Collinear Structure Research Articles

A note on the limitations of the magnetic axis direction determination by neutron powder diffraction

Rotation crystal symmetry analysis of the magnetic intensities in neutron powder diffraction from magnetically ordered, collinear structures is performed. This analysis, making no reference to a specific crystal system, leads to the well-known limitations on the direction of magnetic axis determination by neutron powder diffraction. It shows that due to the second-order dependence of the magnetic intensity on the magnetic axis components, these limitations result solely from the crystal rotation symmetry in the magnetically ordered state.

Magnetic structure and transport properties of noncollinearLaMn2X2(X=Ge,Si)systems

Electronic, magnetic, and transport properties of the noncollinear naturally multilayered compounds ${\mathrm{LaMn}}_{2}{\mathrm{Ge}}_{2}$ and ${\mathrm{LaMn}}_{2}{\mathrm{Si}}_{2}$ are addressed by first-principles calculations based on the density-functional theory. At low temperatures, these systems show a magnetic state with the $\mathrm{Mn}$ moments ordered in a conical arrangement (spin spiral) with a ferromagnetic coupling along the $c$ axis and an in-plane antiferromagnetic coupling. The magnetic structures are studied by means of the full-potential linearized augmented-plane-wave method within both the generalized-gradient approximation and the local-density approximation. In both compounds, a conical magnetic state is obtained with energies lower than canted and collinear structures. The trends in the experimentally observed magnetic configuration when replacing $\mathrm{Ge}$ by $\mathrm{Si}$ are discussed. The origin of the experimentally observed inverse giant magnetoresistance in ${\mathrm{LaMn}}_{2}{\mathrm{Ge}}_{2}$ is traced back to the presence of many noncollinear low-energy magnetic configurations.

On the possible coexistence of spiral and collinear structures in antiferromagnetic KFe(MoO4)2

The static and resonance properties of a quasi-two-dimensional antiferromagnet phase on a distorted triangular lattice of KFe(MoO4)2 have been experimentally studied. Magnetization curves exhibit features corresponding to the spin-flop transition in a collinear biaxial antiferromagnet and simultaneously show a magnetization plateau characteristic of a triangular spin structure. The magnetic resonance spectra also display absorption lines corresponding to the spin structures of both types. The experimental data are described in terms of a model comprising alternating weakly bound magnetic layers, in which the main two exchange integrals have different values. Below the Neel temperature (TN=2.5 K), some of these layers possess a collinear antiferromagnetic structure, while the other layers have a triangular or spiral structure.

Order–disorder transition and magnetic ordering in lithium–titanium ferrites

We have investigated the magnetic properties of Li 0.5+0.5 x Fe 2.5−1.5 x Ti x O 4 samples by means of neutron diffraction, magnetic susceptibility (DC and AC) and magnetization techniques. For the x=1.0 sample a transition from a simple collinear structure to a non-collinear model takes place at 20 K. For the samples x⩾1.28 a spin-glass behaviour was observed. The roles of cation-site occupation and magnetic couplings in governing the different magnetic behaviours exhibited by the samples are discussed.

Higher-order collinear interaction and magnetic excitation in the 5f localized system U3Pd20Si6

The magnetic structure and excitation in a localized 5f system U3Pd20Si6were studied by means of neutron scattering. Our neutron diffraction experiments ona single-domain sample uniquely determined a remarkable collinear structure dueto higher-order exchange interaction. We discovered a new type of spin-flop transitionwith collinear coupling. The localized nature of uranium 5f electrons with a 5f2Γ5ground state was clearly demonstrated by the observed crystalline electric fieldexcitation. We observed beautiful ferromagnetic and antiferromagnetic spin-waveexcitation over a whole Brillouin zone. Surprisingly, however, a clear low-energyquasi-elastic component was also observed around the antiferromagneticzone centre. This low-energy quasi-elastic response is concluded to bethe excitation of the quasi-particles due to hybridization between 5f andconduction electrons. The observation of this localized and itinerant dualnature in magnetic excitation indicates the possibility of partial localizationbased on an itinerant and two localized 5f electrons proposed theoretically.

