Spin Excitation Spectrum Research Articles

Structural Manipulation of Spin Excitations in a Molecular Junction.

Single metallocene molecules act as sensitive spin detectors when decorating the probe of a scanning tunneling microscope (STM). However, the impact of the atomic-scale electrode details on the molecular spin state has remained elusive to date. Here, a nickelocene (Nc) STM junction is manipulated in an atomwise manner showing clearly the dependence of the spin excitation spectrum on the anchoring of Nc to Cu(111), a Cu monomer, and trimer. Moreover, while the spin state of the same Nc tip is a triplet with tunable spin excitation energies upon contacting the surface, it transitions to a Kondo-screened doublet on a Cu atom. Notably, the nontrivial magnetic exchange interaction of the molecular spin with the electron continuum of the substrate determines the spectral line shape of the spin excitations.

Tuning the Spin Interaction in Nonplanar Organic Diradicals through Mechanical Manipulation.

Open-shell polycyclic aromatic hydrocarbons (PAHs) represent promising building blocks for carbon-based functional magnetic materials. Their magnetic properties stem from the presence of unpaired electrons localized in radical states of π character. Consequently, these materials are inclined to exhibit spin delocalization, form extended collective states, and respond to the flexibility of the molecular backbones. However, they are also highly reactive, requiring structural strategies to protect the radical states from reacting with the environment. Here, we demonstrate that the open-shell ground state of the diradical 2-OS survives on a Au(111) substrate as a global singlet formed by two unpaired electrons with antiparallel spins coupled through a conformational-dependent interaction. The 2-OS molecule is a "protected" derivative of the Chichibabin's diradical, featuring a nonplanar geometry that destabilizes the closed-shell quinoidal structure. Using scanning tunneling microscopy (STM), we localized the two interacting spins at the molecular edges, and detected an excited triplet state a few millielectronvolts above the singlet ground state. Mean-field Hubbard simulations reveal that the exchange coupling between the two spins strongly depends on the torsional angles between the different molecular moieties, suggesting the possibility of influencing the molecule's magnetic state through structural changes. This was demonstrated here using the STM tip to manipulate the molecular conformation, while simultaneously detecting changes in the spin excitation spectrum. Our work suggests the potential of these PAHs as all-carbon spin-crossover materials.

Spin and bond-charge excitation spectra in correlated electron systems near an antiferromagnetic phase

Spin and bond-charge excitation spectra in correlated electron systems near an antiferromagnetic phase

Semiclassical approach to spin dynamics of a ferromagnetic S = 1 chain

Abstract Motivated by recent experimental progress on the quasi-one-dimensional quantum magnet NiNb2O6, we study the spin dynamics of an S = 1 ferromagnetic Heisenberg chain with single-ion anisotropy by using a semiclassical molecular dynamics approach. This system undergoes a quantum phase transition from a ferromagnetic to a paramagnetic state under a transverse magnetic field, and the magnetic response reflecting this transition is well described by our semiclassical method. We show that at low temperature the transverse component of the dynamical structure factor depicts clearly the magnon dispersion, and the longitudinal component exhibits two continua associated with single- and two-magnon excitations, respectively. These spin excitation spectra show interesting temperature dependence as effects of magnon interactions. Our findings shed light on the experimental detection of spin excitations in a large class of quasi-one-dimensional magnets.

Spin gap in quasi-one-dimensional S = 3/2 antiferromagnet CoTi2O5

Quasi-one-dimensional (1D) antiferromagnets are known to display intriguing phenomena especially when there is a spin gap in their spin-excitation spectra. Here we demonstrate that a spin gap exists in the quasi-1D Heisenberg antiferromagnet CoTi2O5 with highly ordered Co2+/Ti4+ occupation, in which the Co2+ ions with S = 3/2 form a 1D spin chain along the a-axis. CoTi2O5 undergoes an antiferromagnetic transition at T N ∼ 24 K and exhibits obvious anisotropic magnetic susceptibility even in the paramagnetic region. Although a gapless magnetic ground state is usually expected in a quasi-1D Heisenberg antiferromagnet with half-integer spins, by analyzing the specific heat, the thermal conductivity, and the spin-lattice relaxation rate (1/T 1) as a function of temperature, we found that a spin gap is opened in the spin-excitation spectrum of CoTi2O5 around T N, manifested by the rapid decrease of magnetic specific heat to zero, the double-peak characteristic in thermal conductivity, and the exponential decay of 1/T 1 below T N. Both the magnetic measurements and the first-principles calculations results indicate that there is spin-orbit coupling in CoTi2O5, which induces the magnetic anisotropy in CoTi2O5, and then opens the spin gap at low temperature.

