Stoner Excitations Research Articles

Probing surface magnetism by spin-polarized electron spectroscopy: Fe film on W(110)

The intensity asymmetry of the secondary emission spectra of thin iron films on W(110) excited by spin-polarized electrons was measured at various geometrical arrangements and various primary energies. The magnitude and shape of the Stoner excitation asymmetry provide information on the magnetic state of the film. The geometrical structure of the film influences its magnetism and this is reflected in the asymmetry of the spin polarized electron energy loss spectra (SPEELS). Oxygen adsorption reduces the asymmetry of Stoner excitations, but not as dramatically as in studies of Ni surface. The kinematics of the scattering process influences the asymmetry of the spectra and should be taken into account while using SPEELS for studying surface magnetism. Theoretical analysis of asymmetry spectra measured at various scattering conditions is required.

Chirality-dependent magnon lifetime in a compensated half-metallic ferrimagnet

We report a first-principles investigation of magnetic excitations in a compensated half-metallic ferrimagnet using both the adiabatic Heisenberg model and the dynamic spin susceptibility of the electronic system. The combination of half-metallicity and spin compensation of inequivalent magnetic sublattices generates two acoustic magnon modes characterized by linear dispersions with equal spin wave velocities and an asymmetric Landau damping. The difference in the damping is the consequence of the half-metallicity leading to the gap in the energy of the up-to-down electronic spin-flip excitations, whereas down-to-up excitations are gapless. The engineering of the activation energy of the Stoner excitations opens an avenue for the chirality-selective manipulation of the lifetime of magnons.

Possible occurrence of transition from a Fermi- to a non-Fermi-liquid behavior in epitaxial SrRuO3 thin films

The magnetic and magnetotransport properties of SrRuO3 epitaxial thin films grown on (001)-oriented SrTiO3 substrates by dc magnetron sputtering were studied in detail. The analysis of the electric transport data suggests a crossover from Fermi-liquid to non-Fermi-liquid behavior at ∼50K. Apart from this, a low-temperature upturn in the resistivity of the film is observed which is possibly associated with disorder-induced localization effects. Interestingly, the ρ(T) in the paramagnetic state follows a T1/2 dependence. This behavior is similar to that observed in bulk SRO single-crystals. Most strikingly, the temperature-dependent magnetoresistance exhibits two distinct dips (one around ferromagnetic ordering temperature and the other around 40K), resembling a double-well potential in appearance. Concerning the magnetic behavior of the films, it is found that the low-temperature magnetization diminishes with increasing temperature due, probably, to thermally excited magnons as well as Stoner excitations. In turn, the magnetization near TC follows the scaling law, M∞(TC−T)α, with α≈0.39. The magnitude of α seems to be consistent with three-dimensional (3D) Ising-type ferromagnetic behavior.

Theoretical Study on Gilbert Damping of Nonuniform Magnetization Precession in Ferromagnetic Metals

We study Gilbert damping in bulk metallic ferromagnets containing magnetic and nonmagnetic impurities in the presence of nonuniform magnetization precession. In this model, a microscopic expression for the Gilbert damping tensor is obtained using the linear response theory with respect to the interaction between magnetization and conduction electrons. We especially focus on a diagonal element of the tensor, which is a conventional Gilbert damping constant, and evaluate it numerically as a function of the wave vector q of magnetization precession. We show that the impurity scattering dominates Gilbert damping for 0<| q |< k F↑ - k F↓ , while the Stoner excitation dominates for k F↑ - k F↓ <| q |< k F↑ + k F↓ ( k Fσ is the Fermi wave number for σ spin electrons).

Theoretical study of the temperature dependence of the magnon dispersion relation in transition-metal wires and monolayers

The effects of temperature-induced electronic Stoner excitations on the spin-wave spectrum of one- and two-dimensional 3$d$ transition metals are investigated in the framework of ab initio density-functional theory by using a generalized-gradient approximation to the exchange and correlation energy. The dispersion relation of frozen-magnon spiral states is calculated as a function of spin-wave vector $\stackrel{P\vec}{q}$ and electronic temperature ${T}_{\mathrm{e}}$ for Fe, V, Co, and Ni monoatomic chains and for periodic Ni square lattices. The resulting temperature dependence of the magnetic order and its stability are analyzed in some detail. A variety of element-specific behaviors are identified including ferromagnetic, antiferromagnetic, and spiral orders. In all considered cases, the local magnetic moments are found to be remarkably stable both as a function of $\stackrel{P\vec}{q}$ and ${T}_{\mathrm{e}}$. Effective exchange interactions ${J}_{ij}$ between these moments are derived in the framework of a classical Heisenberg model by fitting the ab initio electronic free energy $\ensuremath{\Omega}$ as a function of $\stackrel{P\vec}{q}$. The changes in the magnetic order as a function of ${T}_{\mathrm{e}}$ are interpreted as the result of the interplay between competing ${J}_{ij}$ among different nearest neighbors. Finally, the electronic internal-energy and entropy contributions to the magnon dispersion relation $\ensuremath{\Omega}(\stackrel{P\vec}{q})$ are discussed.

