Magnetic ground state and spin waves in A(A = K, Rb or Cs)Fe1.5Se2

We present theoretical results on the ground state phase diagram, spin waves and dynamic structure factor on the J₁-J₂ model. In the reasonable physical parameter region corresponding to AFe_1.5Se₂, the A-collinear antiferromagnetic phase is stable. The spin wave spectra have two acoustic branches and four optical branches for this phase on the rhombus-ordered vacancy lattice, and each of them is twofold degenerate. However, they have one nondegenerate acoustic branch and two nondegenerate optical branches on the square-ordered vacancy lattice. To offer the theoretical guidance for the further experiments, we also discuss the magnetic excitation spectra and the inelastic neutron scattering pattern based on linear spin wave theory.     

Elementary excitations in antiferromagnets with degenerate ground state: magnon energies and neutron scattering cross sections for the garnet Fe2Ca3 (GeO4)3

Within linear spin wave theory, we discuss the magnetic order of the antiferromagnetic garnet Fe₂Ca₃ (GeO₄)₃. We present this as an example of a system with a degenerated mean-field ground state, which consists here of a pair of enantiomorphic structures. While in mean field theory the first neighbour interaction cancels out for the magnetic structure, we show that it leads to a splitting of the acoustical spin wave branch. Stability regions in the space of the exchange constants are predicted. Taking into account the full symmetry of the garnet structure, we obtain additional optical branches not considered in earlier publications. For an inelastic neutron scattering experiment, we have calculated the double differential cross section for one magnon processes and predict regions in reciprocal space where the scattering should be strongest.     

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.     

Zero Temperature Phases of the Frustrated <Emphasis Type="Italic">J</Emphasis><Subscript>1</Subscript>–<Emphasis Type="Italic">J</Emphasis><Subscript>2</Subscript> Antiferromagnetic Spin-1/2 Heisenberg Model on a Simple Cubic Lattice

At zero temperature magnetic phases of the quantum spin-1/2 Heisenberg antiferromagnet on a simple cubic lattice with competing first and second neighbor exchanges (J ₁ and J ₂) is investigated using the non-linear spin wave theory. We find existence of two phases: a two sublattice Néel phase for small J ₂ (AF), and a collinear antiferromagnetic phase at large J ₂ (CAF). We obtain the sublattice magnetizations and ground state energies for the two phases and find that there exists a first order phase transition from the AF-phase to the CAF-phase at the critical transition point, p _c =0.56 or J ₂/J ₁=0.28. We also show that the quartic 1/S corrections due spin-wave interactions enhance the sublattice magnetization in both the phases which causes the intermediate paramagnetic phase predicted from linear spin wave theory to disappear.     

Phase transitions in the 2D J 1-J 2 Heisenberg model with arbitrary signs of exchange interactions

The ground state of the J ₁-J ₂ Heisenberg model with arbitrary signs of exchange is studied for spin S = 1/2 in the case of the two-dimensional (2D) square lattice. The states with different types of spin long-range order (antiferromagnetic checkerboard, stripe, collinear ferromagnetic) as well as the disordered spin liquid states are described in the framework of one analytical approach. In particular, it is shown that the phase transition between the ferromagnetic spin liquid and the ferromagnet with long-range order is of the second order. In the vicinity of such transition, we have found the ferromagnetic state with a rapidly varying condensate function.     

Inelastic neutron scattering study of acoustical magnons in MnFe2O4

The room-temperature spin wave spectrum in MnFe₂O₄ has been investigated by means of inelastic neutron scattering using the time-of-flight technique. The acoustical branch could be obtained in the [100]- and the [110]-directions up to nearly the Brillouin zone boundary. Values for the effective exchange parameters J_AB and J_BB have been derived. In both symmetry directions some low lying phonon branches could also be observed.     

Finite temperature properties and frustrated ferromagnetism in a square lattice Heisenberg model

The spin 1/2 Heisenberg model on a square lattice with antiferromagnetic nearest- and next-nearest neighbour interactions (the J ₁-J ₂ model) has long been studied as a paradigm of a two-dimensional frustrated quantum magnet. Only very recently, however, have the first experimental realisations of such systems been synthesized. The newest material, Pb₂VO(PO₄)₂ seems to have mixed ferro- and antiferromagnetic exchange couplings. In the light of this, we extend the semiclassical treatment of the J ₁-J ₂ model to include ferromagnetic interactions, and present an analysis of the finite temperature properties of the model based on the exact diagonalization of 8, 16 and 20 site clusters. We propose that diffuse neutron scattering can be used to resolve the ambiguity inherent in determining the ratio and sign of J ₁ and J ₂ from thermodynamic properties alone, and use a finite temperature Lanczos algorithm to make predictions for the relevant high temperature spin-spin correlation functions. The possibility of a spin-liquid phase occurring for ferromagnetic J ₁ is also briefly discussed.Received: 19 March 2004, Published online: 8 June 2004PACS: 71.27. + a Strongly correlated electron systems; heavy fermions - 71.10.-w Theory and models of many-electron systems - 75.40.Cx Static properties (order parameter, static susceptibility, heat capacities, critical exponents, etc.)     