Larmor precession in strongly correlated itinerant electron systems

Many-electron systems undergo a collective Larmor precession in the presence of a magnetic field. In a paramagnetic metal, the resulting spin wave provides insight into the correlation effects generated by the electron-electron interaction. Here, we use dynamical mean-field theory to investigate the collective Larmor precession in the strongly correlated regime, where dynamical correlation effects such as quasiparticle lifetimes and non-quasiparticle states are essential. We study the spin excitation spectrum, which includes a dispersive Larmor mode as well as electron-hole excitations that lead to Stoner damping. We also extract the momentum-resolved damping of slow spin waves. The accurate theoretical description of these phenomena relies on the Ward identity, which guarantees a precise cancellation of self-energy and vertex corrections at long wavelengths. Our findings pave the way towards a better understanding of spin wave damping in correlated materials.

An overview of the spin dynamics of antiferromagnetic Mn5Si3

The metallic compound Mn5Si3 hosts a series of antiferromagnetic phases that can be controlled by external stimuli, such as temperature and magnetic field. In this work, we investigate the spin-excitation spectrum of bulk Mn5Si3 by combining inelastic neutron scattering measurements and density functional theory calculations. We study the evolution of the dynamical response under external parameters and demonstrate that the spin dynamics of each phase is robust against any combination of temperature and magnetic field. In particular, the high-energy spin dynamics is very characteristic of the different phases consisting of either spin waves or broad fluctuation patterns.

Strong-coupling magnetophononics: Self-blocking, phonon-bitriplons, and spin-band engineering

Magnetophononics, the modulation of magnetic interactions by driving infrared-active lattice excitations, is emerging as a key mechanism for the ultrafast dynamical control of both semiclassical and quantum spin systems by coherent light. We demonstrate that, in a quantum magnet with strong spin-phonon coupling, resonances between the driven phonon and the spin excitation frequencies exhibit an intrinsic self-blocking effect, whereby only a fraction of the available laser power is absorbed by the phonon. Using the quantum master equations governing the nonequilibrium steady states of the coupled spin-lattice system, we show how self-blocking arises from the self-consistent alteration of the resonance frequencies. We link this to the appearance of mutually repelling collective spin-phonon states, which in the regime of strong hybridization become composites of a phonon and two triplons. We then identify the mechanism and optimal phonon frequencies by which to control a global nonequilibrium renormalization of the lattice-driven spin excitation spectrum and demonstrate that this effect should be observable in ultrafast THz experiments on a number of known quantum magnetic materials.

Nutation Excitations in the Gyrotropic Vortex Dynamics in a Circular Magnetic Nanodot.

A significant activity is devoted to the investigation of the ultrafast spin dynamic processes, holding a great potential for science and applications. However, a challenge of the understanding of the mechanisms of underlying spin dynamics in nanomaterials at pico- and femtosecond timescales remains under discussion. In this article, we explore the gyrotropic vortex dynamics in a circular soft magnetic nanodot, highlighting the impacts given by nutations in the high-frequency part of the dot spin excitation spectrum. Using a modified Thiele equation of the vortex core motion with a nutation term, we analyze the dynamic response of the vortex to an oscillating magnetic field applied in the dot plane. It is found that nutations affect the trajectory of the vortex core. Namely, we show that the directions of the vortex core motion in the low-frequency gyrotropic mode and the high-frequency nutation mode are opposite. The resonant frequencies of gyrotropic and nutational vortex core motions reveal themselves on different scales: gigahertz for the gyrotropic motion and terahertz for the nutations. We argue that the nutations induce a dynamic vortex mass, present estimates of the nutational mass, and conduct comparison with the mass appearing due to moving vortex interactions with spin waves and Doering domain wall mass.