Ground-state phases in a system of two competing square-lattice Heisenbergantiferromagnets

We study a two-dimensional (2D) spin-half Heisenbergmodel related to the quasi-2D antiferromagnets (Ba, Sr)2Cu3O4Cl2by means of exact diagonalization and spin-wave theory. The modelconsists of two inequivalent interpenetrating square-lattice Heisenbergantiferromagnets A and B. While the antiferromagnetic interaction JAAwithin the A subsystem is strong the coupling JBBwithin the B subsystem is much weaker. The coupling JABbetween A and B subsystems is competing, giving rise to interestingfrustration effects. In dependence of the strength of JABwe find a collinear Néel phase, non-collinear states with zero magnetizationsas well as canted and collinear ferrimagnetic phases with non-zeromagnetizations. For not too large values of frustration JAB,which correspond to the situation in (Ba, Sr)2Cu3O4Cl2,we have Néel ordering in both subsystems A and B. In the classicallimit these two Néel states are decoupled. Quantum fluctuations leadto a fluctuational coupling between both subsystems (‘order fromdisorder’) and select the collinear structure. For stronger JABwe find evidence for a novel spin state with coexisting Néel ordering in the Asubsystem and disorder in the B subsystem.

Structural and magnetic characterization of RCrO4 oxides (R=Nd, Er and Tm)

The crystal and magnetic structure of RCrO4 oxides (R=Nd, Er and Tm) has been studied by owder neutron diffraction. These compounds crystallize with the zircon-type structure, showing tetragonal symmetry, space group I41/amd. In the case of NdCrO4, magnetic susceptibility measurements reveal the existence of an antiferromagnetic ordering in which both Cr5+ and Nd3+ sublattices are involved. This ordering has been explained on the basis of a propagation vector k=0 and a collinear structure, described by the symmetry mode Ax, the ordered magnetic moments being 0.62 and 0.66μB at 2K for Nd3+ and Cr5+, respectively. Magnetic susceptibility and magnetization measurements reveal that both ErCrO4 and TmCrO4 behave as ferromagnetic compounds with a Curie temperature of 15 and 18K, respectively. Rietveld refinement of the neutron diffraction data for ErCrO4 yields a collinear magnetic structure described with an Fx mode. In the case of the TmCrO4 oxide, the ferromagnetic sublattices of Tm3+ and Cr5+ are aligned antiparallel in the a–b plane, while along the c-axis the magnetic moments point to the same direction. In both compounds, the rather small values obtained for the Er3+ and Tm3+ ordered moments compared with the theoretical ones have been attributed to crystal field effects. The differences in the ferromagnetic structure of these compounds have been explained as the result of the higher rare-earth anisotropy of Tm3+ when compared with Er3+, for which no magnetic component is present along the c-direction.

The van der Waals potential energy surfaces and structures of He–ICl and Ne–ICl clusters

The potential energy surfaces of the ground electronic state of rare gas interhalogen van der Waals molecules, Rg–ICl (Rg=He, Ne), are calculated at CCSD(T) (coupled cluster using single and double excitations with a noniterative perturbation treatment of triple excitations) level of theory. Calculations have been performed with specific augmented correlation consistent basis sets for the noble atom (Rg), supplemented with an additional set of bond functions. For iodine atom a correlation consistent triple zeta valence basis set in conjunction with large-core Stuttgart–Dresden–Bonn relativistic pseudopotential has been employed. The CCSD(T) results predict the existence of three minima on the Rg–ICl potential energy surfaces at collinear (Rg–ICl), antilinear (Rg–ClI), and near T-shaped configurations, with the collinear structure to be the lowest one. Bound states calculated from the intermolecular potential surfaces show that zero-order vibrational corrections do not alter the stability of the three structures. Equilibrium intermolecular distances, binding energies, and isomerization barriers are evaluated using the CCSD(T) potentials and compared with previous theoretical and/or experimental results.

Magnetic structure, phase diagram, and a new type of spin-flop transition dominated by higher order interaction in a localized 5f system U3Pd20Si6.

The magnetic structure of the localized-5f uranium intermetallic compound U3Pd20Si6 has been determined by means of a neutron diffraction experiment. Our data demonstrate that this compound has a collinear coupling of the sublattice ordering of the uranium spins on the 4a and 8c sites. We conclude that higher-order exchange and/or quadrupole interactions are necessary to stabilize this unique collinear structure. We discovered a new type of spin-flop transition against the uniaxial anisotropy induced by this collinear coupling.

