Stoner Excitations Research Articles

Long-lived spin waves in a metallic antiferromagnet

Collective spin excitations in magnetically ordered crystals, called magnons or spin waves, can serve as carriers in novel spintronic devices with ultralow energy consumption. The generation of well-detectable spin flows requires long lifetimes of high-frequency magnons. In general, the lifetime of spin waves in a metal is substantially reduced due to a strong coupling of magnons to the Stoner continuum. This makes metals unattractive for use as components for magnonic devices. Here, we present the metallic antiferromagnet CeCo2P2, which exhibits long-living magnons even in the terahertz (THz) regime. For CeCo2P2, our first-principle calculations predict a suppression of low-energy spin-flip Stoner excitations, which is verified by resonant inelastic X-ray scattering measurements. By comparison to the isostructural compound LaCo2P2, we show how small structural changes can dramatically alter the electronic structure around the Fermi level leading to the classical picture of the strongly damped magnons intrinsic to metallic systems. Our results not only demonstrate that long-lived magnons in the THz regime can exist in bulk metallic systems, but they also open a path for an efficient search for metallic magnetic systems in which undamped THz magnons can be excited.

Correlation driven near-flat band Stoner excitations in a Kagome magnet

Among condensed matter systems, Mott insulators exhibit diverse properties that emerge from electronic correlations. In itinerant metals, correlations are usually weak, but can also be enhanced via geometrical confinement of electrons, that manifest as ‘flat’ dispersionless electronic bands. In the fast developing field of topological materials, which includes Dirac and Weyl semimetals, flat bands are one of the important components that can result in unusual magnetic and transport behaviour. To date, characterisation of flat bands and their magnetism is scarce, hindering the design of novel materials. Here, we investigate the ferromagnetic Kagomé semimetal Co3Sn2S2 using resonant inelastic X-ray scattering. Remarkably, nearly non-dispersive Stoner spin excitation peaks are observed, sharply contrasting with the featureless Stoner continuum expected in conventional ferromagnetic metals. Our band structure and dynamic spin susceptibility calculations, and thermal evolution of the excitations, confirm the nearly non-dispersive Stoner excitations as unique signatures of correlations and spin-polarized electronic flat bands in Co3Sn2S2. These observations serve as a cornerstone for further exploration of band-induced symmetry-breaking orders in topological materials.

Ab initio study of spin fluctuations in the itinerant kagome magnet FeSn

Kagome antiferromagnetic metal FeSn has become an attracting platform for the exploration of novel electronic states, such as topological Dirac states and the formation of flat bands by localized electrons. Apart from the electronic properties, Dirac magnons and flat magnon bands have also been proposed by applying simplified Heisenberg models to kagome magnetic systems.Inelastic neutron scattering studies on FeSn found well defined magnon dispersions at low energies,but magnons at high energies are strongly dampled, which can not be explained by localized spin models. In this paper, we utilize both linear spin wave theory and time-dependent density functional perturbation theory to investigate spin fluctuations of FeSn. Through the comparison of calculated spin wave spectra and Stoner continuum, we explicitly show that the damping of magnons at high energies are due to the Landau damping, and the appearance of high energy optical-magnon like branches at the M and K point are resulted by relatively low Stoner excitation intensity at those regions.

Defect-induced edge ferromagnetism and fractional spin excitations of the SU(4) π-flux Hubbard model on honeycomb lattice

Recently, a SU(4) π-flux Hubbard model on the honeycomb lattice has been proposed to study the spin-orbit excitations of α-ZrCl3 (Yamada et al., 2018 [27]). Based on this model with a zigzag edge, we show the edge defects can induce edge flat bands that result in a SU(4) edge ferromagnetism. We develop an effective one-dimensional interaction Hamiltonian to study the corresponding SU(4) spin excitations. Remarkably, SU(4) spin excitations of the edge ferromagnet appear as a continuum covering the entire energy region rather than usual magnons. Through further entanglement entropy analysis, we suggest that the continuum consists of fractionalized spin excitations from the disappeared magnons, except for that from the particle-hole Stoner excitations. Moreover, in ribbon systems with finite widths, the disappeared magnons can be restored in the gap formed by the finite-size effect and the optical branch of the restored magnons are found to be topological nontrivial.