Lifetimes and chirality of spin waves in antiferromagnetic and ferromagnetic FeRh from the perspective of time-dependent density functional theory

The study of the spin excitations in antiferromagnetic (AFM) and ferromagnetic (FM) phases of FeRh is reported. We demonstrate that although the Fe atomic moments are well defined there is a number of important phenomena absent in the Heisenberg description: Landau damping of spin waves, large Rh moments induced by the AFM magnons, the formation of the optical magnons terminated by Stoner excitations. We relate the properties of the spin-wave damping to the features of the Stoner continuum and compare the chirality of the spin excitations in AFM, FM and paramagnetic (PM) systems.

A Monte Carlo study of the spin polarization of secondary electrons

A spin‐involved Monte Carlo simulation model is developed to study the mechanism of the spin polarization of secondary electrons. The spin‐dependent mean free path asymmetry and the Stoner excitation are considered in modeling electron inelastic scattering, and the spin‐dependent excitation mechanism of cascade electrons is introduced according to the spin density of the state of a magnetism sample. The simulation has been performed for Ni and Fe. The simulated results, including secondary electron yields, secondary electron energy spectrum, and spin polarization of secondary electrons, are in good agreement with experimental results. According to the present simulation results, it is concluded that the high spin polarization of secondary electrons less than approximately 5 eV is inherently related to the cascade production process of secondary electrons; a more obvious effect of Stoner excitation is found for Ni but not for Fe because of the lack of unoccupied 3d states for spin‐majority electrons above the Fermi level for Ni. We have further studied the case that an unpolarized thin layer exists on Fe surface; the results show that the spin polarization of secondary electrons can be greatly affected at low primary energies. Copyright © 2012 John Wiley &amp; Sons, Ltd.

Different dimensionality trends in the Landau damping of magnons in iron, cobalt, and nickel: Time-dependent density functional study

We study the Landau damping of ferromagnetic magnons in Fe, Co, and Ni as the dimensionality of the system is reduced from three to two. We resort to the \textit{ab initio} linear response time dependent density functional theory in the adiabatic local spin density approximation. The numerical scheme is based on the Korringa-Kohn-Rostoker Green's function method. The key points of the theoretical approach and the implementation are discussed. We investigate the transition metals in three different forms: bulk phases, free-standing thin films and thin films supported on a nonmagnetic substrate. We demonstrate that the dimensionality trends in Fe and Ni are opposite: in Fe the transition from bulk bcc crystal to Fe/Cu(100) film reduces the damping whereas in Ni/Cu(100) film the attenuation increases compared to bulk fcc Ni. In Co, the strength of the damping depends relatively weakly on the sample dimensionality. We explain the difference in the trends on the basis of the underlying electronic structure. The influence of the substrate on the spin-wave damping is analyzed by employing Landau maps representing wave-vector resolved spectral density of the Stoner excitations.

Inelastic neutron and x-ray scattering from incommensurate magnetic systems

Neutrons and x-rays are powerful probes for studying magnetic and lattice excitations instrongly correlated materials over very wide ranges of momentum and energy transfers. Inthe focus of the present work are the incommensurate magnetic systems MnSi and Cr.Under application of a magnetic field, helically ordered MnSi transforms intoa weak itinerant ferromagnet. Using polarized neutrons we demonstrate thatthe Stoner excitations are spin-flip excitations. The amplitude (longitudinal)fluctuations associated with the magnon modes are already strong far away fromTc. Interestingly, even the non-spin-flip excitations associated with the Stoner modes areobservable. In Cr, we have observed Kohn anomalies in the phonon spectrum at thoseincommensurate positions in reciprocal space, where the spin density wave is observed. Thecorresponding phonon and magnon modes are not coupled. In addition, an anomaloussoftening of a transverse phonon branch along the N–H zone boundary line is observed thatis caused by strong electron–phonon coupling. High resolution neutron scattering indicatesthat the low energy Fincher–Burke excitations may rather correspond to localized modes inmomentum and energy and not to propagating collective modes. Finally, we demonstratethat in the near future it may become feasible to investigate excitations in verysmall samples, thus allowing us to measure the dynamics of strongly correlatedmaterials under extreme conditions and in the vicinity of quantum phase transitions.