Quantum Hall spin textures far beyond the skyrmion limit

In strongly correlated quantum Hall ferromagnets with noninteger filling factors between $\ensuremath{\nu}=1$ and $\ensuremath{\nu}=3/2$, evidence of offbeat spin textures is obtained. The platforms for the study are two-dimensional electron systems based on MgZnO/ZnO heterostructures, in which the parameters of Zeeman and exchange energies are inconsistent with ordinary skyrmions. Experimental probing of magnetic order is fulfilled via exploration of the spectra of collective spin excitations by means of inelastic light scattering. In addition to the ferromagnetic spin exciton, a low-energy spin mode is observed, bearing witness to broken spin-rotational symmetry in the ground state. The two spin modes exhibit a pronounced anticrossing behavior, depending on the two-dimensional momentum, electron concentration, filling factor, and magnetic field tilt. The properties of the electron system are simulated using the exact diagonalization technique, showing that Landau level mixing and crossing play a key role in the nontrivial spin configuration. The corresponding spin textures emerging between $\ensuremath{\nu}=1$ and $\ensuremath{\nu}=3/2$ involve the orbital degree of freedom and are qualitatively different from skyrmions. Experiments at elevated temperatures show the destruction of this orbital spin texture phase with critical temperature far below the Zeeman energy. On the other side of $\ensuremath{\nu}=1$ the textures are absent.

NMR evidence for a Peierls transition in the layered square-net compound LaAgSb2

We measured the central ($1/2\leftrightarrow -1/2$) and first satellite ($\pm3/2\leftrightarrow \pm1/2$) lines of the \la\ NMR spectra as a function of temperature in LaAgSb$_2$, in order to elucidate the origin and nature of the charge-density-wave (CDW) transitions at $T_\text{CDW1}=207$ K and $T_\text{CDW2}=186$ K. In the normal state, the Knight shift K reveals a fairly linear relationship with decreasing temperature, which is ascribed to a pseudogap in the spin excitation spectrum, pointing towards the material being an unconventional metal. Upon further cooling, K decreases more steeply below $T_\text{CDW1}$, indicative of the partial Fermi surface gap opening on top of the pseudogap. The most remarkable finding in our study is a clear splitting of the satellite lines at $T_\text{CDW1}$ observed for $H\parallel c$, whose temperature dependence behaves as the BCS order parameter in the weak-coupling limit, evidencing that the CDW transition induces the periodic lattice distortion. Our NMR findings therefore demonstrate that the CDW transition in LaAgSb$_2$ is of Peierls type, being driven by the electronic instability in the vicinity of the Fermi level.

Spin Excitation Spectra of Anisotropic Spin-1/2 Triangular Lattice Heisenberg Antiferromagnets.

Investigation of dynamical excitations is difficult but crucial to the understanding of many exotic quantum phenomena discovered in quantum materials. This is particularly true for highly frustrated quantum antiferromagnets whose dynamical properties deviate strongly from theoretical predictions made based on the spin-wave or other approximations. Here, we present a large-scale numerical calculation on the dynamical correlation functions of spin-1/2 triangular Heisenberg model using a state-of-the-art tensor network renormalization group method. The calculated results allow us to gain for the first time a comprehensive picture on the nature of spin excitation spectra in this highly frustrated quantum system. It provides a quantitative account for all the key features of the dynamical spectra disclosed by inelastic neutron scattering measurements for Ba_{3}CoSb_{2}O_{9}, revealing the importance of the interplay between low- and high-energy excitations and its renormalization effect to the low-energy magnon bands and high-energy continuums. We identify the longitudinal Higgs modes in the intermediate-energy scale and predict the energy and momentum dependence of spectral functions along the three principal axes that can be verified by polarized neutron scattering experiments. Furthermore, we find that the spin excitation spectra weakly depend on the anisotropic ratio of the antiferromagnetic interaction.

Spin interaction and magnetism in cobaltate Kitaev candidate materials: An ab initio and model Hamiltonian approach

In the quest for materials hosting Kitaev spin liquids, much of the efforts have been focused on the fourth- and fifth-row transition metal compounds, which are spin-orbit coupling assisted Mott insulators. Here, we study the structural and magnetic properties of 3$d$ transition metal oxides, Na$_2$Co$_2$TeO$_6$ and Na$_3$Co$_2$SbO$_6$. The partial occupancy of sodium in former compound is addressed using a cluster expansion, and a honeycomb lattice of sodiums is found to be energetically favored. Starting from the \textit{ab initio} band structures, a many-body second order perturbation theory leads to a pseudospin-$\frac{1}{2}$ Hamiltonian with estimated magnetic interactions. We show that the experimentally observed zigzag magnetic state is stabilized only when the first neighbor Kitaev coupling dominates over the Heisenberg term, both of which are highly suppressed due to presence of $e_g$ orbitals. A third neighbor Heisenberg interaction is found dominant in both these compounds. We also present a phase diagram for Na$_2$Co$_2$TeO$_6$ by varying the electron-electron and spin-orbit interactions. The computed spin excitation spectra are found to capture essential features of recent experimental magnon spectrum, lending support to our results.

