Spin waves and exchange interactions in the antiferromagnetic garnets with Fe3+ in the octahedral sites

The results of an inelastic neutron scattering study of the spin wave spectrum for the garnet Fe₂Ca₃Si₃O₁₂(FeSiG) are presented. We compare the exchange parameters for this garnet and for the Ge-species (Fe₂Ca₃Ge₃O₁₂(feGeG)) having the same magnetic structure. We relate the differences found with structural information from powder neutron diffraction. In this way the super exchange paths viap orbitals of intermediate oxygen atoms can be identified. We discuss the effect of a small number (3.2(5)%) of Mn²⁺ impurities in the 24c sites. These lead to an effective ferromagnetic exchange between the Fe³⁺ ions and drastically renormalize the average exchange constants. An estimate for the Fe³⁺–Mn²⁺ indirect exchange between a and c sites of 6(1) K is obtained. The exchange parameters for the pure FeSiG are found to beJ ₁=1.16(4) K,J ₁=0.96(4K andJ ₂=–1.24(4) K for nearest and next nearest neighbours, respectively. These values apply for a moment of 4.02(4) _B per iron atom as obtained from a structure refinement of powder diffraction data. Finally we present results for FeSiG of a high resolution study of the excitations at the zone centre in an attempt to verify our earlier findings of a quantum spin wave gap for FeGeG. In contrast to the earlier measurements, we could follow the acoustical branch to much lower energies using a timeof-flight spectrometer. We found indications for a crossing of the two low lying spin wave branches, the acoustical one extrapolating to the anisotropy gap of 0.005 THz and the antiphase branch extrapolating to the quantum gap of 0.02 THz.     

Spin wave spectrum and exchange interactions in the antiferromagnetic garnet Ca3Cr2Ge3O12 by inelastic neutron scattering

We have measured the spin wave spectrum for the garnet Ca₃Cr₂Ge₃O₁₂ by means of inelastic neutron scattering. The data can be well described in the framework of linear spin wave theory if we assume a Heisenberg model with two exchange parameters up to the next nearest neighbours (J ₁ andJ ₂) and a staggered anisotropy field (A). A least squares fit to the observed dispersion relations yield the following values for these parameters: J ₁=–0.582(8)K,J ₂=0.416(4)K,A=0.25(8)K. Although symmetry requires that two nearest neighbour exchange constantsJ ₁ andJ ₁ ^' must be distinguished, only the average J ₁=(J ₁+3J ₁ ^' )/4 and the condition –0.35 K <J ₁=J ₁-J ₁ ^' <0.50 K could be deduced from the experiment. The most striking result is the positive value ofJ ₂. We discuss the implications for an understanding of superexchange mediated by more than one oxygen atom. In an extension of the conventional analysis we have calculated the integrated intensities in order to check the eigenvectors directly. Good agreement between observed and calculated intensities was obtained.     

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

The spin wave properties of disordered two-dimensional and quasi two-dimensional disordered Heisenberg spin systems, with a ferromagnetic ground state induced by single-ion anisotropy, are discussed within a Coherent Exchange Cluster Approach (Cluster CEA). The configuration averaged Green's function is described by an effective spin wave Hamiltonian, with complex and energy dependent coherent exchange integrals , where, depends only on the distance of the sitesl andm Considering only nearest neighbour clusters, the more distant exchange is neglected, whereas the nearest neighbour coherent exchange integral is determined by the self-consistency requirement that the most important matrix elements of the scatteringT matrix vanish when the configuration averaging has been performed. The approximations inherent within this approach are discussed, and it is argued that it is practically impossible to improve it essentially.The results of numerical calculations for the square lattice are presented: The parameters have been chosen as to discuss, in a somewhat hypothetical way, the properties of Fe–Ni monolayers on a Cu substrate, especially for dominating Fe concentration, where experiments are still lacking. In contrast to the oversimplified standard Single Bond CEA, the Cluster CEA yields a considerable structure within the density of states. Furthermore, for the almost dilute case, with Ni concentrationc _Ni=0.2 and exchange integralsJ _{Ni, Fe}=2.5·J _{Ni, Ni},J _{Fe, Fe}=0.3·J _{Ni, Ni}, there is even a gap, as expected from exact calculations for isolated impurities. Even within this case, the Green's functions and self-energies are analytic, in contrast to certain generalizations of the well-known CPA method for electronic systems.Concerning the critical concentrations for the appearance of a spin wave instability with negative Fe–Fe exchange, the Cluster CEA yields much better results than the Single Bond CEA.     

