Spin Excitation Spectrum Research Articles

Field-dependent shape and magnetic spectrum of magnetic bimeron

Magnetic bimeron composed of a meron and an antimeron can be considered as a magnetic skyrmion in the in-plane magnet and have great potential for spintronic devices. Here, we explored the effect of static magnetic fields on the shape of bimeron. It is found that the size of the bimeron can be adjusted by magnetic fields in an anisotropic direction. Then we study the field-tuned spin excitation spectrum of magnetic bimeron. Unlike the common breathing mode and the two rotation modes, novel resonance modes, which can be considered as a combination of the breathing and rocking-rotation modes, are observed. The results presented in this study can help to open novel research into the spintronics of magnetic bimeron.

Solitonic excitations in the Ising anisotropic chain BaCo2V2O8 under large transverse magnetic field

We study the dynamics of the quasi-one-dimensional Ising-Heisenberg antiferromagnet ${\mathrm{BaCo}}_{2}{\mathrm{V}}_{2}{\mathrm{O}}_{8}$ under a transverse magnetic field. Combining inelastic neutron scattering experiments and theoretical analyses by field theories and numerical simulations, we mainly elucidate the structure of the spin excitation spectrum in the high-field phase, appearing above the quantum phase transition point ${\ensuremath{\mu}}_{0}{H}_{c}\ensuremath{\approx}10\phantom{\rule{0.28em}{0ex}}\mathrm{T}$. We find that it is characterized by collective solitonic excitations superimposed on a continuum. These solitons are strongly bound in pairs due to the effective staggered field induced by the nondiagonal $g$ tensor of the compound and are topologically different from the fractionalized spinons in the weak-field region. The dynamical susceptibility numerically calculated with the infinite time-evolving block decimation method shows an excellent agreement with the measured spectra, which enables us to identify the dispersion branches with elementary excitations. The lowest-energy dispersion has an incommensurate nature and has a local minimum at an irrational wave number due to the applied transverse field.

Spin dynamics of the spin-chain antiferromagnet RbFeS2

We report transport and inelastic neutron scattering studies on electronic properties and spin dynamics of the quasi-one-dimensional spin-chain antiferromagnet ${\mathrm{RbFeS}}_{2}$. An antiferromagnetic phase transition at ${T}_{N}\ensuremath{\approx}195$ K and dispersive spin waves with a spin gap of 5 meV are observed. By modeling the spin excitation spectra using linear spin wave theory, intra and interchain exchange interactions are found to be $S{J}_{1}=100(5)$ meV and $S{J}_{3}=0.9(3)$ meV, respectively, together with a small single-ion anisotropy of $S{D}_{zz}=0.04(1)$ meV. Comparison with previous results for other materials in the same class of ${\mathrm{Fe}}^{3+}$ spin-chain systems reveals that although the magnetic order sizes show significant variation from 1.8 to $3.0\phantom{\rule{4pt}{0ex}}{\ensuremath{\mu}}_{B}$ within the family of materials, the exchange interactions $SJ$ are nevertheless quite similar, analogous to the iron pnictide superconductors where both localized and delocalized electrons contribute to the spin dynamics.

Spin excitation spectra in helimagnetic states: Proper-screw, cycloid, vortex-crystal, and hedgehog lattices

We investigate the spin excitation spectra in chiral and polar magnets by the linear spin-wave theory for an effective spin model with symmetric and antisymmetric long-range interactions. In one dimension, we obtain the analytic form of the dynamical spin structure factor for proper-screw and cycloidal helical spin states with uniform twists, which shows a gapless mode with strong intensity at the helical wave number. When introducing spin anisotropy in the symmetric interactions, we numerically show that the stable spin spirals become elliptically anisotropic with nonuniform twists and the spin excitation is gapped. In higher dimensions, we find that similar anisotropy stabilizes multiple-$Q$ spin states, such as vortex crystals and hedgehog lattices. We show that the anisotropy in these states manifests itself in the dynamical spin structure factor: a strong intensity in the transverse components to the wave number appears only when the helical wave vector and the corresponding easy axis are perpendicular to each other. Our findings could be useful not only to identify the spin structure but also to deduce the stabilization mechanism by inelastic neutron scattering measurements.

Moiré Tuning of Spin Excitations: Individual Fe Atoms on MoS_{2}/Au(111).

