Nonlinear Decay of Quantum Confined Magnons in Itinerant Ferromagnets.

Quantum confinement leads to the emergence of several magnon modes in ultrathin layered magnetic structures. We probe the lifetime of these quantum confined modes in a model system composed of three atomic layers of Co grown on different surfaces. We demonstrate that the quantum confined magnons exhibit nonlinear decay rates, which strongly depend on the mode number, in sharp contrast to what is assumed in the classical dynamics. Combining the experimental results with those of linear-response density-functional calculations we provide a quantitative explanation for this nonlinear damping effect. The results provide new insights into the decay mechanism of spin excitations in ultrathin films and multilayers and pave the way for tuning the dynamical properties of such structures.

Experimental Realization of Atomic-Scale Magnonic Crystals.

We introduce a new approach of materials design for terahertz magnonics making use of quantum confinement of terahertz magnons in layered ferromagnets. We show that in atomically designed multilayers composed of alternating atomic layers of ferromagnetic metals one can efficiently excite different magnon modes associated with the quantum confinement in the third dimension, i.e., the direction perpendicular to the layers. We demonstrate experimentally that the magnonic band structure of these systems can be tuned by changing the material combination and the number of atomic layers. We realize the idea of opening band gaps, with a size of up to several tens of millielectronvolts, between different terahertz magnon bands and thereby report on the first step toward the realization of atomic-scale magnonic crystals.

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}.

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 3 ML 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.

Long-living terahertz magnons in ultrathin metallic ferromagnets.

The main idea behind magnonics is to use the elementary magnetic excitations (magnons) for information transfer and processing. One of the main challenges, hindering the application of ultrafast terahertz magnons in magnonics, has been the short lifetime of these excitations in metallic ferromagnets. Here, we demonstrate that the engineering of the electronic structure of a ferromagnetic metal, by reducing its dimensionality and changing its chemical composition, opens a possibility to strongly suppress the relaxation channels of terahertz magnons and thereby enhance the magnons' lifetime. For the first time, we report on the long-lived terahertz magnons excited in ultrathin metallic alloy films. On the basis of the first-principles calculations, we explain the microscopic nature of the long lifetime being a consequence of the peculiar electronic hybridizations of the species. We further demonstrate a way of tailoring magnon energies (frequencies) by varying the chemical composition of the film.

Direct probing of the exchange interaction at buried interfaces.

The fundamental interactions between magnetic moments at interfaces have an important impact on the properties of layered magnetic structures. Hence, a direct probing of these interactions is highly desirable for understanding a wide range of phenomena in low-dimensional solids. Here we propose a method for probing the magnetic exchange interaction at buried interfaces using spin-polarized electrons and taking advantage of the collective nature of elementary magnetic excitations (magnons). We demonstrate that, for the case of weak coupling at the interface, the low-energy magnon mode is mainly localized at the interface. Because this mode has the longest lifetime of the modes and has a finite spectral weight across the layers on top, it can be probed by electrons. A comparison of experimental data and first-principles calculations leads to the determination of the interface exchange parameters. This method may help the development of spectroscopy of buried magnetic interfaces.

Impact of atomic structure on the magnon dispersion relation: a comparison between Fe(111)/Au/W(110) and Fe(110)/W(110).

We present a combined experimental and theoretical study of the interplay between the atomic structure and the magnon excitations in low dimensional ferromagnets. Two monolayer thick Fe films on W(110) with and without a Au buffer layer are investigated. Our experiments show that adding the Au layer leads to a significant softening of the magnons. First-principles calculations confirm the experimental results revealing a strong dependency of exchange interactions on the atomic structure. It is observed that the intralayer exchange interactions increase with increasing distance between Fe layers. This unusual relationship is attributed to the complexity of the electronic structure and the contribution of different orbitals to the hybridization and exchange interaction. Our results suggest a way of tailoring magnetic excitations in low-dimensional magnetic structures.

Relaxation time of terahertz magnons excited at ferromagnetic surfaces.

The temporal and spatial properties of terahertz magnons excited at ferromagnetic fcc Co(100) and bcc Fe(110) surfaces are investigated experimentally. The magnon lifetime is found to be a few tens of femtoseconds at low wave vectors, which reduces significantly as the wave vector approaches the Brillouin zone boundary. Surprisingly, the lifetime is very similar in both systems, in spite of the fact that the excitation energy in the Co(100) film is by a factor of two larger than in the Fe(110) film. The magnon wave packets propagate only a few nanometers within their lifetime. In addition to the fact that our results describe the damping mechanism in ultrafast time scales, they may provide a way to predict the ultimate time scale of magnetic switching in nanostructures.

Magnon lifetimes on the Fe(110) surface: the role of spin-orbit coupling.

We provide direct experimental evidence which demonstrates that, in the presence of a large spin-orbit coupling, the lifetime, amplitude, group, and phase velocity of the magnons propagating along two opposite (but crystallographically equivalent) directions perpendicular to the magnetization are different. A real time and space representation reveals that magnons with the same energy (eigenfrequency) propagate differently along two opposite directions. Our findings can inspire ideas for designing new spintronic devices.

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.

Asymmetric spin-wave dispersion on Fe(110): direct evidence of the Dzyaloshinskii-Moriya interaction.

The influence of the Dzyaloshinskii-Moriya interaction on the spin-wave dispersion in an Fe double layer grown on W(110) is measured for the first time. It is demonstrated that the Dzyaloshinskii-Moriya interaction breaks the degeneracy of spin waves and leads to an asymmetric spin-wave dispersion relation. An extended Heisenberg spin Hamiltonian is employed to obtain the longitudinal component of the Dzyaloshinskii-Moriya vectors from the experimentally measured energy asymmetry.

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.

Pd atomic chain formation as a result of submonolayer deposition of 3d metals on Pd(110).

Submonolayer deposition of 3d transition metals such as Cr, Mn, Fe, Co, and Ni on Pd(110) at room temperature causes the formation of monoatomic chains of Pd as identified with scanning tunneling microscopy and spectroscopy. In agreement with recent theoretical predictions [Phys. Rev. B 79, 155410 (2009)], the substitution of Pd substrate atoms with the deposited atoms of 3d metals is found to be responsible for the formation of Pd atomic chains. This finding clarifies the long-debated issue about the chemical composition of the atomic chains grown on Pd(110) and points out the intriguing processes in the formation of self-assembled and self-organized nanostructures.