Fe57 Mössbauer study in cobalt substituted magnetite

The Mössbauer effect has been studied in the mixed ferrites Co _x Fe_3–x O₄ (forx=0.8, 0.9 and 1) with the spinel structure in the temperature range between 78 and 380 K. The composition withx=1, showed an expected Zeeman spectrum with two overlapping magnetic hyperfine patterns related to the Fe³⁺ ions in tetrahedral and octahedral sites. While for samples withx=0.8 and 0.9 the Mössbauer spectrum for each compound was successfully analysed into three different patterns corresponding to the ferric ions placed at the tetrahedral and octahedral sites and ferrous ions at the octahedral sites, indicating no electron transfer between Fe³⁺ and Fe²⁺, where the quantity of cobalt is sufficiently large to be located at the six nearest neighbours to ferrous ions. The Mössbauer effect parameters were calculated for these observed sites and their variation with temperature reported. The reduced hyperfine magnetic fields of the Fe³⁺ (B) ions were found to follow the Brillouin curve forS=5/2 and one third power law. The magnetic ordering temperature was determined to be 815 K and the possible magnetic interactions were discussed.     

Excitations in Heisenberg spin glasses

Within the RPA approach forT=0, the excitations of the Heisenberg spin glass system Eu _x Sr_1–x S are studied by numerical methods, using a continued fraction algorithm. Both the density of statesg(E) and also the spectral functionS(q,E) are calculated for systems with (16)³ sites, withx=0.4, 0.5, and 0.6 (spin glass phase), and also forx0.7 (ferromagnetic phase). Forq-vectors within the (1,1,1) plane,S(q,E) shows magnon peaks even in the spin glass phase, over the whole range ofq. However, these peaks are quite broad, and there is considerable intensity at small energies even for largeq, leading to a finite intercept ofg(E) forE0. Over a large temperature range, the specific heat is approximately linear inT forx0.7.     

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.     

A possible coupling mechanism between magnetism and dielectric properties in EuTiO3

The dielectric constant of an incipient ferroelectric EuTiO₃ exhibits a sharp decrease at about 5.5K, at which the antiferromagnetic ordering of the Eu spins simultaneously appears. This fact indicates the existence of a coupling between the magnetism and dielectric properties of EuTiO₃. We propose a possible coupling mechanism between the magnetic and electrical subsystems as -g\dsum_l \dsum_〈i,j〉q²_l\vec S_i·\vec S_j. In the framework of soft-mode theory, we have obtained analytically a dielectric constant expression related to the spin correlation of nearest neighbours of Eu ions.     

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.     

Magnetic susceptibility of a one-dimensional Fermi system and dielectric function of a two-dimensional Coulomb gas

A relation between the magnetic susceptibility(k, ) of an interacting 1-D Fermi system and the dielectric function(q) of a 2-D Coulomb gas is established. By applying a cluster-expansion technique and by using known results for the pair-correlation function of the Coulomb gas we obtain a number of expressions for(q) which apply in different regions of theq-plane and in different temperature intervals. These results supplement the existing picture of the transition from non-metallic to metallic behaviour occurring in the 2-D Coulomb gas as the temperature increases. The relation between(q) and(k, ) is then used to derive explicit expressions for(k, ) from these results for(q). The change in the dielectric response of the 2-D Coulomb gas is reflected by a change in the magnetic response of the 1-D Fermi system: as a function of the spin non-flip coupling constant the susceptibility of the Fermi system changes from normal paramagnetic behaviour to non-magnetic behaviour characteristic of a bound singlet-spin ground state, as decreases. Our result for the gap in the spin excitation spectrum of the Fermi system is in agreement with the results of other authors.On sabbatical leave from Institut für Theoretische Physik, TU Hannover, GermanyWork at U.C.S.B. supported in part by the National Science Foundation     

Magnetic phase diagram of spinel spin-glasses

The article by Villain [Z. Phys. B — Condensed Matter33, 31 (1979)] is discussed and a modified magnetic phase diagram is suggested for the spinel system (AB₂O₄) in which theA andB sites are partially (or completely) occupied by magnetic atoms. This diagram takes into account the antiferromagnetic exchange interactionsJ _AA,J _BB andJ _AB between nearest neighbor cations of various types. Regions of paramagnetic, antiferromagnetic, ferrimagnetic and possible spin glass behaviour are indicated on the diagram.Supported by the National Science Foundation under Grant ISP-80-11451     

DPAC measurement of the hyperfine fields in100RhCo and100RhFe

Using the 85–75 keV -cascade of¹⁰⁰Rh, we report the first DPAC measurement of the hyperfine field in¹⁰⁰RhCo and¹⁰⁰RhFe. Our results were made possible by continued improvement in time resolution using BaF₂ scintillators. At room temperature we obtained fields of 420.6(1.3) kG and 540.4(1.5) kG for¹⁰⁰RhCo and¹⁰⁰RhFe, respectively. The former revises an earlier spin echo result by Kontani and Itoh by 9%; the latter is consistent with the work of Matthiaset al. using resonant destruction of angular correlations.     