Wannier-function approach to spin excitations in solids

We present a computational scheme to study spin excitations in magnetic materials from first principles. The central quantity is the transverse spin susceptibility, from which the complete excitation spectrum, including single-particle spin-flip Stoner excitations and collective spin-wave modes, can be obtained. The susceptibility is derived from many-body perturbation theory and includes dynamic correlation through a summation over ladder diagrams that describe the coupling of electrons and holes with opposite spins. In contrast to earlier studies, we do not use a model potential with adjustable parameters for the electron-hole interaction but employ the random-phase approximation. To reduce the numerical cost for the calculation of the four-point scattering matrix we perform a projection onto maximally localized Wannier functions, which allows us to truncate the matrix efficiently by exploiting the short spatial range of electronic correlation in the partially filled d or f orbitals. Our implementation is based on the FLAPW method. Starting from a ground-state calculation within the LSDA, we first analyze the matrix elements of the screened Coulomb potential in the Wannier basis for the 3d transition-metal series. In particular, we discuss the differences between a constrained nonmagnetic and a proper spin-polarized treatment for the ferromagnets Fe, Co, and Ni. The spectrum of single-particle and collective spin excitations in fcc Ni is then studied in detail. The calculated spin-wave dispersion is in good overall agreement with experimental data and contains both an acoustic and an optical branch for intermediate wave vectors along the [100] direction. In addition, we find evidence for a similar double-peak structure in the spectral function along the [111] direction.

Nonextensive quantum method for itinerant-electron ferromagnetism: Factorization approach

Magnetic and thermodynamical properties of itinerant-electron (metallic) ferromagnets described by the Hubbard model have been discussed with the use of the generalized Fermi–Dirac (GFD) distribution for nonextensive quantum systems. We have derived the GFD distribution within the superstatistics, which is equivalent to that obtained by the maximum-entropy method to the Tsallis entropy with the factorization approximation. By using the Hartree–Fock approximation to the electron–electron interaction in the Hubbard model, we have calculated magnetic moment, energy, specific heat and Curie–Weiss-type spin susceptibility, as functions of the temperature and entropic index q expressing the degree of the nonextensivity: q = 1.0 corresponds to the Boltzmann–Gibbs statistics. It has been shown that by increasing the nonextensivity of | q − 1 | , the temperature dependence of magnetic moment becomes more significant and the low-temperature electronic specific heat is very much increased. This is attributed to enlarged Stoner excitations in the GFD distribution, which is elucidated by an analysis with the use of the generalized Sommerfeld expansion. We discuss the difference and similarity between the effects of the nonextensivity on metallic and insulating ferromagnets.

Magnetic moment of iron atoms in Fe-Al body-centered cubic alloys as a function of the nearest environment

The Fe-Al systems in the concentration range from 29 to 44 at. % Al are investigated in terms of the density functional theory. It is shown that, in the system under consideration, there can exist three magnetic states with close energies. Two of these three magnetic states have collinear magnetic moments (the ferromagnetic and antiferromagnetic states), and the third is a spin-spiral state. In collinear magnetic structures, the local magnetic moments are determined by the nearest chemical environment and, in the antiferromagnetic state, the iron atoms surrounded by a large number of aluminum atoms in their environment have a negative magnetic moment. The results obtained substantiate the applicability of modified models of the Jaccarino-Walker type for the interpretation of the experimental data obtained for Fe-Al alloys. The results of the calculations also indicate a significant role of Stoner excitations in the formation of magnetic order in these alloys.

Spin-charge coupling in a band ferromagnet: Magnon-energy reduction, anomalous softening, and damping

The effects of correlation-induced coupling between spin and charge fluctuations on spin-wave excitations in a band ferromagnet are investigated by including self-energy and vertex corrections within a systematic inverse-degeneracy expansion scheme which explicitly preserves the Goldstone mode. Arising from the scattering of a magnon into intermediate spin-excitation states (including both magnon and Stoner excitations) accompanied with charge fluctuations in the majority-spin band, this spin-charge coupling results not only in a substantial reduction of magnon energies but also in anomalous softening and significant magnon damping for zone-boundary modes lying within the Stoner gap. Our results are in good qualitative agreement with recent spin-wave excitation measurements in colossal magnetoresistive manganites and ferromagnetic ultrathin films of transition metals.

