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ARPES Provides Direct Evidence of Spin-Wave Coupling Print

The electronic properties of a metal are determined by the dynamical behavior of its conduction electrons. Conventional band theory accounts for the interaction of the electrons with the static ion lattice. However, coupling to further microscopic degrees of freedom can alter the electron dynamics considerably. For example, "conventional" superconductivity emerges as a result of the electrons' interaction with lattice vibrations (phonons). In magnetic materials, coupling with spin waves (magnons) is also expected. Such interactions may contribute to high-temperature superconductivity in novel materials. Unfortunately, lattice vibrations and spin waves have similar energy scales, hindering detailed study. Researchers have taken a new approach in analyzing the electron bands of ferromagnetic iron. Angle-resolved photoemission spectroscopy (ARPES) provides direct spectroscopic evidence of altered electron mass and energy (quasiparticle formation) in a magnetic solid due to coupling with spin waves.

All Dressed Up…

A crystal lattice at the atomic level is far from a static structure frozen in space: atoms and ions vibrate, and electron spins rotate and flip. Such lattice "excitations" can occur randomly, manifesting on the macroscopic scale as heat. They can also occur in coordinated waves, with the excitations rippling through the lattice like spectators doing "The Wave" at a sporting event. In quantum physics, waves are often quantized as particles. Thus, in the quantum world inside a crystal, vibrational waves can be treated as particles known as phonons, and spin waves (where it's the electron spins that are doing the waving) can be treated as particles dubbed "magnons." If the crystal happens to be a conductor, then mobile conduction electrons are added to the mix, and they can become "dressed" by a cloud of lattice perturbations. An electron coupled with its associated magnon forms a quasiparticle of increased effective mass and reduced Fermi velocity. This type of coupling is thought to underlie unusual phenomena of great practical and theoretical interest such as high-temperature superconductivity.

Schematics of quasiparticle formation. Top: Electron–phonon coupling. Bottom: Electron–magnon coupling.

When conduction electrons interact with excitations in a solid, the electrons become "dressed" by the excitations, forming quasiparticles of increased effective mass. This is reflected in the electron band by a reduction in the slope of the energy–momentum relationship, the slope being inversely proportional to the electron mass. Beyond a characteristic energy scale ω0, determined by the excitation spectrum, the electrons lose their dressing. Spin-wave energies in iron are exceptionally high, making it a good candidate for such studies.

The formation of electronic quasiparticles is best studied by ARPES on sharp surface states. The (110) surface of ferromagnetic iron provides such states with the required metallic character. They overlap in energy with bulk bands of opposite spin, thereby enabling spin-flip scattering processes between them. Samples of high purity were generated by evaporating thick iron films onto a tungsten substrate. ARPES was performed at the Electronic Structure Factory endstation of ALS Beamline 7.0.1.

ARPES data from the iron (110) surface state. Left: Raw data, showing the intense quasiparticle region. Right: Electron band dispersion (E vs. k|| ) extracted from the data reveals a weak "kink" in the region between 0.1 and 0.2 eV below EF.

Band-map data provide the basis of the electron energy analysis. In the raw data of the surface state, the dressed quasiparticle shows up with high intensity, extending beyond 0.1 eV below the Fermi energy, EF. A graph of the dispersion (E vs. k||) of the surface state exhibits a weak "kink" in the region between 0.1 and 0.2 eV below EF. An accurate determination of the peak position and width was obtained from a fit of the momentum spectra. A band corresponding to the noninteracting case (no spin-wave coupling) was obtained by parabolic interpolation between the lowest data points and the Fermi-level crossing, making the kink-like deviation more apparent. This "kink" reflects the interaction experienced by the electrons.

The width of the momentum spectra, also referred to as the imaginary part of the self-energy, ImΣ(ω), reflects scattering processes that become increasingly dominant with increasing (more negative) binding energy. A pronounced increase in the scattering with binding energy saturates at about 160 meV.

Energy range of the interaction experienced by the electrons, as reflected by a broadening of the photoemission spectra for two different surface states, S1 and S2. The observed 160-meV interaction range corresponds well to that of spin waves.

The large energy scale of about 160 meV rules out electron–lattice coupling effects, and we are left to consider magnetic excitations. Spin waves (magnons) in ferromagnetic iron are known from inelastic neutron scattering. Both experiment and theory find that, between approximately 100 and 200 meV, there are two magnon branches, one "acoustic" and one "optical," separated by a gap in which sharply defined spin waves do not exist. Assuming that the electrons couple predominantly to the lower, acoustic, branch provides a natural explanation of the observed effect. Independent evidence comes from spin-polarized electron-energy-loss spectroscopy on the iron (110) surface. A loss structure at 170–200 meV is interpreted as the result of exchange scattering by spin waves from spin-down surface states into spin-up bulk states, in very good agreement with the ARPES data. The observations confirm fundamentally that mass enhancement seen by ARPES can result from coupling to magnetic excitations, an important prerequisite for models of high-temperature superconductivity.

Research conducted by J. Schäfer, D. Schrupp, and R. Claessen (Universität Augsburg); E. Rotenberg, K. Rossnagel, and H. Koh (ALS); and P. Blaha (Vienna University of Technology).

Research funding: Deutsche Forschungsgemeinschaft (German Research Foundation) and the Bavaria California Technology Center. Operation of the ALS is supported by the U.S. Department of Energy, Office of Basic Energy Sciences.

Publication about this research: J. Schäfer, D. Schrupp, E. Rotenberg, K. Rossnagel, H. Koh, P. Blaha, and R. Claessen, "Electronic quasiparticle renormalization on the spin wave energy scale," Phys. Rev. Lett. 92, 097205 (2004).