Magnetic adatoms on properly designed surfaces constitute exquisite systems for addressing, controlling, and manipulating single quantum spins. Here, we show that monolayers of MoS_{2} on a Au(111) surface provide a versatile platform for controllably tuning the coupling between adatom spins and substrate electrons. Even for equivalent adsorption sites with respect to the atomic MoS_{2} lattice, we observe that Fe adatoms exhibit behaviors ranging from pure spin excitations, characteristic of negligible exchange and dominant single-ion anisotropy, to a fully developed Kondo resonance, indicating strong exchange and negligible single-ion anisotropy. This tunability emerges from a moiré structure of MoS_{2} on Au(111) in conjunction with pronounced many-body renormalizations. We also find striking spectral variations in the immediate vicinity of the Fe atoms, which we explain by quantum interference reflecting the formation of Fe-S hybrid states despite the nominally inert nature of the substrate. Our work establishes monolayer MoS_{2} as a tuning layer for adjusting the quantum spin properties over an extraordinarily broad parameter range. The considerable variability can be exploited for quantum spin manipulations.

Spin excitation spectrum of a magnetic hopfion

Magnetic hopfions are three-dimensional topological solitons with a nontrivial Hopf index. Here, we theoretically investigated the spin excitation spectrum and revealed corresponding spin-wave modes of a magnetic hopfion. Compared with skyrmion tubes, the hopfions have distinctly less resonance peaks due to the suppression of vertical spin-wave modes by the internal topological defect. We also found that breathing and rotating modes could hybridize in hopfions under z-direction excitations and, thus, characterized the five individual resonance modes by a set of number pair (b, r). The results provide a fundamental understanding of the spin-wave modes of magnetic hopfions and open a route to detect and manipulate 3D topological solitons using microwave magnetic fields.

Dimerized nature of magnetic interactions in the S = 1/2 quantum antiferromagnet Cu(en)2SO4

Specific heat, magnetic susceptibility and magnetization of Cu(en)2SO4 single crystal were investigated in the field applied along the b-axis. The analysis of the susceptibility within the Curie-Weiss law indicates the antiferromagnetic nature of the exchange coupling between Cu(II) ions with zJ/kB = −6.4 K. Considering the structure of this material, the formation of magnetic dimers can be expected. Very good description of susceptibility data was achieved using the Heisenberg antiferromagnetic dimer model with intra-dimer coupling J/kB = −5.52 K, effective inter-dimer coupling J'/kB = −0.3 K and gb = 2.12. The energy gap in the spin excitation spectrum was estimated Δ/kB ≈ 11 K and corresponding critical field Bcb ≈ 7.8 T required for closing the gap. The dimerized nature of magnetic interactions was also confirmed by specific heat and isothermal magnetization data which manifest qualitatively the same behavior as the aforementioned dimer model. The possibility of further low-temperature experiments in the closed gap regime is discussed to obtain more detailed concept of magnetic interactions in this interesting compound.

Dirac-Type Nodal Spin Liquid Revealed by Refined Quantum Many-Body Solver Using Neural-Network Wave Function, Correlation Ratio, and Level Spectroscopy

Pursuing fractionalized particles that do not bear properties of conventional measurable objects, exemplified by bare particles in the vacuum such as electrons and elementary excitations such as magnons, is a challenge in physics. Here we show that a machine-learning method for quantum many-body systems that has achieved state-of-the-art accuracy reveals the existence of a quantum spin liquid (QSL) phase in the region $0.49\lesssim J_2/J_1\lesssim0.54$ convincingly in spin-1/2 frustrated Heisenberg model with the nearest and next-nearest neighbor exchanges, $J_1$ and $J_2$, respectively, on the square lattice. This is achieved by combining with the cutting-edge computational schemes known as the correlation ratio and level spectroscopy methods to mitigate the finite-size effects. The quantitative one-to-one correspondence between the correlations in the ground state and the excitation spectra enables the reliable identification and estimation of the QSL and its nature. The spin excitation spectra containing both singlet and triplet gapless Dirac-like dispersions signal the emergence of gapless fractionalized spin-1/2 Dirac-type spinons in the distinctive QSL phase. Unexplored critical behavior with coexisting and dual power-law decays of N\'{e}el antiferromagnetic and dimer correlations is revealed. The power-law decay exponents of the two correlations differently vary with $J_2/J_1$ in the QSL phase and thus have different values except for a single point satisfying the symmetry of the two correlations. The isomorph of excitations with the cuprate $d$-wave superconductors implies a tight connection between the present QSL and superconductivity. This achievement demonstrates that the quantum-state representation using machine learning techniques, which had mostly been limited to benchmarks, is a promising tool for investigating grand challenges in quantum many-body physics.

