Spin-polarized Electron Energy Loss Spectroscopy Research Articles

Theory of spin-polarized high-resolution electron energy loss spectroscopy from nonmagnetic surfaces with a large spin-orbit coupling

The scattering theory of low-energy (slow) electrons has been developed by Evans and Mills [Phys. Rev. B 5, 4126 (1972)]. The formalism is merely based on the electrostatic Coulomb interaction of the scattering electrons with the charge-density fluctuations above the surface and can describe most of the interesting features observed in the high-resolution electron energy-loss spectroscopy experiments. Here we extend this theory by including the spin-orbit coupling in the scattering process. We discuss the impact of this interaction on the scattering cross section. In particular, we discuss cases in which a spin-polarized electron beam is scattered from nonmagnetic surfaces with a strong spin-orbit coupling. We show that under some assumptions one can derive an expression for the scattering cross section, which can be used for numerical calculations of the spin-polarized spectra recorded by spin-polarized high-resolution electron energy-loss spectroscopy experiments.

First-principles perspective on magnetic second sound

The fluctuations of the magnetic order parameter, or longitudinal spin excitations, are investigated theoretically in the ferromagnetic Fe and Ni as well as in the antiferromagnetic phase of the pnictide superconductor FeSe. The charge and spin dynamics of these systems is described by evaluating the generalized charge and spin density response function calculated from first-principles linear response time dependent density functional theory within adiabatic local spin density approximation. We observe that the formally non-interacting Kohn-Sham system features strong coupling between the magnetization and charge dynamics in the longitudinal channel and that the coupling is effectively removed upon the inclusion of the Coulomb interaction in the charge channel and the resulting appearance of plasmons. The longitudinal spin fluctuations acquire a collective character without the emergence of the Goldstone boson, similar to the case of paramagnon excitations in non-magnetic metals like Pd. In ferromagnetic Fe and Ni the longitudinal spin dynamics is governed by interactions between low-energy intraband electron-hole pairs while in quasi two dimensional antiferromagnet FeSe it is dominated by the interband transitions with energies of the order of exchange splitting. In the later material, the collective longitudinal magnetization fluctuations feature well defined energies and long life times for small momenta and appear below the particle-hole continuum. The modes become strongly Landau-damped for growing wave-vectors. We relate our theoretical findings to existing experimental spin-polarized electron energy loss spectroscopy results. In bulk bcc Fe, the longitudinal magnetic modes appear above the typical energies of transverse spin-waves, have energies comparable with the Stoner spin-flip excitation continuum, and are order of magnitude less energetic than the charge dynamics.

Group Velocity Engineering of Confined Ultrafast Magnons.

Quantum confinement permits the existence of multiple terahertz magnon modes in atomically engineered ultrathin magnetic films and multilayers. By means of spin-polarized high-resolution electron energy-loss spectroscopy, we report on the direct experimental detection of all exchange-dominated terahertz confined magnon modes in a 3ML Co film. We demonstrate that, by tuning the structural and magnetic properties of the Co film, through its epitaxial growth on different surfaces, e.g., Ir(001), Cu(001), and Pt(111), one can achieve entirely different in-plane magnon dispersions, characterized by positive and negative group velocities. Our first-principles calculations show that spin-dependent many-body correlation effects in Co films play an important role in the determination of the energies of confined magnon modes. Our results suggest a pathway towards the engineering of the group velocity of confined ultrafast magnons.

Temperature Dependence of Magnetic Excitations: Terahertz Magnons above the Curie Temperature.