Coherent Exchange Cluster calculations for antiferromagnetic disordered systems

The Coherent Exchange Cluster Approach developed in three preceding papers is applied to three-dimensional disordered antiferromagnetic Heisenberg spin systems with Perovskite structure, e.g. to KNi _x Mn_1–x F₃ and KNi _x Zn_1–x F₃. Both the level density of spin wave excitations, and the differential cross sections for inelastic neutron scattering are calculated. The results are compared with recent experiments, and also with results of simpler theories.It is found that the characteristic features of the excitation spectrum can be quite different even for binary alloys, i.e. besides the cases with one or two broadened magnon branches there might also exist systems with a more complicated spectrum.Dedicated to Prof. Dr. W. Döring on the occasion of his 65th birthday.     

Combination of muon spin relaxation and neutron scattering studies on magnetism

We combine the results from muon spin relaxation (μSR) and neutron scattering measurements performed on the same specimen (or system) of magnetic materials. The example on a spin glassCuMn (5%) shows that the two techniques have complementary time windows for studying dynamic spin fluctuations. In combining the results, one should note that muons and neutrons probe dynamic phenomena with different wavevectors. The results on antiferromagnetic La₂CuO_4−y illustrate the difference in the spatial range of static spin correlations reflected in the μSR precession frequency and the neutron Bragg peak intensity. With the examples of CeCu_2.1Si₂, YBa₂Cu₃O_x and Bi₂Sr₂YCu₂O_8+y , we point out that μSR is a superb tool for discovering static magnetic order while neutron scattering is the unique method to determine the spin structure. We emphasize that it is very fruitful to perform μSR and neutron experiments on the same specimen and to compare and combine the results for the better understanding of magnetism of various system.     

Spin configurations in hexagonal antiferromagnets with competing interactions

The ordered phase of the most part of ABX₃ antiferromagnets appears as a stacking of 120°-three sublattice spin layers with alternate spin direction along thec-axis. This configuration is easy to be explained because it is the minimum energy configuration of the Heisenberg hexagonal model with nearest neighbour antiferromagnetic interaction. However we show that moderate competitive interactions between in plane next nearest and third nearest neighbours stabilize incommensurate spin configurations. This gives some insight into the unexplained spin configuration observed in RbMnBr₃ by elastic neutron scattering experiment.     

Magnetic excitations in antiferromagnetic Bi<Subscript>2</Subscript>CuO<Subscript>4</Subscript>

Magnetic excitations in the antiferromagnetic Bi₂CuO₄ (T _N =42K) are investigated on the basis of anisotropic exchange interaction between spins of Cu²⁺ ions. We calculate the dispersion curves and evaluate the intensity of the inelastic neutron scattering by spin wave excitations. Spin contraction at OK and the effect of spin wave interaction are studied.     

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.     

Luttinger stripes in antiferromagnets

We propose a model for the physics of stripes in antiferromagnets in which the stripes are described by Luttinger liquids hybridized with antiferromagnetic domains. Using bosonization techniques we study the model in the limit where the magnetic correlation length is larger than the inter-stripe distance and propose an explanation for the commensurate-incommensurate phase transition seen in neutron scattering in the underdoped regime of La₂-_χx Sr_χx Cu O₄. The explanation is based on a phase to anti-phase domain transition in the spin configuration which is associated with the transverse motion of the stripes. Using a non-linear σ model to describe the antiferromagnetic regions we conjecture the crystalization of the stripes in the magnetically ordered phase.     

Dynamic magnetic properties of ferromagnetic and antiferromagnetic Heusler alloys

Inelastic neutron scattering measurements on a ferromagnetic Heusler alloy, Pd₂MnIn_1?xSn_x at the composition x = 0.75, have established the spin wave dispersion in the three principal symmetry directions. The results have been interpreted using a simple Heisenberg model in which the exchange constants are of long range, extending beyond 12 Å. The Curie temperature, spin wave stiffness constant and the thermal variation of the magnetisation, calculated using the derived exchange parameters are in close agreement with observation.Anomalies in the spin wave dispersion, which are also present to a lesser degree in Pd₂MnSn, have been interpreted as precursor effects associated with the onset of antiferromagnetic ordering, type AF3A, which is the magnetic structure observed in the range 0.2 ? x ? 0.6.     

