Ferromagnetic Resonance Analysis on Periodic Surface Defects: The Transition from Perturbed Thin Films to Magnonic Crystals

The magnetic relaxation in 1-dimensional periodic nanostructures (quasi magnonic crystals) is investigated by ferromagnetic resonance (FMR). In thin ferromagnetic films, the magnetization dynamics are governed by intrinsic effects like Gilbert damping and spin-pumping but also by extrinsic effects like two-magnon scattering (TMS). The latter is in demand for latest research and can be induced within magnetic thin films by defects and inhomogeneities. Thereby, acting as scattering centers, defects cause a dipolar field at the film surface crucial for the magnon-magnon interaction. By ion Irradiation of the material, a local variation of the magnetic properties can be achieved [1], where the TMS strength is set by the properties of the modification such as the reduction of the effective magnetic moment and the geometry (depth d , periodicity a 0 ). The investigated films consist of 30 nm thick permalloy (Ni80Fe20) deposited by molecular beam epitaxy at room temperature on Si/SiO2 substrate. All films are protected by a Cr Cap layer of 3 – 5 nm. On top of the structure, PMMA resist of 140 nm thickness was added and patterned by EBL, to create a symmetric array of stripe defects with a periodicity ranging from 100 – 400 nm optimal for the investigation of TMS. Subsequently, the mask was employed for ion beam patterning. Parameters for the Cr ion irradiation were selected according to Monte-Carlo simulations calculating the effects of the ion irradiation on the depth-dependent composition using SRIM [2] and TRIDYN [3]. The irradiation energies were defined in the range of 5 – 10 keV in which the fluence varies from 5·1015 1/cm2 to 8·1015 1/cm2. Due to the lowering of the Curie temperature underneath room temperature when Cr content in permalloy is extending 8 at.% [4], after irradiation, magnetically dead layers are generated. For lower Cr concentrations, the saturation magnetization of permalloy is reduced and hence, the dead layers are accompanied by a concentration gradient where MS increases gradually to the value of the saturation magnetization of permalloy. By varying the ion energy and fluence, this gradient and hence, the effective defect depth can be set. This allows the investigation of the transition from a surface perturbed thin film to a full magnonic crystal. The energies and fluences used to prepare the samples presented in this work are summarized in Table I. The spin wave dynamics and TMS are studied using FMR and Brillouin light scattering (BLS). The dispersion relation of backward volume modes in an unperturbed thin film is known to be quadratically dependent on the wave vector k due to exchange interaction. If an array of surface perturbations is assumed to exist on the surface of such a thin film, an additional dipolar field contribution to the magnons dispersion must be taken into account. This term is proportional to –k (for ultrathin films: k ·d << 1) and hence, causes a degeneration. Investigating such system by FMR, spin wave excitation is carried out uniformly. Thus, to scatter into the degenerate spin wave mode, the k -vector must match a multiple reciprocal lattice vector g 0 = 2/a 0 . If this is valid, TMS can be observed and mode repulsion takes place. We measured the FMR spectra f (H ) of different defect samples showing repulsion at each crossing point of higher spin wave modes with the uniform mode. Theoretical calculations based on a model using perturbation theory [5] are accompanied and reveal a good agreement of experiment and theory. Applying the external field parallel to the axis of the stripe’s edge, the f (H ) measurement of the FMR signal reveals one single FMR mode, referred to as the Kittel mode, equal to the one of unperturbed films. Since in this orientation magnetization aligns parallel to the stripe axis, there are no dipolar fields present to generate a coupling between several magnons. By a field rotation towards the axis perpendicular to the stripes, the TMS is switched on and multiple resonance modes can be observed with a culminating mode splitting at a field direction perpendicular to the stripe axis. The f (H ) mode spectra of Sample 1 (for details see Table I) for several in-plane field angles were measured to show the gradual development of TMS-induced mode splitting and are accompanied by theoretical calculations. The angular dependent measurement of the same sample for a fixed frequency of 15 GHz can be found in Fig. 1. To study the impact of the defect depth on the resonance mode positions, the resonance spectra f (H ) perpendicular to the stripe axis were analyzed for all samples shown in Table I. Again, the available theoretical model was used to explain the observed mode structures. For a precise determination of the dispersion relation of the magnons in such systems, BLS measurements have been performed showing a good Agreement to the theoretically predicted band structure.