When an ordered spin system of a given dimensionality undergoes a second order phase transition, the dependence of the order parameter, i.e., magnetization on temperature, can be well described by thermal excitations of elementary collective spin excitations (magnons). However, the behavior of magnons themselves, as a function of temperature and across the transition temperature T_{C}, is an unknown issue. Utilizing spin-polarized high resolution electron energy loss spectroscopy, we monitor the high-energy (terahertz) magnons, excited in an ultrathin ferromagnet, as a function of temperature. We show that the magnons' energy and lifetime decrease with temperature. The temperature-induced renormalization of the magnons' energy and lifetime depends on the wave vector. We provide quantitative results on the temperature-induced damping and discuss the possible mechanism, e.g., multimagnon scattering. A careful investigation of physical quantities determining the magnons' propagation indicates that terahertz magnons sustain their propagating character even at temperatures far above T_{C}.

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.

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.

Transverse dynamical magnetic susceptibilities from regular static density functional theory: Evaluation of damping andgshifts of spin excitations

The dynamical transverse magnetic Kohn-Sham susceptibility calculated within time-dependent density functional theory shows a fairly linear behavior for a finite energy window. This observation is used to propose a scheme where the computation of this quantity is greatly simplified. Regular simulations based on static density functional theory can be used to extract the dynamical behavior of the magnetic response function. Besides the ability to calculate elegantly damping of magnetic excitations, we derive along the way useful equations giving the main characteristics of these excitations: effective $g$-factors and the resonance frequencies that can be accessed experimentally using inelastic scanning tunneling spectroscopy or spin-polarized electron energy loss spectroscopy.

Magnetic properties and magnon excitations in Fe(001) films grown on Ir(001)

We present a comprehensive study of magnetic properties and high wave-vector magnon excitations in epitaxial Fe(001) films grown on Ir(001) substrate. The magnetic properties are investigated by magneto-optical Kerr effect for various thicknesses of Fe film from 4 up to 27 monolayers. The magnon dispersion relation is obtained by means of spin-polarized electron energy loss spectroscopy. By comparing the experimental and theoretical results, we comment on the effect of the strain induced tetragonal distortion in the Fe film and the electronic hybridizations between the film and the substrate on the exchange interaction and magnon dispersion relation. The thickness-dependent measurements show that the magnon dispersion relation does not change significantly while changing the film thickness in the regime, where the film is uniformly strained. In addition, the measurements are also performed on thicker Fe films, where the films are relaxed into a bulklike structure. The magnon energies close to the zone boundary differ from the ones measured on thick Fe(110) films on W(110). However, the magnon dispersion relation measured for both systems can be well described within the Heisenberg model by using the same effective exchange parameters.

Magnons in ultrathin ferromagnetic films with a large perpendicular magnetic anisotropy

We report on an experimental observation of high-energy magnon excitations in ultrathin ferromagnetic films with a perpendicular easy axis. We demonstrate that a transversally spin-polarized beam can be used to excite and probe the high-energy magnons within spin-polarized electron energy-loss spectroscopy experiments. The magnon dispersion relation and lifetime are probed over the entire surface Brillouin zone for a set of body-centered tetragonal FeCo films with a large perpendicular magnetic anisotropy. First-principles calculations reveal that in addition to the tetragonal distortion, which is the origin of the large perpendicular magnetic anisotropy, the interfacial electronic hybridization also has a considerable impact on the properties of magnons.

Easy-axis ferromagnetic chain on a metallic surface

The phases and excitation spectrum of an easy-axis ferromagnetic chain of S = 1/2 magnetic impurities built on the top of a clean metallic surface are studied. As a function of the (Kondo) coupling to the metallic surface and at low temperatures, the spin chain exhibits a quantum phase transition from an Ising ferromagnetic phase with long-range order to a paramagnetic phase where quantum fluctuations destroy the magnetic order. In the paramagnetic phase, the system consists of a chain of Kondo singlets where the impurities are completely screened by the metallic host. In the ferromagnetic phase, the excitations above the Ising gap are damped magnons, with a finite lifetime arising due to the coupling to the substrate. We discuss the experimental consequences of our results to spin-polarized electron energy loss spectroscopy, and we finally analyze possible extensions to spin chains with S > 1/2.