Element-selective ultrafast magnetization dynamics of hybrid Stoner-Heisenberg magnets

Stoner and Heisenberg excitations in magnetic materials are inherently different. The first involves an effective reduction of the exchange splitting, whereas the second comprises excitation of spin waves. In this work, we test the impact of these two excitations in the hybrid Stoner-Heisenberg system of FePd. We present a microscopic picture of ultrafast demagnetization dynamics in this alloy, which represents both components of strong local exchange splitting in Fe and induced polarization in Pd. We identify the spin-orbit coupling (SOC) and the optical intersite spin transfer (OISTR) as the two dominant factors for demagnetization at ultrashort timescales. Remarkably, the drastic difference in the origin of the magnetic moment of the Fe and Pd species is not deciding the initial magnetization dynamics in this alloy. By tuning the external laser pulse, the extrinsic OISTR can be manipulated for site-selective demagnetization on femtosecond timescales providing the fastest way for optical and selective control of the magnetization dynamics in alloys. Saliently, our results signify why various experiments demonstrating OISTR might obtain conflicting results.

Electron\u2013plasmon and electron\u2013magnon scattering in ferromagnets from first principles by combining GW and GT self-energies

This work combines two powerful self-energy techniques: the well-known GW method and a self-energy recently developed by us that describes renormalization effects caused by the scattering of electrons with magnons and Stoner excitations. This GT self-energy, which is fully k-dependent and contains infinitely many spin-flip ladder diagrams, was shown to have a profound impact on the electronic band structure of Fe, Co, and Ni. In the present work, we refine the method by combining GT with the GW self-energy. The resulting GWT spectral functions exhibit strong lifetime effects and emergent dispersion anomalies. They are in an overall better agreement with experimental spectra than those obtained with GW or GT alone, even showing partial improvements over local-spin-density approximation dynamical mean-field theory. The performed analysis provides a basis for applying the GWT technique to a wider class of magnetic materials.

Nonlinear Extension of the Dynamical Linear Response of Spin: Extended Heisenberg Model

We introduce a new extended Heisenberg model. The model contains the orbital-dependent spins together with the retarded effects of spin torque. The model is directly derived from the dynamical linear response functions on the transversal spin fluctuation. Our model allows us to address effects which are not accessible via the usual Heisenberg model. With the model, we can describe not only the relaxation effects due to the Landau damping caused by the Stoner excitations, but also the nesting effects of the Fermi surface. We discuss possibilities of the extended Heisenberg model based on the high-resolution plots of the spin susceptibility for Fe.

Universal spin wave damping in magnetic Weyl semimetals

We analyze the decay of spin waves into Stoner excitations in magnetic Weyl semimetals. The lifetime of a mode is found to have a universal dependence on its frequency and momentum, and on a few parameters that characterize the relativistic Weyl spectrum. At the same time, Gilbert damping by Weyl electrons is absent. The decay rate of spin waves is calculated perturbatively using the s-d model of itinerant Weyl or Dirac electrons coupled to local moments. We show that many details of the Weyl spectrum, such as the momentum-space locations, dispersions and sizes of the Weyl Fermi pockets, can be deduced indirectly by probing the spin waves of local moments using inelastic neutron scattering.