Spin relaxation in a strongly correlated quantum Hall ferromagnet

The spin relaxation of a strongly correlated electron system hosted in a narrow AlAs quantum well is studied experimentally in the regime of the quantum Hall ferromagnet, i.e., near odd fillings of the integer quantum Hall effect. The relaxation rate is evaluated by analyzing the linewidth of the electrically detected electron-spin resonance. The measured spin dynamics is shown to undergo a radical modification in tilted magnetic fields. Increasing of the tilt angle resulted not only in the decrease of the relaxation time at the exact odd fillings by almost an order of magnitude, but also in the essentially different dependence of the relaxation rate on the filling factor at highest tilt angles. In the case of a perpendicular magnetic field the relaxation rate reached its minimal value near the exact odd filling and slowly increased when the filling factor $\ensuremath{\nu}$ was altered. In contrast, at large tilt angles relaxation turned out to be the fastest at some $\ensuremath{\nu}$ in close vicinity of the exactly odd number. The observed effects may be ascribed to the renormalization of the spin excitation spectra by the strong e-e interaction.

Orbital effects and Affleck-Haldane-type spin dimerization in Ba4Ru3O10

${\mathrm{Ba}}_{4}{\mathrm{Ru}}_{3}{\mathrm{O}}_{10}$, the quasi-one-dimensional spin-1 ($S$ = 1) compound, has rather intricate magnetic properties. The compound consists of structural Ru trimers, which together form the zig-zag chains where the Ru has two inequivalent crystallographic sites. While at high temperature both the inequivalent Ru ions stay in the $4+$ state with effective $S=$ 1 spin state, upon lowering the temperature, the magnetic moment of the central Ru atom is completely quenched accompanied by a change in the octahedral environment. This effectively gives rise to a bond-alternating chain and provides an opportunity to study the excitation of such a spin network in a real material. We have used microscopic tools such as neutron scattering and muon spin relaxation along with the density functional theory based calculations to address the spin state of the two inequivalent Ru ions in this material. From our neutron powder diffraction, on lowering of temperature, we find a large tetragonal distortion of the central ${\mathrm{RuO}}_{6}$ octahedra of the trimer. The splitting of the ${t}_{2g}$ level of the central Ru due to this distortion is found to be significant leading to the quenching of the moment underscoring the Hund's exchange. The nonmagnetic central Ru promotes a strong antiferromagnetic superexchange between the other two Ru ions in the trimer, which gives rise to a dimeric state. The presence of spin dimers is reflected by the manifestation of a gap in the spin excitation spectra. The spin-dimer formation in ${\mathrm{Ba}}_{4}{\mathrm{Ru}}_{3}{\mathrm{O}}_{10}$ is at par with the effective model proposed by Affleck and Haldane for the $S$ = 1 bond alternating chains in the light of valence bond solid formalism. Eventually, at a lower temperature, a long-range ordered antiferromagnetic state emerges from the gapped dimer state due to the significant interdimer interactions.

Breakdown of charge homogeneity in the two-dimensional Hubbard model: Slave-boson study of magnetic order

We study the two-dimensional one-band Hubbard model on the square lattice through the spin rotation invariant Kotliar-Ruckenstein slave-boson method, with an emphasis on the electron-doped regime. The phase diagram determined within mean field approximation reveals three different magnetically ordered phases separated by first-order transitions, and a wide instability region as indicated by a negative compressibility. We show that this conundrum of the unstable mean field domain is resolved by spatially mixed phases of neighboring stable states. We also find charge density wave type instabilities in the antiferromagnetically ordered (AFM) state at wave vectors commensurate with the doping. The corresponding charge and spin density response functions are calculated from a Gaussian fluctuations formalism about a magnetic saddle point, for which we provide a detailed derivation. Further, we present density and spin excitation spectra in the AFM phase, allowing for a quantitative calculation of the spin wave parameters, the gap in the longitudinal spin excitation spectrum, and the density excitations in the upper Hubbard band.

Classical magnetic vortex liquid and large thermal Hall conductivity in frustrated magnets with bond-dependent interactions

Recently, the observation of large thermal Hall conductivities in correlated insulators with no apparent broken symmetry has generated immense interest and debates on the underlying ground states. Here, considering frustrated magnets with bond-dependent interactions, which are realized in the so-called Kitaev materials, we theoretically demonstrate that a large thermal Hall conductivity can originate from a classical ground state without any magnetic order. We discover a liquid state of magnetic vortices, which are inhomogeneous spin textures embedded in the background of polarized spins, under out-of-plane magnetic fields. In the classical regime, different configurations of vortices form an effectively degenerate manifold. We study the static and dynamical properties of the magnetic vortex liquid state at zero and finite temperatures. In particular, we show that the spin excitation spectrum resembles a continuum of nearly flat Chern bands, which ultimately leads to a large thermal Hall conductivity. Possible connections to experiments are discussed.

