We investigate the spectroscopic magnetic excitations in molecular magnets with complex intermediate structure among the magnetic ions. Our approach consists in introducing a modified spin Hamiltonian that allows for discrete coupling parameters accounting for all energetically favorable spatial distributions of the valence electrons along the exchange bridges connecting the constituent magnetic ions. We discuss the physical relevance of the constructed Hamiltonian and derive its eigenvalues. The model is applied to explore the magnetic excitations of the tetrameric molecular magnet Ni$_4$Mo$_{12}$. Our results are in a very good agreement with the available experimental data. We show that the experimental magnetic excitations in the named tetramer can be traced back to the specific geometry and complex chemical structure of the exchange bridges leading to the splitting and broadness of the peaks centered about 0.5 meV and 1.7 meV.
Magnetic properties of a completely frustrated tetrahedral chain are briefly summarized. Using exact diagonalization, and bond-operator theory results for the ground-state phase diagram, the one-triplet excitations and the Raman spectrum are given. The link to novel tellurate materials is clarified.
We discuss the magnetic properties of a dimerized and completely frustrated tetrahedral spin-1/2 chain. Using a combination of exact diagonalization and bond-operator theory the quantum phase diagram is shown to incorporate a singlet-product, a dimer, and a Haldane phase. In addition we consider one-, and two-triplet excitations in the dimer phase and evaluate the magnetic Raman cross section which is found to be strongly renormalized by the presence of a two-triplet bound state. The link to a novel tellurate materials is clarified.
We consider the spin-1/2 antiferromagnetic Heisenberg model on two one-dimensional frustrated lattices, double-tetrahedral chain and octahedral chain, with almost dispersionless (flat) lowest magnon band in a strong magnetic field. Using the localized magnons picture, we construct an effective description of the one-dimensional chains with triangle and square traps within the strong coupling approximation. We perform extensive exact diagonalization and density matrix renormalization group calculations to check the validity of the obtained effective Hamiltonians by comparison with the initial m…
We study the magnetism of a lattice of coupled tetrahedral spin-1/2 clusters which might be of relevance to the tellurate compounds Cu2Te2O5X2, with X=Cl, Br. Using the flow equation method we perform a series expansion in terms of the inter-tetrahedral exchange couplings starting from the quadrumer limit. Results will be given for the magnetic instabilities of the quadrumer phase and the dispersion of elementary triplet excitations. In limiting cases of our model of one- or two dimensional character we show our results to be consistent with findings on previously investigated decoupled tetrah…
The intersection of topology, symmetry, and magnetism yields a rich structure of possible phases. In this work, we study theoretically the consequences of magnetism on IrF4, which was recently identified as a possible candidate topological nodal chain semimetal in the absence of magnetic order. We show that the spin-orbital nature of the Ir moments gives rise to strongly anisotropic magnetic couplings resembling a tetrahedral compass model on a diamond lattice. The predicted magnetic ground state preserves key symmetries protecting the nodal lines, such that they persist into the ordered phase…
CaBaFe4O7 is a mixed-valent transition metal oxide having both Fe2+ and Fe3+ ions in tetrahedral coordination. Here we characterize its magnetic properties by magnetization measurements and investigate its local electronic structure using soft x-ray absorption spectroscopy at the Fe L2,3 edges, in combination with multiplet cluster and spin-resolved band structure calculations. We found that the Fe2+ ion in the unusual tetrahedral coordination is Jahn-Teller active with the high-spin e^2 (up) t2^3 (up) e^1 (down) configuration having a x^2-y^2-like electron for the minority spin. We deduce tha…
Cd2Os2O7 shows a peculiar metal-insulator transition at 227 K with magnetic ordering in a frustrated pyrochlore lattice, but its magnetic structure in the ordered state and the transition origin are yet uncovered. We observed a commensurate magnetic peak by resonant x-ray scattering in a high-quality single crystal. X-ray diffraction and Raman scattering experiments confirmed that the transition is not accompanied with any spatial symmetry breaking. We propose a noncollinear all-in/all-out spin arrangement on the tetrahedral network made of Os atoms. Based on this we suggest that the transitio…
A quantum mean field theory of the pyrochlore lattice is presented. The starting point is not the individual magnetic ions, as in the usual Curie-Weiss mean field theory, but a set of interacting corner sharing tetrahedra. We check the consistency of the model against magnetic susceptibility data, and find a good agreement between the theoretical predictions and the experimental data. Implications of the model and future extensions are also discussed.
