Transverse Spin Excitations Research Articles

Commensurate and spiral magnetic order in the doped two-dimensional Hubbard model: Dynamical mean-field theory analysis

We develop a dynamical mean-field theory approach for the spiral magnetic order, changing to a local coordinate frame with preferable spin alignment along the $z$-axis, which can be considered with the impurity solvers treating the spin diagonal local Green's function. We furthermore solve the Bethe-Salpeter equations for nonuniform dynamic magnetic susceptibilities in the local coordinate frame. We apply this approach to describe the evolution of magnetic order with doping in the $t-t'$ Hubbard model with $t'=0.15$, which is appropriate for the description of the doped La$_2$CuO$_4$ high-temperature superconductor. We find that with doping the antiferromagnetic order changes to the $(Q,\pi)$ incommensurate one, and then to the paramagnetic phase. The spectral weight at the Fermi level is suppressed near half filling and continuously increases with doping. The dispersion of holes in the antiferromagnetic phase shows qualitative agreement with the results of the $t$-$J$ model consideration. In the incommensurate phase we find two branches of hole dispersions, one of which crosses the Fermi level. The resulting Fermi surface forms hole pockets. We also consider the dispersion of the magnetic excitations, obtained from the non-local dynamic magnetic susceptibilities. The transverse spin excitations are gapless, fulfilling the Goldstone theorem; in contrast to the mean-field approach the obtained magnetic state is found to be stable. The longitudinal excitations are characterized by a small gap, showing the rigidity of the spin excitations. For realistic hopping and interaction parameters we reproduce the experimentally measured spin-wave dispersion of La$_2$CuO$_4$.

Manipulation of an elongated internal Josephson junction of bosonic atoms

We report on the experimental characterization of a spatially extended Josephson junction realized with a coherently coupled two-spin-component Bose-Einstein condensate. The cloud is trapped in an elongated potential such that transverse spin excitations are frozen. We extract the nonlinear parameter with three different manipulation protocols. The outcomes are all consistent with a simple local density approximation of the spin hydrodynamics, i.e., of the so-called Bose-Josephson junction equations. We also identify a method to produce states with a well-defined uniform magnetization.

Theory ofCa10Cr7O28as a bilayer breathing-kagome magnet: Classical thermodynamics and semiclassical dynamics

Ca$_{10}$Cr$_7$O$_{28}$ is a novel spin-$1/2$ magnet exhibiting spin liquid behaviour which sets it apart from any previously studied model or material. However, understanding Ca$_{10}$Cr$_7$O$_{28}$ presents a significant challenge, because the low symmetry of the crystal structure leads to very complex interactions, with up to seven inequivalent coupling parameters in the unit cell. Here we explore the origin of the spin-liquid behaviour in Ca$_{10}$Cr$_7$O$_{28}$, starting from the simplest microscopic model consistent with experiment - a Heisenberg model on a single bilayer of the breathing-kagome (BBK) lattice. We use a combination of classical Monte Carlo (MC) simulation and (semi-)classical Molecular Dynamics (MD) simulation to explore the thermodynamic and dynamic properties of this model, and compare these with experimental results for Ca$_{10}$Cr$_7$O$_{28}$. We uncover qualitatively different behaviours on different timescales, and argue that the ground state of Ca$_{10}$Cr$_7$O$_{28}$ is born out of a slowly-fluctuating "spiral spin liquid", while faster fluctuations echo the U(1) spin liquid found in the kagome antiferromagnet. We also identify key differences between longitudinal and transverse spin excitations in applied magnetic field, and argue that these are a distinguishing feature of the spin liquid in the BBK model.

Strong local moment antiferromagnetic spin fluctuations in V-doped LiFeAs

We use neutron scattering to study Vanadium (hole)-doped LiFe1−xVxAs. In the undoped state, LiFeAs exhibits superconductivity at Tc = 18 K and transverse incommensurate spin excitations similar to electron overdoped iron pnictides. Upon Vanadium doping to form LiFe0.955V0.045, the transverse incommensurate spin excitations in LiFeAs transform into longitudinally elongated ones in a similar fashion to that of potassium (hole)-doped Ba0.7K0.3Fe2As2 but with dramatically enhanced magnetic scattering and elimination of superconductivity. This is different from the suppression of the overall magnetic excitations in hole-doped BaFe2As2 and the enhancement of superconductivity near optimal hole doping. These results are consistent with density function theory plus dynamic mean field theory calculations, suggesting that Vanadium doping in LiFeAs may induce an enlarged effective magnetic moment Seff with a spin crossover ground state arising from the inter-orbital scattering of itinerant electrons.