Tuning spin excitations in magnetic films by confinement.

Spin excitations of magnetic thin films are the founding element for magnetic devices in general. While spin dynamics have been extensively studied in bulk materials, the behaviour in mesoscopic films is less known due to experimental limitations. Here, we employ resonant inelastic X-ray scattering to investigate the spectrum of spin excitations in mesoscopic Fe films, from bulk-like films down to three unit cells. In bulk samples, we find isotropic, dispersive ferromagnons consistent with previous neutron scattering results for bulk single crystals. As the thickness is reduced, these ferromagnetic spin excitations renormalize to lower energies along the out-of-plane direction while retaining their dispersion in the in-plane direction. This thickness dependence is captured by simple Heisenberg model calculations accounting for the confinement in the out-of-plane direction through the loss of Fe bonds. Our findings highlight the effects of mesoscopic scaling on spin dynamics and identify thickness as a knob for fine tuning and controlling magnetic properties.

Spin waves in the collinear antiferromagnetic phase of Mn5Si3

By combining two independent approaches, inelastic neutron-scattering measurements and density-functional-theory calculations, we study the spin waves in the collinear antiferromagnetic phase (AFM2) of ${\mathrm{Mn}}_{5}{\mathrm{Si}}_{3}$. We obtain its magnetic ground-state properties and electronic structure. This study allowed us to determine the dominant magnetic exchange interactions and magnetocrystalline anisotropy in the AFM2 phase of ${\mathrm{Mn}}_{5}{\mathrm{Si}}_{3}$. Moreover, the evolution of the spin excitation spectrum is investigated under the influence of an external magnetic field perpendicular to the anisotropy easy axis. The low-energy magnon modes show a different magnetic field dependence, which is a direct consequence of their different precessional nature. Finally, possible effects related to the Dzyaloshinskii-Moriya interaction are also considered.

Fractionalized spin excitations in the ferromagnetic edge state of graphene: Signature of the ferromagnetic Luttinger liquid

The elementary excitations from the conventional magnetic ordered states, such as ferromagnets and antiferromagnets, are magnons. Here, we elaborate a case where the well-defined magnons are absent completely and the spin excitation spectra exhibit an entire continuum in the itinerant edge ferromagnetic state of graphene arising from the flatband edge electronic states. Based on the further studies of the entanglement entropy and finite-size analysis, we show that the continuum other than the Stoner part results from the spin-1/2 spinons deconfined from magnons. The spinon continuum in a magnetically ordered state is ascribed to a ferromagnetic Luttinger liquid in this edge ferromagnet. The investigation is carried out by using the numerical exact diagonalization method with a projection of the interacting Hamiltonian onto the flat band.

Spin resonances in iron selenide high- Tc superconductors by proximity to a hidden spin density wave

Recent inelastic neutron scattering studies by Pan et al., Nature Communications 8, 123 (2017), find evidence for spin excitations at energies above the quasi-particle gap in an iron-selenide high-Tc superconductor. The momenta of the spin excitations form a diamond around the checkerboard wavevector, Q_AF, that is associated with the square lattice of iron atoms that makes up the system. It has been suggested that such a "hollowed-out" spin-excitation spectrum is due to hidden Neel order. We study such a hidden spin-density wave (hSDW) state that results from nested Fermi surfaces at the center and at the corner of the unfolded Brillouin zone. It emerges within mean field theory from an extended Hubbard model over a square lattice of iron atoms that contain the minimal d_xz and d_yz orbitals. Opposing Neel order exists over the isotropic d+ = d_xz + i d_yz and d- = d_xz - i d_yz orbitals. The dynamical spin susceptibility of the hSDW is computed within the random phase approximation, at perfect nesting. Unobservable Goldstone modes that disperse acoustically are found at Q_AF. A threshold is found in the spectrum of observable spin excitations that forms a "floating ring" at Q_AF also. The ring threshold moves down in energy toward zero with increasing Hund's Rule coupling, while it moves up in energy with increasing magnetic frustration. Comparison with the normal-state features of the spin-excitation spectrum shown by electron-doped iron selenide is made. Also, recent predictions of a Lifshitz transition from the nested Fermi surfaces to Fermi surface pockets at the corner of the folded Brillouin zone will be discussed.