Resistivity, magnetic susceptibility, neutron scattering and x-ray crystallography measurements were used to study the evolution of magnetic order and crystallographic structure in single-crystal samples of the Ba1-xSrxFe2As2 and Sr1-yCayFe2As2 series. A non-monotonic dependence of the magnetic ordering temperature T0 on chemical pressure is compared to the progression of the antiferromagnetic staggered moment, characteristics of the ordering transition and structural parameters to reveal a distinct relationship between the magnetic energy scale and the tetrahedral bond angle, even far above T…
The double-tetrahedral chain in a longitudinal magnetic field, whose nodal lattice sites occupied by the localized Ising spins regularly alternate with triangular plaquettes with the dynamics described by the Hubbard model, is rigorously investigated. It is demonstrated that the uniform change of electron concentration controlled by the chemical potential in a combination with the competition between model parameters and the external magnetic field leads to the formation of one chiral and seven non-chiral phases at the absolute zero temperature. Rational plateaux at one-third and one-half of t…
We have investigated the structural and magnetic transitions in CsCoO$_2$ using calorimetric measurements, neutron powder diffraction (NPD), density functional theory (DFT) calculations and muon-spin relaxation ($μ$SR) measurements. CsCoO$_2$ exhibits three-dimensional long-range antiferromagnetic (AFM) order at 424~K, resulting in antiferromagnetic alignment of chains of ferromagnetically ordered Co-Co spin dimers. Although there is no change in magnetic structure around a structural transition at $T^{*}=100$~K, the resulting bifurcation of corner-shared Co--O--Co bond angles causes a weakeni…
Raman light-scattering experiments in the antiferromagnetic phase of the Cu_2Te_2O_5(Br_(1-x)Cl_x)_2 compounds are analyzed in terms of a dimerized spin model for the tetrahedral Cu-clusters. It is shown that the longitudinal magnetic excitation in the pure Br system hybridizes with a localized singlet excitation due to the presence of a Dzyaloshinskii-Moriya anisotropy term. The drastic change of the magnetic scattering intensities observed when a proportion of Br is replaced by Cl ions, is proposed to be caused by a change of the magnetic order parameter. Instead of being parallel/antiparall…
We study the multiferroic properties in the distorted tetrahedral quasi-one dimensional spin system Cu$_3$Mo$_2$O$_9$, in which the effects of the low dimensionality and the magnetic frustration are expected to appear simultaneously. We clarify that the antiferromagnetic order is formed together with ferroelectric properties at $T_{\rm N}=7.9$ K under zero magnetic field and obtain the magnetic-field-temperature phase diagram by measuring dielectric constant and spontaneous electric polarization. It is found that the antiferromagnetic phase possesses a spontaneous electric polarization paralle…
$\mathbb{Z}_2$ Vortex Crystals in Tetrahedral Antiferromagnets: Fractional Charges and Topological Magnons
Aoyama Gakuin University（青山学院大学）；University of Münster（明斯特大学）；Johannes Gutenberg University Mainz（美因茨约翰内斯·古腾堡大学）；University of Duisburg-Essen（杜伊斯堡-埃森大学）
We investigated the static and dynamic magnetic properties of the polar ferrimagnet Mn$_2$Mo$_3$O$_8$ in three magnetically ordered phases via magnetization, magnetic torque, and THz absorption spectroscopy measurements. The observed magnetic field dependence of the spin-wave resonances, including Brillouin zone-center and zone-boundary excitations, magnetization, and torque, are well described by an extended two-sublattice antiferromagnetic classical mean-field model. In this orbitally quenched system, the competing weak easy-plane and easy-axis single-ion anisotropies of the two crystallogra…
We propose a quartic chiral term $m_x m_y m_z \nabla \cdot \mathbf{m}$ for the energy density of a cubic ferromagnet with broken parity symmetry (point group $T_d$). We demonstrate that this interaction causes a phase transition from a collinear ferromagnetic state to a non-collinear magnetic cone ground state provided its strength exceeds the geometric mean of magnetic exchange and cubic anisotropy. The corresponding non-collinear ground state may also be additionally stabilized by an external magnetic field pointing along certain crystallographic directions. The four-spin chiral exchange doe…
We present a comprehensive study of the coupled tetrahedra-compound Cu2Te2O5Br2 by theory and experiments in external magnetic fields. We report the observation of a longitudinal magnon in Raman scattering in the ordered state close to quantum criticality. We show that the excited tetrahedral-singlet sets the energy scale for the magnetic ordering temperature T_N. This energy is determined experimentally. The ordering temperature T_N has an inverse-log dependence on the coupling parameters near quantum criticality.