Magnetic properties of a mixed-valence (III/IV) terbium fluoride KTb3F12

The mixed-valence terbium (III/IV) fluoride KTb3F12 crystallizes with the tetragonal symmetry, space group I4/m. Below TN=3.6±0.1 K this compound exhibits an antiferromagnetic collinear structure with k=0 characterized by ferromagnetic chains of edge-sharing Tb4+ polyhedra and an antiferromagnetic order between the nearest chains. The magnetic moments of the Tb4+ ions deduced from neutron diffraction are equal to 6.95(4) μB at 1.4 K and aligned along the c axis. The Tb3+ ions lie in a special position with zero magnetic moments due to a symmetry cancellation effect of the internal molecular field. In other words, Tb3+ ions present a zero time-averaged magnetic moments in the ordered state, whereas TN corresponds to the long-range antiferromagnetic ordering of the moments of the Tb4+ ions. From the thermal variation of the reciprocal magnetic susceptibility a molar Curie constant of 27.97(1) emu K mol−1 has been obtained, in good agreement with the theoretical value of 27.64 expected for two Tb4+ and one Tb3+ free ions. The Tb4+ contribution to the magnetization is approximated by the Langevin function and then the Tb3+ contribution is obtained by subtracting the calculated Tb4+ contribution to the total magnetization.

Magnetic Structure Determination from Powder Diffraction Symmetry Analysis and Simulated Annealing

The classical approach for solving magnetic structures is the “trial and error” (TE) method. The reason is that many studies have been performed on relatively simple systems and the fact that the dominant isotropic exchange interactions, in absence of frustration, favour simple collinear structures. The improvement of the resolution of neutron powder diffractometers has allowed handling complex incommensurate magnetic systems. For solving complex magnetic structures the TE method is unable to provide appropriate results and other methods have to be used. In this communication the techniques for magnetic structure determination from neutron powder diffraction (NPD) data are reviewed. In the general case the magnetic moment of an atom in the crystal is given as a Fourier series. The Fourier coefficients, S , are complex vectors constituting the “unknowns” to be determined. These vectors define the magnetic structure and they correspond to the “atom positions” of an unknown crystal structure. The steps for solving magnetic structures from NPD are the following: i) Search for the propagation vector(s) {k}. The set {k} provides the translation symmetry of the spin configuration. ii) Symmetry analysis is needed to find the smallest set of free parameters. In general the vectors S are linear combinations of the basis functions of the irreducible representations of the wave vector group G j k

Short-range magnetic order in a spin density wave in Cr-based multilayers

A mechanism of the formation of the short antiferromagnetic order with a spin density wave (SDW) in the vicinity of the interfaces in the Fe/Cr type multilayers is proposed. The main reason behind the emergence of magnetic ordering with SDWs is the redistribution of charge (and, hence, spin) density in the vicinity of Fe/Cr interfaces, which leads to the paramagnetic phase instability at a temperature considerably higher than the Neel temperature in chromium. The Ginzburg-Landau expansion for the free energy of the system is used for determining the inhomogeneous collinear structures of CDWs and for constructing the phase diagram (the dependence of the transition temperature on the thickness of the antiferromagnetic interlayer). The obtained results are used for discussing the experimental data on neutron scattering and tunnel microscopy.

Neutron spin rotation in magnetic mirror

Polarized neutron reflectivity measurements on magnetic films, containing amagnetic collinear structure, yield simple and transparent information on thedirection of the magnetization. Yet the phenomenology of the neutron spinbehaviour is surprisingly rich. We show that, in the region of totalreflection, films magnetized in a direction different from the neutronpolarization axis cause a rotation of spin of the reflected neutrons that maybe linearly dependent on the neutron momentum transfer. As a function ofmomentum transfer, the spin-analysed reflectivities oscillate with anamplitude directly linked to the angle between the polarization axis and themagnetization in the film.

反強磁性Ｍｎ‐Ｐｔ合金／強磁性積層界面の磁気構造

Monte Carlo calculation for the classical Heisenberg model was performed to investigate the magnetic structure of the antiferromagnetic (AFM) and ferromagnetic (FM) bilayer system. In the case of MnPt with Co, the spin structure obtained at the interface was a “spin flop structure” as given by Koon, in which the direction of spins is relaxed from the original collinear structure. A similar relaxation of spins was observed in the case of Mn3Pt with Co, where the triangular spin structure appears in the Mn3Pt layer. This relaxation of spins is strongly related to the exchange bias in an AFM and FM bilayer system, and the canting angle of spins corresponds to the strength of the exchange bias.