Analysis of the linear relationship between asymmetry and magnetic moment at the M edge of 3d transition metals

The magneto-optical response of Fe and Ni during ultrafast demagnetization is studied experimentally and theoretically. We have performed pump-probe experiments in the transverse magneto-optical Kerr effect (T-MOKE) geometry using photon energies that cover the M-absorption edges of Fe and Ni between 40 to 72 eV. The asymmetry was detected by measuring the reflection of light for two different orientations of the sample magnetization. Density functional theory (DFT) wasused to calculate the magneto-optical response of different magnetic configurations, representing different types of excitations: long-wavelength magnons, short wavelength magnons, and Stoner excitations. In the case of Fe, we find that the calculated asymmetry is strongly dependent on the specific type of magnetic excitation. Our modelling also reveals that during remagnetization Fe is, to a reasonable approximation, described by magnons, even though small non-linear contributions could indicate some degree of Stoner excitations as well. In contrast, we find that the calculated asymmetry in Ni is rather insensitive to the type of magnetic excitations. However, there is a weak non-linearity in the relation between asymmetry and the off-diagonal component of the dielectric tensor, which does not originate from the modifications of the electronic structure. Our experimental and theoretical results thus emphasize the need of considering a coupling between asymmetry and magnetization that may be more complex that a simple linear relationship. This insight is crucial for the microscopic interpretation of ultrafast magnetization experiments.

Electron-magnon scattering in elementary ferromagnets from first principles: Lifetime broadening and band anomalies

We study the electron-magnon scattering in bulk Fe, Co, and Ni within the framework of many-body perturbation theory implemented in the full-potential linearized augmented-plane-wave method. To this end, a $\mathbf{k}$-dependent self-energy ($GT$ self-energy) describing the scattering of electrons and magnons is constructed from the solution of a Bethe-Salpeter equation for the two-particle (electron-hole) Green function, in which single-particle Stoner and collective spin-wave excitations (magnons) are treated on the same footing. Partial self-consistency is achieved by the alignment of the chemical potentials. The resulting renormalized electronic band structures exhibit strong spin-dependent lifetime effects close to the Fermi energy, which are strongest in Fe. The renormalization can give rise to a loss of quasiparticle character close to the Fermi energy, which we attribute to electron scattering with spatially extended spin waves. This scattering is also responsible for dispersion anomalies in conduction bands of iron and for the formation of satellite bands in nickel. Furthermore, we find a band anomaly at a binding energy of 1.5~eV in iron, which results from a coupling of the quasihole with single-particle excitations that form a peak in the Stoner continuum. This band anomaly was recently observed in photoemission experiments. On the theory side, we show that the contribution of the Goldstone mode to the $GT$ self-energy is expected to (nearly) vanish in the long-wavelength limit. We also present an in-depth discussion about the possible violation of causality when an incomplete subset of self-energy diagrams is chosen.

Strong Spin Dependence of Correlation Effects in Ni Due to Stoner Excitations.

Using high-resolution angle-resolved photoemission, we observe a strong spin-dependent renormalization and lifetime broadening of the quasiparticle excitations in the electronic band structure of Ni(111) in an energy window of ∼0.3 eV below the Fermi level. We derive a quantitative result for the spin-dependent lifetime broadening by comparing the scattering rates of majority and minority d states, and further show that spin-dependent electron correlations are instead negligible for sp states. From our analysis we experimentally determine the effective on-site Coulomb interaction U caused by Stoner-like interband transitions between majority and minority d states. The present results demonstrate the remarkable impact of spin-dependent electron correlation effects originating from single-particle excitations in a prototypical 3d transition metal, paving the way for further refinement of current many-body theoretical approaches.

Photocontrol of magnetic structure in an itinerant magnet

We study the photoinduced magnetic transition in an itinerant magnet described by the double-exchange model, in which conduction electrons couple with localized spins through the ferromagnetic (FM) Hund coupling. It is shown that intense light applied to the FM ground state induces an antiferromagnetic (AFM) order, in contrast to the AFM-to-FM transition due to the photocarrier injection. In particular, we focus on the mechanism for instability of the FM structure by the light irradiation. The magnon spectrum in the Floquet state is formulated on the basis of the pertrubative expansion of the Floquet Green function. The magnon dispersion shows softening at momentum $(\pi,\pi)$ in the square lattice with increasing the light amplitude, implying photoinduced AFM instability. This result is mainly attributed to a nonequilibrium electron distribution, which promotes low-energy Stoner excitations. The transient optical conductivity spectra characterized by interband excitations and Floquet sidepeaks are available to identify the photoinduced AFM state.