Surface magnons probed by spin-polarized electron energy loss spectroscopy

Short-wavelength magnons at ferromagnetic surfaces can be probed by electrons. The unique property of electrons, i.e. having a very strong interaction with the surface together with the spin degree of freedom enables one to investigate the spin dependent quasi-particles, e.g. magnons at magnetic surfaces.We review the experimental results of short-wavelength magnons probed at ferromagnetic Co(0001) and Fe(110) surfaces by spin-polarized electron energy-loss spectroscopy. The differences and similarities to their bulk counterpart are discussed in detail. Although in the case of Co(0001) surface magnons behave similar to the ones in bulk Co, in the case of Fe(110) they possess a smaller exchange stiffness meaning that the effective exchange coupling is smaller at the surface. In both cases, surface magnons have an extremely short lifetime being in the order of a few tens of femtosecond.

Suppression of Standing Spin Waves in Low-Dimensional Ferromagnets

We examine the experimental absence of standing spin wave modes in thin magnetic films, by means of atomistic spin dynamics simulations. Using Co on Cu(001) as a model system, we demonstrate that by increasing the number of layers, the optical branches predicted from adiabatic first-principles calculations are strongly suppressed, in agreement with spin-polarized electron energy loss spectroscopy measurements reported in the literature. Our results suggest that a dynamical analysis of the Heisenberg model is sufficient in order to capture the strong damping of the standing modes.

Magnon excitations in ultrathin Fe layers: The influence of the Dzyaloshinskii-Moriya interaction

High wave-vector magnon excitations in ferromagnetic Fe monolayer and double-layer grown on W(110) are investigated using spin-polarized electron energy loss spectroscopy. The magnon dispersion relation is obtained up to the Brillouin zone boundary. A direct comparison among different systems shows that the magnons in the Fe monolayer are extremely soft and are even softer than the acoustic surface mode of Fe(110).By measuring the spectra in both energy loss and gain regions on a double-layer Fe film at room temperature and by reversing the sample magnetization, it is demonstrated that the magnon dispersion is asymmetric with respect to the sign of the wave-vector. The asymmetric dispersion relation is attributed to the degeneracy breaking of the magnons due to the presence of the Dzyaloshinskii-Moriya interaction.

Elementary Excitations at Magnetic Surfaces and Their Spin Dependence

The elementary surface excitations are studied by spin-polarized electron energy loss spectroscopy on a prototype oxide surface [an oxygen passivated Fe(001)-p(1×1) surface], where the various excitations coexist. For the first time, the surface phonons and magnons are measured simultaneously and are distinguished based on their different spin nature. The dispersion relation of all excitations is probed over the entire Brillouin zone. The different phonon modes observed in our experiment are described by means of ab initio calculations.

Magnons in a Ferromagnetic Monolayer

We report the first observation of high wave vector magnon excitations in a ferromagnetic monolayer. Using spin-polarized electron energy loss spectroscopy, we observed the magnon dispersion in one atomic layer (ML) of Fe on W(110) at 120 K. The magnon energies are small in comparison to the bulk and surface Fe(110) excitations. We find an exchange parameter and magnetic anisotropy similar to that from static measurements. Our results are in sharp contrast to theoretical calculations, indicating that the present understanding of magnetism of the ML Fe requires considerable revision.

Large Wave Vector Spin Waves and Dispersion in Two Monolayer Fe onW(110)

We present the first surface spin-wave (SW) dispersion measurements up to the surface Brillouin zone boundary of a two monolayer Fe film on W(110) by using spin-polarized electron energy loss spectroscopy. Pronounced features of SW peaks are observed in the spectra at room temperature. We found that the SW energies in the Fe film are strongly reduced compared to spin waves in bulk Fe and to theoretical predictions. Our results suggest that this reduction is caused by the reduction of exchange interaction within the 2 ML Fe on W(110) as compared to bulk Fe.