Magnetic properties of BaFe12−2xZnxZrxO19 particles

ZnZr doped barium ferrite single domain particles BaFe12−2xZnxZrxO19 with 0⩽x⩽0.8 were prepared by the chemical coprecipitation method. With increasing doping concentration x, the magnetocrystalline anisotropy and thus the coercivity was drastically decreased. This was mainly due to the substitution of Fe3+ ions in the magnetoplumbite structure and strongly affected by the selective occupation of nonmagnetic cations on sublattice sites. Compared with coercivity, the zero-field saturation magnetization decreased much slower. The particle size decreased with x, while both of the lattice parameters “a” and “c” increased. The high-field differential susceptibility showed an increase with increasing doping concentration x, revealing the breakdown of the magnetic collinear structure and subsequently increased fraction of surface canted spins.

Fluctuation-Induced Magnetic Order of RbFeCl3in a Magnetic Field

Mean-field theory is insufficient to explain the magnetic order of RbFeCl 3 in a magnetic field applied in the c plane. Specifically, quantum and thermal fluctuations induce magnetic structures which do not otherwise appear, as found also for CsCuCl 3 . We derive microscopically an expression for the free energy which describes both kinds of fluctuations on an equal basis. Our result includes mean-field theory, but goes beyond it to include terms which lift the nontrivial degeneracy. In addition to the modified 120° structure at low fields and the aligned state at high fields, we find an up-up-down-type collinear structure and a coplanar structure at intermediate fields. Our theory explains qualitatively experimental results at low temperatures, but detailed confirmation requires further experiments including the neutron scattering.

Nuclear magnetic resonance of 55Mn in the antiferromagnet CsMnBr3 in a variable longitudinal magnetic field

The spectrum and intensities of NMR lines are investigated experimentally and theoretically for excitation by an alternating magnetic field h‖ parallel to a static field H in the quasi-one-dimensional, six-sublattice antiferromagnet CsMnBr3. According to theory, two new NMR lines, which are not excited by a transverse magnetic field h⊥, are observed near the phase transition from triangular to collinear structure (H=Hc) [JETP 86, 197 (1998)].

Ab initio test study of the N2…H2 and N2…He van der Waals dimers

Quantum chemical fully ab initio conformational calculations was performed for the weakly bound van der Waals N2…H2 and N2…He dimers in the framework of the supermolecule approach. The counterpoise-corrected interaction energies were computed through fourth order MBPT using basis sets constructed to give accurate values for the electric moments, polarizabilities and dispersion energy contributions. The best size-to-performance ratio basis set found in the present study, predicts the T-shaped structure to be the most stable configuration for N2…He, with a well depth Deof 2.68meV at a minimum distance Re of 3.44Å, in close agreement with calculations performed with larger basis sets. The relative stability of the configurations studied for N2…H2 were: collinear structure > parallel structure > T-shaped structures. The collinear structure represent the most stable configuration, with a De value of 8.35meV at a equilibrium distance Re of 7.60a0.

Spin configurations in the absence of an external magnetic field in a magnetic bilayer with in-plane cubic or uniaxial anisotropies

The spin configurations in the absence of an external magnetic field have been systematically investigated for a magnetic bilayer system consisting of two ferromagnetic layers separated by a non-magnetic layer with interlayer exchange coupling. Based on a phenomenological model, the conditions for the existence of collinear and non-collinear spin structures were derived for three kinds of magnetic bilayers with different combinations of in-plane cubic and uniaxial anisotropies for the two ferromagnetic layers. The phase diagrams of the spin configurations at zero field were drawn, taking into account the lowest-order anisotropy parameters of both the ferromagnetic layers. The values of the canting angle have been derived analytically and then numerically plotted.

Light pair correction to Bhabha scattering at small angle

This work deals with the computation of electron pair correction to small angle Bhabha scattering, in order to contribute to the improvement of luminometry precision at LEP/SLC below 0.1% theoretical accuracy. The exact QED four-fermion matrix element for e + e − → e + e − e + e −, including all diagrams and mass terms, is computed and different Feynman graph topologies are studied to quantify the error of approximate calculations present in the literature. Several numerical results, obtained by a Monte Carlo program with full matrix element, initial-state radiation via collinear structure functions, and realistic event selections, are shown and critically compared with the existing ones. The present calculation, together with recent progress in the sector of O( α 2) purely photonic corrections, contributes to achieve a total theoretical error in luminometry at the 0.05% level, close to the current experimental precision and important in view of the final analysis of the electroweak precision data.