Electromagnetic modes from Stoner enhancement: Graphene as a case study

In systems with substantial spin fluctuations, dressing the polarization function by ladder diagram of Stoner (spin-flip) excitations can drastically modify the electromagnetic response. As a case study, we provide the detailed analysis of the corrections to the non-local optical conductivity of both doped and undoped graphene. While the resummation of ladder diagram of Stoner excitations does not affect the TE mode in doped graphene, it allows for a new undamped TM mode in undoped graphene. This is the sole effect of corrections arising from ladder diagrams and is dominated by Stoner excitations along the ladder rung which goes away by turning off the source of spin-flip interactions. In the case of doped graphene, the inclusion of spin-flip particle-hole fluctuations reduces the energy of plasmon mode.

Ferromagnetic and Spin-Wave Resonance on Heavy-Metal-Doped Permalloy Films: Temperature Effects

Broadband ferromagnetic resonance (FMR) spectroscopy is used to study the temperature $(T)$ and dopant-concentration dependence of the magnetodynamic properties of Permalloy $({\hbox{Py}} = {\hbox{Ni}}_{80}{\hbox{Fe}}_{20})$ and Py $_{100-x}$ M $_{x}$ films, where the dopant ${\hbox{M}} = {\hbox{Pt}}$ , Au, and Ag. The saturation magnetization $(M_{\text{S}})$ and Gilbert damping constant $(\alpha)$ are determined from the uniform FMR mode, while the spin wave stiffness $(D)$ is extracted using the first perpendicular standing spin-wave mode. The temperature dependence of $D$ is best described by a $T^{2}$ law, which suggests a noticeable effect of the itinerant character of the electrons. The spin wave stiffness is also estimated using Bloch's law and the two methods are compared. The results strongly imply that not only spin wave and Stoner excitations, but also other mechanisms contribute to the reduction of $M_{\mathrm{S}}$ . The damping increases with $T$ for all samples, but the enhancement is most pronounced for Py doped with 30 at.% Au.

Elastic versus inelastic spin-polarized electron scattering from a ferromagnetic surface

Spin-polarized electron energy loss spectroscopy was applied to study the intensity asymmetry upon the reversal of the incident spin polarization of elastically and inelastically scattered polarized electrons from an epitaxial ferromagnetic Fe layer on W(110). The polarization of the incident beam was always collinear with the magnetic moment (magnetization) of the sample, and the asymmetries were measured for two opposite magnetizations of the sample. They allowed extracting the exchange and the spin-orbit components from the measured asymmetry. A strong asymmetry of Stoner excitations in an Fe film on W(110) is observed, as expected, at about 3 eV energy loss. The value of the asymmetry declines but is still observable when the surface is contaminated. The asymmetry of elastic scattering for normal incidence and a 50\ifmmode^\circ\else\textdegree\fi{} detection angle is close to zero in contrast to the Stoner excitation asymmetry (inelastic scattering). However, the asymmetry of elastic scattering increases substantially at two specular geometries with 25\ifmmode^\circ\else\textdegree\fi{} and 72\ifmmode^\circ\else\textdegree\fi{} angles of incidence, compared to the normal incidence, and may be even larger than the asymmetry of Stoner excitations. The sign of elastic scattering asymmetry changes upon the reversal of the sample magnetization, indicating the magnetic origin of this asymmetry, i.e., spin-dependent electron-electron scattering with electron exchange. The calculation of the asymmetry of elastic spin-polarized electron scattering from a spin-dependent surface potential barrier shows a qualitative agreement with the measurements.

