnetic to antiferromagnetic. Our results for phase diagram, susceptibility etc. are compared to recent data on the Eu _x Sr_1–x S system and very good agreement is found.     

Phase diagram of the Ising Model on a Cayley tree in the presence of competing interactions and magnetic field

We study the phase diagram for the Ising Model on a Cayley tree with competing nearest-neighbor interactionsJ ₁ and next-nearest-neighbor interactionsJ ₂ andJ ₃ in the presence of an external magnetic field. To perform this study, an iterative scheme similar to that appearing in real space renormalization group frameworks is established; it recovers, as particular cases, previous works by Vannimenus and by Inawashiroet al. At vanishing temperature, the phase diagram is fully determined, for all values and signs ofJ ₂/J ₁ andJ ₃/J ₂; in particular, we verify that values ofJ ₃/J ₂ high enough favor the paramagnetic phase. At finite temperatures, several interesting features (evolution of reentrances, separation of the modulated region into two disconnected pieces, etc.) are exhibited for typical values ofJ ₂/J ₁ andJ ₃/J ₂.Partially supported by the Brazilian Agencies CNPq and FINEP.     

Spin Dynamics and Dirac Nodes in a Kagome Lattice

Herein, the spin dynamics for various magnetic configurations arranged on a Kagome lattice is investigated. Using a Holstein–Primakoff expansion of the isotropic Heisenberg Hamiltonian with multiple exchange parameters, the development and evolution of magnetic Dirac nodes with both anisotropy and magnetic field are examined. From the classical energies, the phase diagrams for the ferromagnetic (FM), antiferrimagnetic (AfM), and the 120°  phases are shown as functions of J₁, J₂, J₃, and anisotropy. Furthermore, the production of bosonic Dirac and Weyl nodes in the spin-wave spectra is shown. Through frustration of the magnetic geometry, a connection to the asymmetric properties of the Kagome lattice and the various antiferromagnetic configurations is discerned. Most interesting is the 120°  phase, which does not have Dirac nodes when considering only J₁ due to the formation of an analogous antiferromagnetic honeycomb lattice, but gains Dirac symmetry with next-nearest neighbor interactions. Additionally, the presence of flat modes that are characteristic of cluster excitations is shown. Further study of external frustrations from a magnetic field and anisotropy reveals a tunability of the exchange interactions and nodal points.     

Macroscopic quantum tunneling in small magnetic particles

Macroscopic quantum tunneling of magnetization in small antiferromagnetic clusters is studied for the spin-1/2 anisotropic (J _z ≡ J, J _x =J _y ≡J _xy ) Heisenberg model with the use of both perturbation theory and an exact numerical diagonalization technique. Splitting of the two lowest levels due to the lifting of the degeneracy between them (in the case J _xy =0) by the in-plane exchange (J _xy ≠ 0) is found to occur in the N/2th order of perturbation theory. Tunneling is absent in systems with an odd number of sites, in which the levels are doubly degenerate in zero magnetic field. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 9, 688–693 (10 May 1996) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Crystallographic anisotropy and distortions in helicoidal magnetic structure

The appearance and development of aperiodic distortions in a helicoidal, layered magnetic structure with increasing crystallographic magnetic anisotropy in the magnetization rotation plane have been theoretically studied. A simple phase diagram for this system is proposed. It is established that, at a weak anisotropy, the spiral splits into regions of various lengths with an approximately uniform rotation of the magnetization in each region and a deviation from uniformity at the boundaries; the stronger the anisotropy, the shorter the regions and the greater the deviations. In the limit of high anisotropy, the minimum energy of the system corresponds (depending on the ratio of interlayer exchange integrals J ₁ and J ₂) to either a spiral with constant angular pitch (a multiple of the angle between easy axes) or a double antiferromagnetic structure with a four-layer period. In the case of sixth-order anisotropy with |J ₁| = −J ₂, the energies of phases with different periods (four and six layers for J ₁ > 0; four and three layers for J ₁ < 0) coincide and the excess boundary energy vanishes. In the case of a fourth- and second-order anisotropy, the analogous anomalies appear at |J ₁| = −2J ₂. As a result, the magnetic structure at these points becomes unstable and the phase diagram exhibits the corresponding singularities.     