Experimental determination of spin-rotation and spin-spin magnetic interactions in by nuclear spin conversion

When a gas sample of ¹³CH₃F is prepared with a population of isomers (ortho and para forms) far from the equilibrium given by nuclear spin statistics, it relaxes towards this equilibrium with an exponential decay rate. This phenomenon called nuclear spin conversion is mainly governed by intramolecular spin-spin and spin-rotation interactions. In the quantum relaxation model [P.L. Chapovsky, Phys. Rev. A 43, 3624 (1991)], two pairs of ortho-para levels (J = 9, K = 3; J' = 11, K' = 1) and (J = 20, K = 3; J' = 21, K' = 1) are principally responsible for the conversion. The levels of the second pair are coupled by both spin-spin and spin-rotation interactions. The application of an electric field (up to 10 kV/cm) induces a crossing of the Stark components of this pair, which is observed for the first time. A specific experimental set-up based on an electric field of alternating triangular shape is used, which allows the determination of the strength of both interactions via the measurement of the spin conversion decay rates. This work yields the first experimental value for the electronic contribution to the spin-rotation interaction in ¹³CH₃F. Received 23 May 2002 / Received in final form 18 September 2002 Published online 21 January 2003 RID="a" ID="a"e-mail: Patrice.Cacciani@univ-lille1.fr     

Collective excitations in the 1-D-ferromagnet CsFeCl3 with singlet ground state

By means of inalastic neutron scattering we have determined the dispersion relation of the magnetic excitations in CsFeCl₃ at different temperatures.The dispersion in c-direction, along the Fe-chains is typically ferromagnetic and in the hexagonal plane antiferromagnetic. Due to the lack of an applicable theory the data were parametrized by the simple heuristic formula:?ω = [2J[1 - cos πq_c] [A + 2J(1 - cos π)q_c)] + [C + J' (1.5 + γ(q))]²]^{$\text{1}\text{2}$}The gap was found to be C = 0.148 THz, the easy plane anisotropy A = 0.308 THz, the ferromagnetic interaction J = 0.148 THz and the antiferromagnetic interaction J' = -0.04 THz. At 1.25 K all excitations had a width smaller than the instrumental resolution ΔE = 0.025 THz. These results can be interpreted as follows: CsFeCl₃ is a singlet ground state system with strong ferromagnetic interaction J along the crystallographic c-axis and weak antiferromagnetic interaction J' in the plane perpendicular to c.In addition we have measured the influence of a magnetic field along the hexagonal c-axis. The splitting found agrees with the assumed level scheme yielding g = 2.5 for the first excited level.     

Aspects of magnetic ordering in the system (FexCr1−x )2O3

Anomalon in temperature dependence of the magnetic moment (FexCr_1−x )₂O₃ single crystal has been observed which can be explained by antiparallel orientation of the mean weakly-ferromagnetic moments of the d subsystems (weak ferromagnetism). The disappearance of the linear magneto-electric effect for x=0.1 below 45 K is explained by a spontaneous phase transition from a conical spiral to a cycloidal spin structure, which is found to agree with a thermodynamic treatment. Fiz. Tverd. Tela (St. Petersburg) 39, 112–114 (January 1997)     

Investigation of the magnetic properties of chains with alternating ferro-and antiferromagnetic exchange interactions in the Heisenberg model with spin S=1/2

The quantum Monte Carlo method is used to calculate the susceptibility and pairwise spin-spin correlation functions of chains with alternating ferro (K)-and antiferromagnetic (J)-exchange interactions within the Heisenberg model with spin S=1/2. From the susceptibility, the energy gap between the ground state and excited triplet states is determined or arbitrary ratios K/J. The value of the gap coincides with the Haldane gap for spin S=1 when K/J>1.25. Fiz. Tverd. Tela (St. Petersburg) 41, 1650–1651 (September 1999)     