Electron spectrometers for inelastic scattering from magnetic surface excitations

AbstractThis paper compares the performance of two different designs for electron spectrometers to be used for inelastic scattering of spin‐polarized electrons from surface magnons and Stoner excitations. The recently proposed combination of monochromators with 90° and 180° deflection angles ensures a maximum spin asymmetry signal while providing still a good quality of the monochromatic beam. Higher intensities, however, are obtained with the classical 146° /146° combination, which features a spin polarization longitudinal to the beam direction at the target. We present calculations for the monochromatic current for both combinations and argue that the use of the classical spectrometer type may be advantageous. Copyright © 2006 John Wiley &amp; Sons, Ltd.

Lifetimes and inelastic mean free path of low-energy excited electrons in Fe, Ni, Pt, and Au:Ab initioGW+Tcalculations

We present the results of the $\mathrm{GW}+\mathrm{T}$ ab initio calculations for the inelastic lifetimes and mean free path (IMFP) of low-energy excited electrons in Fe, Ni, Pt, and Au. For Fe and Ni we show that the $T$-matrix terms, incorporating the Stoner's excitations and spin-wave emission, contribute to the IMFP of the spin-minority electrons with excitation energy below $1.2\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$, whereas the GW term dominates at higher energy. We find that the spin dependence of IMFP in Ni is governed mainly by the spin dependence of lifetimes, but in Fe it relates mainly to the spin dependence of group velocities. We show that the ``random $k$'' model of the electron decay with fixed matrix element well agrees with the GW term of the lifetimes thus showing that the energy and spin dependence of the lifetimes are determined mainly by the convolutions of densities of states. For Au the inclusion of $T$-matrix terms with electron-hole scattering greatly reduces the calculated IMFP, bringing them into better agreement with experimental data.

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 $({E}_{\mathrm{kin}}&lt;10\phantom{\rule{0.3em}{0ex}}\mathrm{eV})$.

Monte Carlo study of the spin polarization enhancement in the low‐energy secondary electron emission from ferromagnetic materials

AbstractThe spin polarization enhancement of secondary electrons emitted from ferromagnetic materials at low kinetic energies is studied by a Monte Carlo simulation of electron scattering that considers the spin direction of generated secondary electrons. A modified model of electron scattering in the magnetic materials is proposed that introduces electron–hole pair excitation processes with opposite spin (Stoner excitations). The two major characteristics—the primary energy dependence and the spectrum of secondary electron spin polarization—are studied with both the previous and the modified simulation models. A better agreement with experimental measurements is obtained in both characteristics with the modified model. The enhancement of the secondary spin polarization at low energies is reproduced by the introduction of Stoner excitation processes into the simulation. Copyright © 2003 John Wiley &amp; Sons, Ltd.

The role of scattering angle in spin-polarised electron energy loss spectroscopy

We study the dependence on scattering angle of the Stoner excitation spectrum of model itinerant-electron ferromagnets in spin-polarised electron energy loss spectroscopy (SPEELS) experiments. It is found that, changing the scattering angle, essentially changes the weight of the contributions to the spectrum of the various possible interband excitations. Thus, high resolution SPEELS measurements may be used to probe the predicted interband density of Stoner states and the underlying band structure of materials exhibiting itinerant magnetism.

Time-dependent functional Schrödinger picture approach to many-particle systems

A time-dependent many-body theory for many-particle systems is formulated using the functional Schr?dinger picture. Taking a Gaussian trial wave functional and using the variational principle, the equations of motion are obtained. The equations of motion are solved in the small oscillation regime to yield the generalized RPA results. The electron?hole excitation, the collective plasma oscillation for the paramagnetic state, the Stoner excitation and the spin wave for the ferromagnetic state are derived and discussed. As a further test on the versatility of the present method, the formalism is applied to the bound states of the exciton problem and shown to yield the governing equation in a straightforward manner.

Spin excitations in ferromagnetic Ni: Electrons and neutrons as a probe

We present theoretical calculations of the contribution to the spin polarized electron energy loss spectrum of ferromagnetic Ni. We find, save for the wave-vector transfer near the center of the Brillouin zone, the spin-wave loss feature is obscured by low-lying Stoner excitations, in contrast to Fe. Our calculations, and earlier work, show that in inelastic neutron-scattering studies of spin waves in Ni, the spin-wave loss peak dominates. The physical reason for this difference is discussed.