Spin waves in the block checkerboard antiferromagnetic phase

Motivated by the discovery of a new family of 122 iron-based superconductors, we present the theoretical results on the ground state phase diagram, spin wave, and dynamic structure factor obtained from the extended J₁-J₂ Heisenberg model. In the reasonable physical parameter region of K₂Fe₄Se₅, we find that the block checkerboard antiferromagnetic order phase is stable. There are two acoustic spin wave branches and six optical spin wave branches in the block checkerboard antiferromagnetic phase, which have analytic expressions at the high-symmetry points. To further compare the experimental data on neutron scattering, we investigate the saddlepoint structure of the magnetic excitation spectrum and the inelastic neutron scattering pattern based on linear spin wave theory.     

Polarized photofluorescence excitation spectroscopy

When a triatomic molecule ABC is photolysed by a beam of light to produce the fragments AB and C, the directional nature of the photo-dissociation process manifests itself in a number of ways; in particular, the angular distribution of each fragment is anisotropic, and the angular momentum vector J of the AB photofragment points in space with a preferential distribution with respect to the direction of the light beam. If the AB diatomic fragment is electronically excited, then the emission from AB* will, in the absence of collisions, be polarized, and a measurement of the degree of polarization, p, will provide information about the symmetry nature and dissociation dynamics of the photoexcited state (ABC)*. A number of limiting cases are presented for the sign and magnitude of p, calculated in the classical high J limit, following dissociation of both linear and bent triatomic molecules.     

Transport properties of antiferromagnetic fcc-iron alloys

A study is reported of the electrical resistance and thermopower of Fe_xNi_80−x Cr₂₀ fcc alloys within the 44⩽x⩽70 at. % range. It is shown that, at low temperatures, they typically exhibit minima in the temperature dependences of electrical resistance. The appearance of these anomalies is attributed to the formation of a gap in the conduction electron spectrum due to the onset of long-or short-range antiferromagnetic order in the alloys. The effect of magnetic field on the magnetic states appearing in frustrated antiferromagnetic alloys has been studied, and an H-T magnetic phase diagram constructed. Fiz. Tverd. Tela (St. Petersburg) 40, 101–105 (January 1998)     

Magnetic and non-magnetic ground states of the Kondo lattice

We use the variational method to investigate the ground state phase diagram of the Kondo lattice Hamiltonian for arbitraryJ/W, and conduction electron concentrationn _c (J is the Kondo coupling andW the bandwidth). We are particularly interested in the question under which circumstances the globally singlet (collective Kondo) Fermi liquid type ground state becomes unstable against magnetic ordering. For the collective Kondo singlet we use the lattice generalization of Yosida's wavefunction which implies the existence of a large Fermi volume, in accordance with Luttinger's theorem. Using the Gutzwiller approximation, we derive closed-form results for the ground state energy at arbitraryJ/W andn _c, and for the Kondo gap atn _c=1. We introduce simple trial states to describe ferromagnetic, antiferromagnetic, and spiral ordering in the small-J (RKKY) regime, and Nagaoka type ferromagnetism at largeJ/W. We study three particular cases: a band with a constant density of states, and the (tight binding) linear chain, and square lattice periodic Kondo models. We find that the lattice enhancement of the Kondo effect, which is described in our theory of the Fermi liquid state, pushes the RKKY-to-nonmagnetic phase boundary to much smaller values ofJ/W than it was previously thought. In our study of the square lattice case, we also find a region of itinerant, Nagaoka-type ferromagnetism at largeJ/W forn _c 1/3.     

Magnetic phases in quasi-binary (Fe1−x Cox)Ge2 intermetallic compounds

Magnetic neutron diffractometry revealed the existence in (Fe_1−x Co_x)Ge₂ solid solutions (x<0.5) with C16 structure of only two magnetic phases, namely, low-temperature (AFI) and high-temperature (AFII). A third magnetic phase, AFIII, suggested by earlier magnetic measurements, has not been found. The AFI and AFII phases have a commensurate and an incommensurate antiferromagnetic structure with the wave vectors k ₀=2π/a (1,0,0) and k=k ₀+δ k, respectively. The regions of their existence are shown in the magnetic phase diagram. Neutron diffraction measurements yielded the concentration dependence of the average magnetic moment per atom in the antiferromagnetic sublattice of a 3d metal, which, similarly to the dependence of the Néel point on x, was found to be nonlinear. An analysis of these dependences suggests that substitution of cobalt for iron is accompanied, on the one hand, by a decrease of the local spin density on the iron atoms in the nearest environment of a cobalt atom and, on the other hand, by an increase of the effective exchange integral between the nearest-neighbor iron atoms located along the tetragonal axis. Fiz. Tverd. Tela (St. Petersburg) 41, 283–289 (February 1999)     