High resolution electron energy loss spectroscopy of spin waves in ultra‐thin cobalt films

Electron energy loss spectroscopy has successfully established itself as the experimental method to study exchange‐dominated, high‐momentum spin waves in ultra‐thin films. Because of insufficient energy resolution, previous studies were limited to spin waves in the high energy range and to wave vectors larger than about q|| = 0.4 Å−1. In this regime, spin waves are strongly damped by decay into Stoner excitations. Furthermore, the spin wave signal of a multilayer film consists of several overlapping modes. After implementation of several technical modifications, our electron spectrometer now enables the study of spin waves with an energy resolution down to 2 meV, and thereby the discrimination of several spin wave modes in ultra‐thin films as well as the study of the intrinsic width of modes down to 1 meV. Examples are presented for fcc and hcp cobalt films and discussed in terms of current theoretical models. Copyright © 2016 John Wiley & Sons, Ltd.

Zero-Point Spin-Fluctuations of Single Adatoms.

Stabilizing the magnetic signal of single adatoms is a crucial step toward their successful usage in widespread technological applications such as high-density magnetic data storage devices. The quantum mechanical nature of these tiny objects, however, introduces intrinsic zero-point spin-fluctuations that tend to destabilize the local magnetic moment of interest by dwindling the magnetic anisotropy potential barrier even at absolute zero temperature. Here, we elucidate the origins and quantify the effect of the fundamental ingredients determining the magnitude of the fluctuations, namely, the (i) local magnetic moment, (ii) spin-orbit coupling, and (iii) electron-hole Stoner excitations. Based on a systematic first-principles study of 3d and 4d adatoms, we demonstrate that the transverse contribution of the fluctuations is comparable in size to the magnetic moment itself, leading to a remarkable ≳50% reduction of the magnetic anisotropy energy. Our analysis gives rise to a comprehensible diagram relating the fluctuation magnitude to characteristic features of adatoms, providing practical guidelines for designing magnetically stable nanomagnets with minimal quantum fluctuations.

Excitation of plasmons in Ag/Fe/W structure by spin-polarized electrons

Using Spin-polarized Electron-Energy Loss Spectroscopy (SPEELS), the plasmon excitations were probed in a few atomic layers thick Ag film deposited on an Fe layer or on a single crystal of W(110). The measurements were performed at two specular geometries with either a 25° or 72° angle of incidence. On a clean Fe layer (10 atomic layers thick), Stoner excitation asymmetry was observed, as expected. Deposition of a silver film on top of the Fe layer dramatically changed the asymmetry of the SPEELS spectra. The spin-effect depends on the kinematics of the scattering: angles of incidence and detection. The spin-dependence of the plasmon excitations in the silver film on the W(110) surface and on the ferromagnetic Fe film is suggested to arise from the spin-active Ag/W or Ag/Fe interfaces.

Controlling spin–orbit interaction in a ferromagnetic Fe/Au double layer

Using spin-polarized single- and two-electron spectroscopy, we probe exchange and spin–orbit interaction in a double layer of Fe and Au on W(110) and measure the spin asymmetry of the Bloch spectral density function of the sample. In a 5 ML iron film, the spin-orbit contribution to the measured asymmetry of the (e,2e) spectra was not detectable, whereas a deposition of about 1 ML of gold introduced a substantial spin-orbit component in the measured asymmetry. At the same time, this double layer still exhibits ferromagnetic properties: (i) the spectral density function asymmetry demonstrate imbalance of spin-up and spin-down electron densities in the valence band and (ii) the Stoner excitation asymmetry has almost the same value as in a pure Fe film.

Fundamental Limitations of Half-Metallicity in Spintronic Materials

Zero-point spin fluctuations are shown to strongly influence the ground state of ferromagnetic metals and to impose limitations for the fully spin polarized state assumed in half-metallic ferromagnets, which may influence their applications in spintronics. This phenomenon leads to the low-frequency Stoner excitations and cause strong damping and softening of magnons in magnetoresistive manganites observed experimentally.