Spin dynamics of 3d and 4d impurities embedded in prototypical topological insulators

Topological insulators are insulating bulk materials hosting conducting surface states. Their magnetic doping breaks time-reversal symmetry and generates numerous interesting effects such as dissipationless transport. Nonetheless, their dynamical properties are still poorly understood. Here, we perform a systematic investigation of transverse spin excitations of $3d$ and $4d$ single impurities embedded in two prototypical topological insulators (Bi$_2$Te$_3$ and Bi$_2$Se$_3$). The impurity-induced states within the bulk gap of the topological insulators are found to have a drastic impact on the spin excitation spectra, resulting in very high lifetimes reaching up to ${microseconds}$. An intuitive picture of the spin dynamics is obtained by mapping onto a generalized Landau-Lifshitz-Gilbert phenomenological model. The first quantity extracted from this mapping procedure is the magnetic anisotropy energy, which is then compared to the one provided by the magnetic force theorem. This uncovers some difficulties encountered with the latter, which can provide erroneous results for impurities with a high density of states at the Fermi energy. Moreover, the Gilbert damping and nutation tensors are obtained. The nutation effects can lead to a non-negligible shift in the spin excitation resonance in the high-frequency regime. Finally, we study the impact of the surface state on the spin dynamics, which may be severely altered due to the repositioning of the impurity-induced state in comparison to the bulk case. Our systematic investigation of this series of magnetic impurities sheds light on their spin dynamics within topological insulators, with implications for available and future experimental studies as, for instance, on the viability of using such impurities for solid-state qubits.

Magnetic Spin-Wave Properties of Ferromagnetic Nanosystems of Various Shapes. Peculiarities of the Border Conditions Accounting in the Process of the Wavenumber Values Spectrum Finding

Background. The paper continues the investigation of linear dipole-exchange spin waves in ferromagnetic nanosystems started by the author in previous papers. The known papers investigating dipole-exchange spin waves obtain their spectral characteristics only for a narrow range of special cases. In the presented paper, an approach that allows expanding substantially this range of cases is described and applied. Objective. The aim of the paper is to develop a method – based on the use of boundary conditions – for obtaining the spectral characteristics of dipole-exchange spin waves in a number of nanosystems’ configurations as well as an application of this method to specific configurations. Methods. A method for obtaining a values’ spectrum of the wavenumbers for dipole-exchange spin waves in ferromagnetic nanosystems of a series of typical configurations is proposed. The method does not require specific assumptions, e.g. the absence of transverse spin excitations or the presence of a high-conductivity metal outside the ferromagnet. The method uses imposition of boundary conditions for the magnetic field and the magnetization on the boundary of the ferromagnetic medium for a linear spin wave in the magnetostatic approximation. This method allows obtaining the above-mentioned spectral characteristics for a wider range of cases compared to the known previous papers. Results. The results of the paper are conditions for the magnetic potential – that imply from the above-mentioned boundary conditions – of a linear spin wave on the boundary of a ferromagnetic nanosystem as well as the spectrum of the wavenumbers’ values of such wave for the investigated nanosystems (in the implicit form). In particular, for a ferromagnetic nanosystem of an arbitrary cross section with a one-dimensional translational symmetry, the conditions specifying this spectrum are found. Such conditions are specified – and an implicit expression for this spectrum is obtained – for the case when such nanosystem is a nanotube with a circular cross section. The analysis of the obtai­ned results is carried out. Conclusions. The obtained expressions for the spectrum of the values of the investigated spin waves’ wavenumbers can be used for a wider range of cases than the ones obtained in the previous papers dedicated to the investigated configurations of nanosystems. For a nanotube of the circular cross-section with small (compared to the inverse characteristic size of the nanotube cross-section) values of the longitudinal wave number, the dependence of the latter on the transverse wave number is weak, as well as for the big longitudinal to transverse wavenumber component ratio. The obtained dependence is also represented graphically.

Phase diagram and collective excitations in an excitonic insulator from an orbital physics viewpoint

Excitonic insulating system is studied from the viewpoints of the orbital physics in strongly correlated electron systems. An effective model Hamiltonian for low-energy electronic states is derived from the two-orbital Hubbard model with a finite energy difference corresponding to the crystalline field splitting. The effective model is represented by the spin operators and the pseudo-spin operators for the spin-state degrees of freedom. The ground state phase diagram is analyzed by the mean-field approximation. In addition to the low-spin state and high-spin state phases, two kinds of the excitonic insulating phases emerge as a consequence of the competition between the crystalline field effect and the Hund coupling. The excitonic transition is classified to be an Ising-like transition reflecting a spontaneous breaking of the $Z_2$ symmetry. Magnetic structures in the two excitonic insulating phases are different from each other; an antiferromagnetic order and a spin nematic order. Collective excitations in each phase are examined by using the generalized spin-wave method. The Goldstone modes in the excitonic insulating phases appear in the dynamical correlation functions for the spins and pseudo-spin operators. Both the transverse and longitudinal spin excitation modes are active in the two excitonic insulating phases in contrast to the low-spin state and high-spin state phases. Connections of the present results to the perovskite cobalt oxides are discussed.