Quasi-one-dimensional antiferromagnet LiCuVO4

An antiferromagnetic transition is observed in the quasi-one-dimensional metal-oxide compound LiCuVO₄. A wide peak is observed in the temperature dependence of the magnetic susceptibility at T _M =28 K, and the magnetic susceptibility exhibits a sharp drop at T _N ≈4 K. As the magnetic field increases, the antiferromagnetic-ordering temperature T _N =2.3 K at first increases somewhat and then decreases rapidly. The exchange interaction in the chains of copper-oxygen octahedra is estimated to be J ₁=22.5 K. The interchain interaction is estimated to be J ₂∼1 K. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 11, 828–831 (10 June 1999)     

Spin state and exchange in the quasi-one-dimensional antiferromagnet KFeS2

We report the optical spectra and single crystal magnetic susceptibility of the one-dimensional antiferromagnet KFeS₂. Measurements have been carried out to ascertain the spin state of Fe³⁺ and the nature of the magnetic interactions in this compound. The optical spectra and magnetic susceptibility could be consistently interpreted using aS=1/2 spin ground state for the Fe³⁺ ion. The features in the optical spectra have been assigned to transitions within thed-electron manifold of the Fe³⁺ ion, and analysed in the strong field limit of the ligand field theory. The high temperature isotropic magnetic susceptibility is typical of a low-dimensional system and exhibits a broad maximum at ∼565K. The susceptibility shows a well defined transition to a three dimensionally ordered antiferromagnetic state atT _N=250 K. The intra and interchain exchange constants,J andJ′, have been evaluated from the experimental susceptibilities using the relationship between these quantities, andχ _max,T _max, andT _N for a spin 1/2 one-dimensional chain. The values areJ=−440.71 K, andJ′=53.94 K. Using these values ofJ andJ′, the susceptibility of a spin 1/2 Heisenberg chain was calculated. A non-interacting spin wave model was used belowT _N. The susceptibility in the paramagnetic region was calculated from the theoretical curves for an infiniteS=1/2 chain. The calculated susceptibility compares well with the experimental data of KFeS₂. Further support for a one-dimensional spin 1/2 model comes from the fact that the calculated perpendicular susceptibility at 0K (2.75×10⁻⁴ emu/mol) evaluated considering the zero point reduction in magnetization from spin wave theory is close to the projected value (2.7×10⁻⁴ emu/mol) obtained from the experimental data.     

Transition De Phase Metamagnetique Du Bromure Ferreux

In a magnetic field parallel to the magnetization axis of an antiferromagnetic Fe Br₂ single crystal, a caracteristic metamagnetic behaviour is observed. The transition from an antiferromagnetic phase to a paramagnetic phase is studied by help of magnetization measurements in a steady field (H < 60 kOe). The measurement precision has allowed a detailed study of the magnetization isotherms, caracteristic of a first order magnetization phase transition (T < T_c = 4, 7 K) and of a second order phase transition (T_c < T < T_N = 14, 2 K).We have observed an original phase diagram. In a certain temperature and field range, the ordered phase is stable on the high temperature side of the transition point. Some theoretical studies in an Ising model, or in the hypothesis of a strong magnetoelastic coupling forecast the existence of such a magnetic phase diagram.At present, we proceed to a theoretical study, in a molecular field approximation, of the magnetic phase diagram of compounds similar to Fe Br₂ where we take into account the relative values of parameters J₁, J₂ and D associated with ferromagnetic and antiferromagnetic interactions and crystalline anisotropy.     

Coherent Exchange Cluster Approach for two-dimensional disordered Heisenberg spin systems

The spin wave properties of disordered two-dimensional and quasi two-dimensional Heisenberg spin systems, with an antiferromagnetic ground state (Neèl state) induced by single-ion anisotropy, are discussed within a Coherent Exchange Cluster Approach (Cluster CEA).The configuration averaged Green's functions are described by an effective spin wave Hamiltonian, with two sets of complex and energy dependent coherent exchange integralsJ _lm ¹ (E) andJ _lm ² (E) appropriate to the consideration of two different spins of the binary alloy constituents.J _lm ¹ andJ _lm ² , depending only on the distance of the sitesl andm, are taken to be non zero only for nearest neighbours. The remaining two quantitiesJ ¹(E) andJ ²(E) are determined self-consistently from the requirement that the most important matrix elements of the scatteringT matrix vanish when the configuration averaging has been performed.Numerical results are presented for the antiferromagnetic quasi two-dimensional systems K₂Ni _c Mn_1-c F₄ and Rb₂Fe _c Mn_1-c F₄.Both the density of states and the transverse susceptibilities, determining essentially the neutron scattering cross-sections, are calculated.The density of spin wave states for K₂Ni _c Mn_1-c F₄ is compared for different concentrations with exact computer calculations for finite 30 × 30 arrays. The agreement is excellent.Based on the thesis of H.J. Schlichting, Fachbereich Physik der Universität Hamburg, 1974.     