Determinant quantum Monte Carlo for the half-filled Hubbard model with nonlocal density-density interactions

We design a novel formalism of determinant quantum Monte Carlo method for the half-filled Hubbard model with on-site Hubbard interaction $U$ and nearest neighbor density-density interaction $V$ on the square lattice. The formalism is free of sign problem for $|U|\ge 4|V|$, and is achieved by introducing discrete auxiliary fields on the nearest-neighbor bonds alone. Based on this formalism, we study the ground state phase diagram of the model systematically using the projector algorithm. Within the sign-problem free parameter space $|U|\ge 4|V|$, we obtain antiferromagnetism for $U\ge 4|V|>0$, charge density wave for $U0$, s-wave superconductivity for $U<0$ and small negative $V$, and phase separation for $U<0$ and a larger negative $V$. We also obtain the single particle gap and spin excitation spectra, and by comparison to mean field results, as well as available literatures, we discuss the possible phase boundary beyond the sign-problem free region. The unbiased numerically exact results can be taken as benchmarks in future studies. Finally, we discuss possible extension for longer-range interactions in the model.

Low-energy spin excitations of the frustrated ferromagnetic J1−J2 chain material linarite PbCuSO4(OH)2 in applied magnetic fields parallel to the b axis

We report a study of the spin dynamics of the frustrated ferromagnetic $J_1$-$J_2$ chain compound linarite, PbCuSO$_4$(OH)$_2$, in applied magnetic fields up to field polarization. By means of an extreme-environment inelastic neutron scattering experiment, we have measured the low-energy spin excitations of linarite in fields up to 8.8 T for $\mathbf{H} \parallel b$ axis. We have recorded the spin excitation spectra along $h$, $k$ and $l$ for the field-induced magnetic phases IV, V and the field polarized state close to saturation. By employing first-principles calculations, we estimate the leading magnetic exchanges out of the $bc$ plane and model the dispersion relations using linear spin-wave theory. In this way, we find evidence for a (very weak) residual magnetic exchange coupling out of the $bc$ plane. Together with the previously established dominant intrachain couplings $J_1$ and $J_2$ and the interchain coupling $J_3$, we derive an effective set of exchange couplings for a microscopic description of linarite. Further, we find that the peculiar character of phase V manifests itself in the measured spin dynamics.

Measuring Magnetic Excitation Spectra Using Resonant Inelastic X-ray Scattering

The advent of modern synchrotron radiation facilities providing extremely intense x-rays has enabled measuring momentum-resolved spin excitation spectra of magnetic materials, which have long been exclusively accessible through inelastic neutron scattering. In this article, we briefly review the recent development of hard x-ray resonant inelastic x-ray scattering (RIXS) and discuss few examples of RIXS measurements on iridium oxides.

Frustrated magnetic interactions in FeSe

The structurally simplest high-temperature superconductor FeSe exhibits an intriguing superconducting nematic paramagnetic phase with unusual spin excitation spectra that are different from typical spin waves; thus, determining its effective magnetic exchange interactions is challenging. Here we report neutron scattering measurements of spin fluctuations of FeSe in the tetragonal paramagnetic phase. We show that the equal-time magnetic structure factor, $\mathcal{S}(\mathbf{Q})$, can be effectively modeled using the self-consistent Gaussian approximation calculation with highly frustrated nearest-neighbor (${J}_{1}$) and next-nearest-neighbor (${J}_{2}$) exchange couplings, and very weak further neighbor exchange interaction. Our results elucidate the frustrated magnetism in FeSe, which provides a natural explanation for the highly tunable superconductivity and nematicity in FeSe and related materials.