Using series expansion by continuous unitary transformations we study the magnetic properties of a frustrated tetrahedral spin-1/2 chain. Starting from the limit of isolated tetrahedra we analyze the evolution of the ground state energy and the elementary triplet dispersion as a function of the inter-tetrahedral coupling. The quantum phase diagram is evaluated and is shown to incorporate a singlet product, a dimer, and a Haldane phase. Comparison of our results with those from several other techniques, such as density matrix renormalization group, exact diagonalization and bond-operator theory…
Fedotovite K$_2$Cu$_3$O(SO$_4$)$_3$ is a candidate of new quantum spin systems, in which the edge-shared tetrahedral (EST) spin-clusters consisting of Cu$^{2+}$ are connected by weak inter-cluster couplings to from one-dimensional array. Comprehensive experimental studies by magnetic susceptibility, magnetization, heat capacity, and inelastic neutron scattering measurements reveal the presence of an effective $S$ = 1 Haldane state below $T \cong 4$ K. Rigorous theoretical studies provide an insight into the magnetic state of K$_2$Cu$_3$O(SO$_4$)$_3$: an EST cluster makes a triplet in the groun…
Recently, it has been rigorously verified that several one-dimensional (1D) spin models may exhibit a peculiar pseudo-transition accompanied with anomalous response of thermodynamic quantities in a close vicinity of pseudo-critical temperature. In the present work we will introduce and exactly solve a mixed spin-(1/2,1) Ising-Heisenberg double-tetrahedral chain in an external magnetic field as another particular example of 1D lattice-statistical model with short-range interactions that displays a pseudo-transition of this type. The investigated model exhibits at zero temperature three ferrimag…
Neutron scattering studies on powder and single crystals have provided new evidences for unconventional magnetism in Cu2Te2O5Cl2. The compound is built from tetrahedral clusters of S=1/2 Cu2+ spins located on a tetragonal lattice. Magnetic ordering, emerging at TN=18.2 K, leads to a very complex multi-domain, most likely degenerate, ground state, which is characterized by an incommensurate (ICM) wave vector k ~ [0.15, 0.42,1/2]. The Cu2+ ions carry a magnetic moment of 0.67(1) mB/ Cu2+ at 1.5 K and form a four helices spin arrangement with two canted pairs within the tetrahedra. A domain redis…
It has recently been demonstrated that dynamical magnetic correlations measured by neutron scattering in iron chalcogenides can be described with models of short-range correlations characterized by particular {choices of four-spin plaquettes, where the appropriate choice changes as the} parent material is doped towards superconductivity. Here we apply such models to describe measured maps of magnetic scattering as a function of two-dimensional wave vectors obtained for optimally superconducting crystals of FeTe$_{1-x}$Se$_x$. We show that the characteristic antiferromagnetic wave vector evolve…
We study the effects of quantum fluctuations on a non-coplanar tetrahedral spin structure, which has a scalar chiral order, in the spin-1/2 multiple-spin exchange model with up to the six-spin exchange interactions on a triangular lattice. We find that, in the linear spin-wave approximation, the tetrahedral structure survives the quantum fluctuations because spin waves do not soften in the whole parameter region of the tetrahedral-structure phase evaluated for the classical system. In the quantum corrections to the ground-state energy, sublattice magnetization, and scalar chirality, the effect…
We study the behavior of the magnetization and the magnetic susceptibility of molecular magnets with complex bridging structure. Our computations are based on a post-Hartree-Fock method accounting for the intricate network of interatomic bonds and an effective spin-like Hamiltonian that captures the essential magnetic features of magnetic molecules. The devised method and the constructed Hamiltonian are further employed to characterize the magnetic properties of the molecular magnet Ni$_4$Mo$_{12}$. The obtained results reproduce both quantitatively and qualitatively the main features of the m…
Chiral Magnetism and Quantum Anomalous Hall Effect in a Low-energy Kondo Model on the Triangular Lattice
University of California Santa Barbara（加州大学圣塔芭芭拉分校）；Kavli Institute for Theoretical Physics, University of California, Santa Barbara（加州大学圣塔芭芭拉分校卡弗里理论物理研究所）；French American Center for Theoretical Science, CNRS, KITP, Santa Barbara, California（法国美国理论科学中心）；Canadian Institute for Advanced Research（加拿大高级研究院）
Co$_{4}$B$_{6}$O$_{13}$ contains undistorted tetrahedral clusters of magnetic Co$^{2+}$ ions. The high-field magnetization of this magnet exhibits a periodic undulation indicating quantization of the total spin number per cluster. Measurements of magnetic susceptibility and specific heat reveal that the ground state is composed of several different singlet states, reflecting the high symmetry of the spin tetrahedron. An exact diagonalization calculation taking account of single-ion type anisotropies and Dzyaloshinsky-Moriya interactions reproduces the expretimental results very well.
Effective actions, such as nonlinear sigma models, are important tools in studying low-energy fluctuations of magnetically ordered states. Here we derive an effective action for the smooth order-parameter distortions of noncoplanar magnetic textures [with an SO(3) order parameter, as opposed to the SO(3)/SO(2)=S^2 of collinear magnets] coupled to itinerant electrons. Noncoplanar magnetic textures commonly arise in the presence of electron-mediated long-range spin exchange interactions, giving rise to the emergence of rich electronic phenomena such as anomalous quantum Hall effect. We parameter…
Structural and magnetic properties of the geometrically frustrated layered compound YBaCo4O7 have been studied by magnetization and neutron diffraction. A layered type crystal structure, with alternating tetrahedral layers of Kagomé and triangular types, along the c axis (hexagonal symmetry, space group P63mc) has been found. The oxygen content of the present compound was determined by iodometric titration to be 7.00{\pm}0.01. Presence of a short-range antiferromagnetic ordering (below TN ~ 110 K) has been concluded from the appearance of an addition broad magnetic peak (at Q ~ 1.35 Å-1) in th…