Dynamical interaction of antiferromagnetic subsystems: a neutron scattering study of the spinwave spectrum of the garnet Fe2Ca3(GeO4)3

The Fe³⁺ ions in the garnet Ca₃Fe₂Ge₃O₁₂ form two identical antiferromagnetic subsystems. The interaction between the two subsystems is vanishing within molecular field approximation forq=0. A coupling appears due to the spin fluctuations. The dynamics of the system is described by the Hamiltonian for a Heisenberg antiferromagnet. Symmetry requirements impose two exchange parameters between the sublattices (nearest neighbours)J ₁ in the direction of the 3-fold axis andJ' ₁ in the other three space diagonals. The interaction within each sublattice (second nearest neighbours) is described by the exchange parameterJ ₂. The measured spin wave dispersion curves for the three principal symmetry directions are very well reproduced by a model calculation withJ ₁=-0.909(9) K,J' ₁=-0.307(8) K andJ ₂=-0.615(2)K. The observed intensities are in agreement with predictions from the model. Forq0 the model predicts two acoustic branches going towards zero frequency. A calculation beyond linear spin wave theory forq=0 predicts a quantum gap for the lower acoustic branch. This gap has been found at 0.033(4) THz. An anisotropy gap of 0.007 THz has been taken from the literature.     

Mössbauer study of CoFeRhO4

CoFeRhO₄ has been studied by Mössbauer spectroscopy and X-ray diffraction. The crystal is found to have a cubic spinel structure with the lattice constant a₀=8.451±0.005 Å. The iron ions are in ferric states. The temperature dependence of the magnetic hyperfine field is analyzed by the Néel theory of ferrimagnetism. The intersublattice superexchange interaction is antiferromagnetic and strong with a strength of J_AB=−12.39k_B while the intrasublattice superexchange interactions are weak with strengths of J_AA=−4.96k_B and J_BB=6.20k_B. As the temperature increases toward the Néel temperature T_N, a systematic line broadening effect in the Mössbauer spectrum is observed and interpreted to originate from different temperature dependences of the magnetic hyperfine fields at various iron sites.     

Electronic structures of ternary iron arsenides AFe2As2 (A = Ba, Ca, or Sr)

We have studied the electronic and magnetic structures of the ternary iron arsenides AFe₂As₂ (A = Ba, Ca, or Sr) using the first-principles density functional theory. The ground states of these compounds are in a collinear antiferromagnetic order, resulting from the interplay between the nearest and the next-nearest neighbor superexchange antiferromagnetic interactions bridged by As 4p orbitals. The correction from the spin-orbit interaction to the electronic band structure is given. The pressure can reduce dramatically the magnetic moment and diminish the collinear antiferromagnetic order. Based on the calculations, we propose that the low energy dynamics of these materials can be described effectively by a t-J _H -J ₁-J ₂-type model [2008, arXiv: 0806.3526v2].     

Magnetic properties of ferromagnetic diluted Zn x Cd1–x Cr2Se4 spinels are studied by Green's functions,mean field theory and high temperature series expansions theories

The field induced reorientation of the magnetization of ferromagnetic (or antiferromagnetic) structure is treated within the framework of many-body Green's function theory by considering all components of the magnetization. The mean field theory is used to calculate the nearest neighbour and the next-neighbour super-exchange J₁(Cr–Cr) and J₂(Cr–(Zn(Cd)–Se)–Cr), respectively, for the Zn_1–x Cd _x Cr₂Se₄ in the range 0 < x < 1. The intraplanar and the interplanar interactions are deduced. The high temperature series expansions (HTSEs) are derived for the magnetic susceptibility and the two-spin correlation functions for a Heisenberg ferromagnetic model on the B-spinel lattice. The calculations are developed in the framework of the random phase approximation (RPA). The magnetic phase diagram is deduced. A spin glass phase is predicted for intermediate range of concentration. The obtained results are comparable with those obtained by magnetic measurements. The critical exponents associated with the magnetic susceptibility (γ) and the correlation lengths (ν) have been deduced. The obtained values are comparable to those of 3D Heisenberg model.