Exchange interactions in d5 Kitaev materials: From Na2IrO3 to α−RuCl3

We present an analytical study of the exchange interactions between pseudospin one-half ${d}^{5}$ ions in honeycomb lattices with edge-shared octahedra. Various exchange channels involving Hubbard $U$, charge-transfer excitations, and cyclic exchange are considered. Hoppings within ${t}_{2g}$ orbitals as well as between ${t}_{2g}$ and ${e}_{g}$ orbitals are included. Special attention is paid to the trigonal crystal field $\mathrm{\ensuremath{\Delta}}$ effects on the exchange parameters. The obtained exchange Hamiltonian is dominated by ferromagnetic Kitaev interaction $K$ within a wide range of $\mathrm{\ensuremath{\Delta}}$. It is found that a parameter region close to the charge-transfer insulator regime and with a small $\mathrm{\ensuremath{\Delta}}$ is most promising to realize the Kitaev spin liquid phase. Two representative honeycomb materials ${\mathrm{Na}}_{2}{\mathrm{IrO}}_{3}$ and $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$ are discussed based on our theory. We have found that both materials share dominant ferromagnetic $K$ and positive nondiagonal $\mathrm{\ensuremath{\Gamma}}$ values. However, their Heisenberg $J$ terms have opposite signs: AFM $J&gt;0$ in ${\mathrm{Na}}_{2}{\mathrm{IrO}}_{3}$ and FM $J&lt;0$ in $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$. This brings different magnetic fluctuations and results in their different magnetization behaviors and spin excitation spectra. Proximity to FM state due to the large FM $J$ is emphasized in $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$. The differences between the exchange couplings of these two materials originate from the opposite $\mathrm{\ensuremath{\Delta}}$ values, indicating that the crystal field can serve as an efficient control parameter to tune the magnetic properties of ${d}^{5}$ spin-orbit Mott insulators.

Villain transformation for XXZ anisotropic ferrimagnetic spin chain

We investigate the spin excitation spectrum and the thermodynamic properties of the XXZ anisotropic ferrimagnetic spin-(1/2, 1) chain under the presence of a magnetic field using the Villain transformation method. The effect of the XXZ anisotropic parameter and external magnetic field on the thermodynamic observables are calculated at finite temperature. The energy spectra exhibit the coexistence of a gapless branch and a gapful branch, both of them are sensitive to the change of XXZ anisotropic parameter. The gapless branch exhibits a V-shape structure, while the gapful branch is reversed and presents an omega-shape for the XY model which is completely different from previous results for the XXZ model. Thermodynamic quantities such as free energy, internal energy, entropy, specific heat and magnetization are present. These findings for the isotropic case are compared with the results calculated by the other established methods and it turns out that Villain transformation well describes this system at low temperature. • The spin excitation spectrum and thermodynamic properties of the XXZ anisotropic ferrimagetic spin-(1/2, 1) chain under the presence of magnetic field are investigated by the Villain transformation method. • Two branches of the excitation energy spectra are obtained, which are sensitive to the size of the XXZ anisotropic parameter. • The gapless branch exhibits a V-shape structure, while the higher branch is reversed and exhibits an omega-shape structure for the XY model. • The dependence of the thermodynamic quantities on the XXZ anisotropic parameter and magnetic field are studied.

Frustration model and spin excitations in the helimagnet FeP

The metallic compound FeP belongs to the class of materials that feature a complex noncollinear spin order driven by magnetic frustration. While its double-helix magnetic structure with a period $\lambda_{\text{s}} \approx 5c$, where $c$ is the lattice constant, was previously well determined, the relevant spin-spin interactions that lead to that ground state remain unknown. By performing extensive inelastic neutron scattering measurements, we obtained the spin-excitation spectra in a large part of the momentum-energy space. The spectra show that the magnons are gapped with a gap energy of $\sim$5 meV. Despite the 3D crystal structure, the magnon modes display strongly anisotropic dispersions, revealing a quasi-one-dimensional character of the magnetic interactions in FeP. The physics of the material, however, is not determined by the dominating exchange, which is ferromagnetic. Instead, the weaker two-dimensional antiferromagnetic interactions between the rigid ferromagnetic spin chains drive the magnetic frustration. Using linear spin-wave theory, we were able to construct an effective Heisenberg Hamiltonian with an anisotropy term capable of reproducing the observed spectra. This enabled us to quantify the exchange interactions in FeP and determine the mechanism of its magnetic frustration.