Spin Wave Dynamics and the Determination of Intrinsic Damping in Locally Excited Permalloy Thin Films

Abstract

Time-resolved scanning Kerr effect microscopy has been used to study magnetization dynamics in Permalloy thin films excited by transient magnetic pulses generated by a micrometer-scale transmission line structure. The results are consistent with magnetostatic spin wave theory and are supported by micromagnetic simulations. Magnetostatic volume and surface spin waves are measured for the same specimen using different bias field orientations and can be accurately calculated by k-space integrations over all excited plane wave components. A single damping constant of Gilbert form is sufficient to describe both scenarios. The nonuniform pulsed field plays a key role in the spin wave dynamics, with its Fourier transform serving as a weighting function for the participating modes. The intrinsic Gilbert damping parameter α is most conveniently measured when the spin waves are effectively stationary.PACS numbers: 75.30. Ds, 75.50.Bb, 75.70.Ak, 76.50.+g Interest has been growing for many years in the timedomain investigation of magnetization dynamics in response to a short magnetic pulse. An impulse excitation is broadband, but the dynamics of the magnetic system are also very sensitive to the parameters of the excitation pulse. Time-domain pulse shaping can eliminate ringing for a coherently-switched ferromagnetic element, to greatly enhance the performance for applications [1,2]. In addition, the spatial profile of the pulsed field is critical in dictating the magnetic dynamics. Magnetostatic spin waves generated by such nonuniform transient field have been observed in a number of time-resolved optical [3] and inductive [4,5] experiments, and also in frequencydomain studies [6]. The resulting position-dependent temporal response creates additional challenges for characterizing the dynamics and for determining the intrinsic magnetic damping. The focus of the present work is to address these difficulties within a simple physical framework.Under the condition of linear behavior of the spin wave dynamics in the low amplitude regime [4,5], the magnetic response is the linear superposition of all plane wave components that can be excited by the pulse. Assuming the spin waves propagate only along the x direction (the coordinate system is defined in Fig.1(a)), the out-of-plane component of magnetization can be described by: (1) where τ −1 is the inverse decay time, ω(k) is the dispersion relation, and P (k, ω(k)) is the spectral density of the pulse field determined from its spatial and temporal profiles and acts as a relative weighting factor for the different spin wave components in k-space. The influences of the pulse field parameters, the intrinsic damping, and the dispersion relation of the spin waves are contained explicitly. k c is a cut-off wave number for numerical integration (k c = 5 µm −1 is sufficient for the magnetostatic regime with the stripline dimensions used here). The initial phase angle φ is taken to be independent of frequency on account of the pulse excitation. The longer trailing edge of the pulse cau...

Observation of the propagation and interference of spin waves in ferromagnetic thin films

“…The measured group velocities v G = ‫ץ‬ ‫ץ‬k are highest for the DE geometry ͑up to 17 km/ s͒, while they are smaller for geometries in between the DE and MSBV geometry and close to zero for the MSBV geometry. These values are in the same range as the ones found by Liu and co-workers, 18 who found group velocities of 0.1 km/ s for the MSBV and 4.8 km/ s for a DE geometry ͑for a thinner film and at different bias fields͒.…”

“…17 Using time-resolved ͑TRMOKE͒ magneto-optical Kerr effect scanning microscopy the propagation of spin waves has recently been observed directly in thin Ni 80 Fe 20 films for two distinct geometries. 18 In this paper we report on the propagation of spin waves in 20-nm-thick continuous Ni 80 Fe 20 films. By means of TRMOKE microscopy, we detect the propagation of spin waves excited by continuous-wave ͑cw͒ or pulsedmicrowave fields up to 80 m away from a coplanar strip ͑CPS͒ line.…”

Magnonic Metamaterials

“…Spin waves exhibit most of the properties inherent to waves of other origins, including the excitation and propagation 21,22,23 , reflection and refraction 24,25,26,27,28,29 , interference and diffraction 30,31,32,33,34,35 , focusing and self-focusing 36,37,38,39,40,41 , tunnelling 42,43 , Doppler effect 44,45,46 , and formation of spin-wave envelope solitons 47,48,49,50 . Spin-wave quantization due to the finite size effect was discovered in thin films 51,52 and more recently in laterally confined magnetic structures 53,54,55,56,57,58 , with their effect upon the high frequency permeability and the observation of a negative permeability discussed in Refs.…”

Nonreciprocal emission of spin-wave packet in FeNi film

“…We performed a time-resolved propagating spin wave spectroscopy, [13][14][15][16] for the microfabricated device comprising Fe 19 Ni 81 ͑35 nm͒ / SiO 2 ͑35 nm͒ film with 120 m width ͓see Fig. 1͑a͔͒.…”

“…The signal of spin wave with −k can be detected by launching a voltage pulse into the right strip and connecting the oscilloscope to the left strip. The present study was performed by measuring a set of devices in which the gap distance g between the two ACPSs varies from 5 to 50 m. To improve the signal to noise ratio, we used a background subtraction procedure [13][14][15][16][17] and took the average of 1024 waveforms to produce a single spin wave signal. Figure 2͑a͒ represents the induced voltages in the detection strip antenna for the samples with different gap distances, signaling the spin-wave packets.…”