Magnetic Excitations of Spin Nematic State in Frustrated Ferromagnetic Chain

By exploiting density-matrix renormalization group techniques, we investigate the dynamical spin structure factor of a spin-1/2 Heisenberg chain with ferromagnetic nearest-neighbor and antiferromagnetic next-nearest-neighbor exchange interactions in an applied magnetic field. In a field-induced spin nematic regime, we find gapless longitudinal and gapped transverse spin excitation spectra, in accordance with quasi-long-ranged longitudinal and short-ranged transverse spin correlations, respectively. The gapless point coincides with the dominant longitudinal spin correlation, whereas the gap position exhibits a characteristic field dependence contradicting the dominant transverse spin correlation.

ChemInform Abstract: Unusual Ordered Phases of Highly Frustrated Magnets: A Review

AbstractReview: 194 refs.

Noncollinear spin-fluctuation theory of transition-metal magnetism: Role of transverse spin fluctuations in Fe

A local electronic theory of transition-metal magnetism at finite temperatures is presented, which takes into account longitudinal and transverse spin fluctuations on the same footing. The magnetic properties are determined in the framework of a rotational-invariant $d$-band model Hamiltonian by applying a four-field Hubbard-Stratonovich functional-integral method in the static approximation. The role of transverse spin excitations on the temperature-dependent magnetic properties is investigated by performing alloy averages in the single-site virtual crystal approximation. Bulk Fe is considered as the representative example for the applications. Results are given for the average magnetization $M$, for the spin-excitation energies, and for the transverse and longitudinal contributions to the local magnetic moments ${\ensuremath{\mu}}_{l}$ at atom $l$. The importance of noncollinear spin excitations is quantified by comparison with the corresponding collinear calculations. An important reduction of about 33% of the calculated Curie temperature ${T}_{\mathrm{C}}$ is obtained, which now amounts to 1250 K and is thus relatively close to the experimental value. The longitudinal (transverse) components of ${\ensuremath{\mu}}_{l}$ are found to decrease (increase) as a function of temperature until the full rotational symmetry is reached at ${T}_{C}$. This reflects the increasing importance of the transverse spin fluctuations. The origin of the temperature dependence of $M$ and ${\ensuremath{\mu}}_{l}$ is analyzed in terms of the local spin-fluctuation energies.

Unusual ordered phases of highly frustrated magnets: a review

We review ground states and excitations of a quantum antiferromagnet on triangular and other frustrated lattices. We pay special attention to the combined effects of magnetic field h, spatial anisotropy R and spin magnitude S. The focus of the review is on the novel collinear spin density wave and spin nematic states, which are characterized by fully gapped transverse spin excitations with Sz = ± 1. We discuss extensively the R − h phase diagram of the antiferromagnet, both in the large-S semiclassical limit and the quantum S = 1/2 limit. When possible, we point out connections with experimental findings.

Effects of magnetic anisotropy on spin dynamics of ferromagnetic frustrated chain

By exploiting density-matrix renormalization group techniques, we investigate the spin dynamics of a spin-1/2 one-dimensional J1-J2 XXZ model with competing ferromagnetic J1 and antiferromagnetic J2 exchange couplings under applied magnetic fields. Numerical results of spin excitation spectra show that in the field-induced spin quadrupole regime, the longitudinal component has a gapless mode and the transverse component has a gapped mode irrespective of the exchange anisotropy. The excitation gap of the transverse spin excitation increases as the exchange anisotropy increases over the XY-like and Ising-like regions, demonstrating that two-magnon bound states are stabilized due to the easy-axis anisotropy.

Anisotropic Spin Fluctuations in the Quasi One-Dimensional Frustrated Magnet LiCuVO4

We report results of NMR experiments on a single crystal of the quasi one-dimensional frustrated magnet LiCuVO_4. The NMR spectra of ^7Li and ^{51}V nuclei indicate a helical spin order in a magnetic field of 4 T with the helical spin plane perpendicular to the field and a spin-density-wave (SDW) order at 10 T with modulation in the magnitude of the moments aligned along the field, in agreement with earlier reports. The nuclear spin-lattice relaxation rate 1/T_1 at ^{51}V nuclei, which is selectively coupled to the transverse spin fluctuations perpendicular to the field, shows a pronounced peak near the helical ordering temperature in the field of 4 T applied along the a-axis. In the field of 10 T, however, such a peak is absent. Instead 1/T_1 at ^7Li nuclei probing longitudinal spin fluctuations shows divergent behavior towards the SDW ordering temperature. These results are qualitatively consistent with the theoretical description that the SDW correlation is due to bound magnon pairs, which produce an energy gap in the transverse spin excitation spectrum.