Dual features of magnetic susceptibility in superconducting cuprates: a comparison to inelastic neutron scattering

Starting from the generalized t−J−G model Hamiltonian, we analyze the spin response in the superconducting cuprates taking into account both local and itinerant spin components which are coupled to each other self-consistently. We demonstrate that derived expression reproduces the basic observations of neutron scattering data in YBa₂Cu₃O_6+y compounds near the optimal doping level.     

Dispersion of acoustical magnons and phonons in Mn1.7Fe1.3O4

The room-temperature spin wave spectrum has been investigated in Mn_1.7Fe_1.3O₄ by means of inelastic neutron scattering. The acoustical branch could be obtained in the symmetry directions. Values for the effective exchange parameters J_AR and J_RR have been derived. Some acoustical phonon branches could also be observed and the elastic constants C₄₄ and (C₁₁ – C₁₂) were estimated.     

The t‐U‐V‐J model in cuprates: Strengths of the interactions

The t‐U‐V‐J model fits together three major parts of the superconductivity puzzle of the cuprite compounds: (i) it describes the opening of a d‐wave pairing gap, (ii) it is consistent with the fact that the basic pairing mechanism arises from the antiferromagnetic exchange correlations, and (iii) it takes into account the charge fluctuations associated with double occupancy of a site which play an essential role in doped systems. The strengths of the interactions U, V and J in YBa₂Cu₃O_6.7 and La_2‐xSr_xCuO₄ (_x = 0.16) samples are obtained by requiring quantitative consistency between the angle‐resolved photoemission spectroscopy (ARPES) measurements, the sharp collective mode at the antiferromagnetic wave vector Q _AF=(π,π), and the observed inelastic neutron scattering resonance (INSR) positions of the incommensurate peaks at wave vectors Q _δ = ((1 ± δ)π,π) and Q _δ = (π(1 ± δ)π).     

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.     

Unconventional spin-charge phase separation in a model 2D cuprate

In this work, we address a challenging problem of a competition of charge and spin orders for high-T _c cuprates within a simplified 2D spin-pseudospin model which takes into account both conventional Heisenberg Cu²⁺?Cu²⁺ antiferromagnetic spin exchange coupling (J) and the on-site (U) and intersite (V) charge correlations in the CuO₂ planes with the on-site Hilbert space reduced to only three effective charge states (nominally Cu^1+;2+;3+). We performed classical Monte Carlo calculations for large square lattices implying the mobile doped charges and focusing on a case of a small intersite repulsion V ? J. The on-site attraction (U < 0) does suppress the antiferromagnetic ordering and gives rise to a checkerboard charge order with the doped charge distributed randomly over a system in the whole temperature range. However, under the on-site repulsion (U > 0) the homogeneous ground state antiferromagnetic solutions of the doped system found in a mean-field approximation are shown to be unstable with respect to a phase separation with the charge and spin subsystems behaving like immiscible quantum liquids. Puzzlingly, with lowering the temperature one can observe two sequential phase transitions: first, an antiferromagnetic ordering in the spin subsystem diluted by randomly distributed charges, then, a charge condensation in the charge droplets. The effects are illustrated by the Monte Carlo calculations of the specific heat and longitudinal magnetic susceptibility.     

Low-energy Ce spin excitations in CeFeAsO and CeFeAsO0.84F0.16

We use inelastic neutron scattering to study the low-energy spin excitations of polycrystalline samples of nonsuperconducting CeFeAsO and superconducting CeFeAsO_0.84F_0.16. Two sharp dispersionless modes are found at 0.85 and 1.16 meV in CeFeAsO below the Ce antiferromagnetic (AF) ordering temperature of T _N ^Ce ˜ 4 K. On warming to above T _N ^Ce ˜ 4 K, these two modes become one broad dispersionless mode that disappears just above the Fe ordering temperature T _N ^Fe ˜ 140 K. For superconducting CeFeAsO_0.84F_0.16, where Fe static AF order is suppressed, we find a weakly dispersive mode center at 0.4 meV that may arise from short-range Ce-Ce exchange interactions. Using a Heisenberg model, we simulate powder-averaged Ce spin wave excitations. Our results show that we need both Ce spin wave and crystal electric field excitations to account for the whole spectra of low-energy spin excitations.