A theorem on the first heteroclinic tangency in two-dimensional maps. Orientation-preserving cases

Using the properties of the Jordan curve, the following theorem on the heteroclinic tangency in orientation-preserving two-dimensional maps is proved: LetT :R ² R ² be a one-parameter family ofC ¹ diffeomorphisms andJ=DetDT be such that 0<J1 or 1J<. LetW _u ⁿ be the unstable manifold of a hyperbolicn-cycle andW _s ^m the stable manifold of a hyperbolicm-cycle. Suppose that for< _c ,W _u ⁿ andW _s ^m have no common points, and that for> _c ,W _u ⁿ andW s/m have a transversal heteroclinic point. Then at= _c ,W _u ⁿ andW _s ^m are in the first asymptotic heteroclinic tangency except for the following three cases: (1)n=m; both cycles are without reflection. (2)m=2n; then- andm-cycles are with and without reflection, respectively; (3)n=2m; then- andm-cycles are without and with reflection, respectively.     

NMR relaxation times and proton motion in HxWO3

The relaxation timesT ₁,T _1q,T _1D, andT ₂ for¹H in the tetragonal-A phase of H_xWO₃ have been measured over the temperature range 190 to 490 K. The¹H relaxation behaviour appears to be governed by diffusion over inequivalent jump distances, approximating to a short range planar diffusion and a long range isotropic diffusion. Parameters for the latter motion are estimated asE _a = 68 kJ/mol and ₀=2.5×10^–13 s. The powder X-ray diffraction pattern for this phase of H_xWO₃ has been studied over the temperature range 300–470 K. The tetragonal distortion diminishes with temperature and H_0.43 WO₃ becomes cubic at about 435 K. Volumetric studies of hydrogen evolution show that decomposition accelerates at approximately this temperature.     

Magnetic field alignment of high-T c superconductorsRBa2Cu3O7–δ (R=rare earth)

Finely ground powders ofRBa₂Cu₃O_{7 –} (R=Y, Nd, Sm, Eu, Dy, Ho, Er, Tm, Yb) have been mixed at dilute 3%-by-volume concentrations into epoxy matrices which were then allowed to harden in applied magnetic fieldsH _A=18 kOe. X-ray diffractometry studies and 4.3 K measurements of supercurrent-induced magnetization hysteresisM are interpreted as indicating at least partial alignment of single-crystal-grain c-axes (1) parallel toH _A forR=Y, Nd, Sm, Dy, Ho (as earlier found by Farrell et al. forR=Y), and (2) perpendicular toH _A forR=Eu, Er, Tm, Yb. With a few exceptions (Y, Sm, Eu) the alignment direction correlates with the sign of the second-order Stevens factor _J of the crystalline electric field Hamiltonian in the manner suggested by Livingston et al. For the best aligned specimens (Ho, Dy) critical current densitiesJ _c (4.3 K, 5 kOe) for individual grains are estimated fromM and the Bean model to be of order 10⁷ A/cm² for the measuring fieldH parallel to the original alignment fieldH _A, and of order 10⁶ A/cm² forH perpendicular toH _A.     

Magnetic order in Sr x Ca1−x Cu0.99 57Fe0.01O2

Sr _x Ca_1–x Cu_0.99 ⁵⁷Fe_0.01O₂ was studied forx=0.13, 0.15, and 0.17. Mössbauer spectroscopy and magnetization measurements indicate magnetic ordering characteristic of spin glass systems withT _f70K forx=0.15 and 0.13.     

Ab initio determination of an extended Heisenberg Hamiltonian in CuO 2 layers

Accurate ab initio calculations on embedded Cu₄O₁₂ square clusters, fragments of the La₂CuO₄ lattice, confirm a value of the nearest neighbor antiferromagnetic coupling (J = 124 meV) previously obtained from ab initio calculations on bicentric clusters and in good agreement with experiment. These calculations predict non negligible antiferromagnetic second-neighbor interaction (J' = 6.5 meV) and four-spin cyclic exchange (K = 14 meV), which may affect the thermodynamic and spectroscopic properties of these materials. The dependence of the magnetic coupling on local lattice distortions has also been investigated. Among them the best candidate to induce a spin-phonon effect seems to be the movement of the Cu atoms, changing the Cu-Cu distance, for which the variation of the nearest neighbor magnetic coupling with the Cu-O distance is Δ J /Δ d _{Cu - O} ∼ 1700 cm^-1?^-1. Received 20 November 2000