Probing the Superconducting Pairing Symmetry from Spin Excitations in BiS2 Based Superconductors

Starting from a two-orbital model and based on the random phase approximation, spin excitations in the superconducting state of the newly discovered BiS2 superconductors with three possible pairing symmetries are studied theoretically. It is found that the spin response is uniquely determined by the pairing symmetry. Possible spin resonance excitations may occur at an incommensurate momentum about (0.7π,0.7π) for the d-wave symmetry, while the transverse spin excitation near (0,0) is enhanced for the p-wave symmetry and no spin resonance signature is seen for the s-wave pairing symmetry. These distinct features may be used for probing or determining the pairing symmetry in this newly discovered compound.

Spin excitations in layered antiferromagnetic metals and superconductors

The proximity of antiferromagnetic order in high-temperature superconducting materials is considered a possible clue to the electronic excitations which form superconducting pairs. Here we study the transverse and longitudinal spin excitation spectrum in a one-band model in the pure spin density wave (SDW) state and in the coexistence state of SDW and the superconductivity. We start from a Stoner insulator and study the evolution of the spectrum with doping, including distinct situations with only hole pockets, with only electron pockets and with pockets of both types. In addition to the usual spin-wave modes, in the partially gapped cases we find significant weight of low-energy particle-hole excitations. We discuss the implications of our findings for neutron scattering experiments and for theories of Cooper-pairing in the metallic SDW state.

Spin Dynamics in a One-Dimensional Ferromagnetic Bose Gas

We investigate the propagation of spin excitations in a one-dimensional ferromagnetic Bose gas. While the spectrum of longitudinal spin waves in this system is soundlike, the dispersion of transverse spin excitations is quadratic, making a direct application of the Luttinger liquid theory impossible. By using a combination of different analytic methods we derive the large time asymptotic behavior of the spin-spin dynamical correlation function for strong interparticle repulsion. The result has an unusual structure associated with a crossover from the regime of trapped spin wave to an open regime and does not have analogues in known low-energy universality classes of quantum 1D systems.

Single-Particle Spectrum in the Electron-Doped Cuprates

We study the evolution of the single-particle spectrum with electron doping in a scheme which adds multiple exchange of transverse spin excitations to the mean-field antiferromagnetic insulator. Away from half-filling small Fermi surface pockets appear first around the X points, and simultaneously new spectral weight grows in the insulating gap. With further doping the in-gap states develop the character of a renormalized quasiparticle band near the chemical potential. The essential features in momentum-energy space agree well with recent studies using angle-resolved photoemission spectroscopy on electron-doped cuprates. We interpret the origins and the nature of the in-gap states using a simple variational wave function.

Spin dynamics of the S = 1/2antiferromagnetic zig-zag ladder with anisotropy

We use exact diagonalization and the modified Lanczos method tostudy the finite-energy and finite-momentum spectral weight ofthe longitudinal and transverse spin excitations of theanisotropic zig-zag ladder. We find that the spin excitationsform continua of gapless or gapped spinons in the differentregions of the phase diagram. The results obtained areconsistent with a picture previously proposed that in theanisotropic case there is a transition from a gapped regime to agapless regime, for small interchain coupling. In the gapless regime wefind a sharp low-energy peak in the structure function for thetransverse spin excitations, consistent with a finite stiffness.

Polarized-Neutron Observation of Longitudinal Haldane-Gap Excitations inNd2BaNiO5

Polarized and unpolarized inelastic neutron scattering is used to study Haldane-gap excitations in the mixed-spin linear-chain antiferromagnet ${\mathrm{Nd}}_{2}{\mathrm{BaNiO}}_{5}$. The longitudinal mode, polarized along the direction of ordered moments, is observed for the first time. The model of isolated Haldane chains in a static staggered exchange field, that is known to work very well for static properties and transverse spin excitations in ${R}_{2}{\mathrm{BaNiO}}_{5}$ compounds, fails to explain new results for the longitudinal spin gap.

Spin interactions in an Anderson-Hubbard model

We study the magnetic properties of a site-disordered Anderson-Hubbard model at half-filling on a simple cubic lattice, via a mapping of its low-frequency transverse spin excitations onto those of an effective underlying Heisenberg model with self-consistently determined exchange couplings. Exact in the strong-coupling limit, the mapping remains accurate over the dominant region of the phase plane where the ground state is a disordered antiferromagnet. The effect of disorder and interaction strength on the resultant exchange couplings is examined in detail, and rationalized microscopically. Frustration is found to occur, even within the antiferromagnetic phase, although the ground state is shown to be stable with respect to zero-point quantum spin fluctuations. To probe finite-temperature magnetic properties, an Onsager reaction-field approach to the effective Heisenberg model in the paramagnetic phase is employed. We focus on the effect of disorder on the Néel temperature and the nature of the thermal transition to the ordered phase.