Anisotropic magnetic excitations of a frustrated bilinear-biquadratic spin model: Implications for spin waves of detwinned iron pnictides

Elucidating the nature of spin excitations is important to understanding the mechanism of superconductivity in the iron pnictides. Motivated by recent inelastic neutron scattering measurements in the nearly 100% detwinned BaFe$_{2}$As$_{2}$, we study the spin dynamics of an $S=1$ frustrated bilinear-biquadratic Heisenberg model in the antiferromagnetic phase with wavevector $(\pi,0)$. The biquadratic interactions are treated in a dynamical way using a flavor-wave theory in an $SU(3)$ representation. Besides the magnon (dipolar) excitations, the biquadratic interactions give rise to quadrupolar excitations at high energies. We find that the quadrupolar wave significantly influences, in an energy dependent way, the anisotropy between the spin excitation spectra along the $(\pi,0)$ and $(0,\pi)$ directions in the wave vector space. Our theoretical results capture the essential behavior of the spin dynamics measured in the antiferromagnetic phase of the detwinned BaFe$_2$As$_2$. More generally, our results underscore the importance of electron correlation effects for the microscopic physics of the iron pnictides.

Magnon spectrum of the Weyl semimetal half-Heusler compound GdPtBi

The compound GdPtBi is known as a material where the non-trivial topology of electronic bands interplays with an antiferromagnetic order, which leads to the emergence of many interesting magnetotransport phenomena. Although the magnetic structure of the compound has previously been reliably determined, the magnetic interactions responsible for this type of order remained controversial. In the present study, we employed time-of-flight inelastic neutron scattering to map out the low-temperature spectrum of spin excitations in single-crystalline GdPtBi. The observed spectra reveal two spectrally sharp dispersive spin-wave modes, which reflects the multi-domain state of the $\mathbf{k} = (\frac{1}{2}\frac{1}{2}\frac{1}{2})$ face-centred cubic antiferromagnet in the absence of a symmetry-breaking magnetic field. The magnon dispersion reaches an energy of $\sim 1.1$~meV and features a gap of $\sim 0.15$~meV. Using linear spin-wave theory, we determined the main magnetic microscopic parameters of the compound that provide good agreement between the simulated spectra and the experimental data. We show that GdPtBi is well within the ($\frac{1}{2}\frac{1}{2}\frac{1}{2}$) phase and is dominated by second-neighbor interactions, thus featuring low frustration.

Field driven recovery of the collective spin dynamics of the chiral soliton lattice

We investigate the magnetic field dependence of the spin excitation spectra of the chiral soliton lattice (CSL) in the helimagnet CrNb3S6, by means of microwave resonance spectroscopy. The CSL is a prototype of a noncollinear spin system that forms periodically over a macroscopic length scale. Following the field initialization of the CSL, we found three collective resonance modes over an exceptionally wide frequency range. Upon further reducing the magnetic field toward 0 T, the spectral weight of these collective modes was disrupted by the emergence of additional resonances whose Kittel-like field dependence was linked to coexisting field polarized magnetic domains. The collective behavior at a macroscopic level was only recovered upon reaching the helical magnetic state at 0 T. The magnetic history of this noncollinear spin system can be utilized to control microwave absorption, with potential use in magnon-driven devices.

Light cone dynamics in excitonic states of two-component Bose and Fermi gases

We consider the non-equilibrium dynamics of two-component one dimensional quantum gases in the limit of extreme population imbalance where the minority species has but a single particle. We consider the situation where the gas is prepared in a state with a single spatially localized exciton: the single particle of the minority species is spatially localized while the density of the majority species in the vicinity of the minority particle sees a depression. Remarkably, we are able to consider cases where the gas contains on the order of N = 100 particles, comparable to that studied in experiments on cold atomic gases. We are able to do so by exploiting the integrability of the gas together with the observation that the excitonic state can be constructed through a simple superposition of exact eigenstates of the gas. The number of states in this superposition, rather than being exponentially large in the number of particles, scales linearly with N.We study the evolution of such spatially localized states in both strongly interacting Bose and Fermi gases. The behavior of the light cones when the interaction strength and density of the gas is varied can be understood from exact results for the spin excitation spectrum in these systems. We argue that the light cone in both cases exhibits scaling collapse. However unique to the Bose gas, we show that the presence of gapped finite-momentum roton-like excitations provide the Bose gas dynamics with secondary light cones.