Spin dependent electron transmission through ferromagnetic thin films

Spin-polarized electron spectroscopies are used to probe the nature of magnetism in surfaces and thin films. Strong inelastic scattering of the electron from particle-hole and collective excitations results in short mean free paths that can be spin dependent. A quantitative understanding of the spin dependence of the inelastic mean free path is critical to the interpretation of results from spin-polarized electron spectroscopies such as spin-polarized low energy electron diffraction, spin-polarized electron energy loss spectroscopy, and spin-polarized photoemission. Substantial spin asymmetry of the photocurrent has been observed and interpreted as being due to the spin-dependence of the photoelectron inelastic mean free path. We have examined such spin dependent behavior of electrons transmitted though magnetic films with higher kinetic energy in order to reduce complications due to spin-flip scattering, which are more prevalent at lower kinetic energy. We present clear evidence of a spin filter effect for the Ag 3d photoelectrons through a ferromagnetic Fe film at 720 eV (kinetic energy).

High-wave-vector spin waves in ultrathin Co films on W(110)

We present an experimental study of high-wave-vector spin waves in 8 monolayer (ML) thick hexagonal closed-packed (hcp) Co films performed by spin-polarized electron energy loss spectroscopy (SPEELS). Using inelastic electron scattering, we were able to follow the spin wave dispersion up to the surface Brillouin zone boundary $(\overline{K})$, i.e., up to a wave-vector transfer of $1.64\phantom{\rule{0.3em}{0ex}}{\mathrm{\AA{}}}^{\ensuremath{-}1}$. The spin wave dispersion was found to agree surprisingly well with the dispersion relation of a surface spin wave calculated by a nearest-neighbor Heisenberg model. From this description, we obtain a value for the product of the exchange coupling constant $(J)$ and the magnetic moment $(S)$ of $JS=14.8\ifmmode\pm\else\textpm\fi{}1\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$. This value, within the error bar, is identical to our results obtained on thin fcc Co films on Cu(001). We also find that the spin wave features measured by SPEELS at high-wave-vectors are strongly broadened. This is in agreement with expectations from nonadiabatic theoretical descriptions in which the broadening is ascribed to a strong damping of these high-wave-vectors spin waves by Stoner excitations. Similar to the observations in previously studied systems, we also observe a strong dependence of the measured spin wave intensities on the kinetic energy of the incident electrons $({E}_{\mathrm{kin}})$. Highest spin wave intensities were found for low kinetic energies $({E}_{\mathrm{kin}}<10\phantom{\rule{0.3em}{0ex}}\mathrm{eV})$.

Spin-wave excitation observed by spin-polarized electron energy loss spectroscopy: a new method for the investigation of surface- and thin-film spin waves on the atomic scale

Spin-polarized electron energy loss spectroscopy (SPEELS) is a unique tool to determine the spin-wave dispersion of ultrathin films and surfaces over the whole Brillouin zone. Ultrathin Co films on Cu(001) show well-defined spin-wave loss peaks in the SPEEL spectra. For 3 ML Fe films on 1 ML Co/Cu(001) the spin-wave peaks are much broader compared to the Co case but show dispersion. In 5-ML-thick bcc Fe films on W(110), a very broad feature assigned to spin-wave excitation was observed as well, which, however, does not show significant dispersion in the investigated range of large wavevectors.

Spin-wave excitation in ultrathin Co and Fe films on Cu(001) by spin-polarized electron energy loss spectroscopy (invited)

We demonstrate, that spin-polarized electron energy loss spectroscopy is a unique tool to determine spin-wave dispersion curves of ultrathin films and surfaces over the whole Brillouin zone. For ultrathin Co films on Cu(001) the excitation of a spin wave appears as a well defined peak in the loss spectrum. 3 ML Fe films on 1 ML Co/Cu(001) films show spin-wave excitation peaks as well though much broader compared to the Co case. The spin-wave energy at the surface zone boundary of about 140 meV for the Fe film is nearly a factor of 2 smaller than that of the Co films.