Imaging small-amplitude magnetization dynamics in a longitudinally magnetized microwire

Abstract

We have used time-resolved scanning Kerr microscopy to study spin waves in a magnetic microwire subjected to a bias magnetic field applied parallel to its long axis. The spin-wave spectra obtained from different points near one end of the wire reveal several normal modes. We found that modes of a higher frequency occupied regions located further from the end of the wire. This was interpreted in terms of the confinement of the spin-wave modes by a nonuniform demagnetizing field. Furthermore, at a particular distance from the end of the wire, two or more modes occupying different regions along the width of the wire were observed. This was interpreted in terms of the confinement of the spin-wave modes due to an asymmetric variation in the local angle between the static magnetization and the effective direction of the wave vector of the confined modes. Images of the dynamic magnetization that are acquired at fixed pump-probe time delays revealed stripes lying perpendicular to the long axis of the wire and, hence, to the applied magnetic field. We interpret the stripe pattern in terms of a collective mode of the quasiperiodic system of ripple domains existing within the polycrystalline sample. Our results give an additional insight into the connection between the nonuniform static magnetic state in small magnetic elements and their precessional dynamics, which is fundamentally important for the design of future high-speed switching and spin-wave logic devices of magnonics. The inherent nonuniformity of magnetization configurations in nonellipsoidal magnetic elements makes them the perfect objects for the investigation of wave phenomena in nonuniform media. The elementary excitations of magnetic media ͑so-called spin waves͒ have a strongly nonlinear dispersion, which is complicated by long-range magnetodipole interaction. In most magnetic elements of finite size, the latter remarkably makes the internal magnetic field nonuniform even when the magnetization configuration is almost uniform. The nonuniform internal field may lead to the spatial confinement of spin-wave modes 1,2 while the dephasing of the modes leads to a nonuniform magnetic response to a uniform pulsed magnetic field. [3][4][5][6][7] Apart from the fundamental interest, the studies of the magnetization dynamics in small magnetic elements are driven by the fast growing market of high-speed magnetic data storage devices. In particular, chips incorporating magnetic random access memory are now becoming available. 8 Time-resolved scanning Kerr microscopy ͑TRSKM͒ 3 has become one of the most widely used tools for imaging the spatial character of the magnetization dynamics within micrometer-sized magnetic disks, 3,6 stripes, 2,9 rectangles, 3,10 and squares. 4,5,7,11,12 Magnetization dynamics in micrometersized magnetic tunnel junctions were imaged in Ref. 13. Although the spatial character of the magnetization dynamics in nanometer-sized elements cannot be directly studied by TRSKM, the lack of a spatial resolution can be circumvented by combining the measur...

Magnonic Metamaterials

“…Each of the resonances is expected to contribute to the susceptibility tensor of the magnetic constituents and correspondingly to the permeability tensor of the whole metamaterial. The resonance frequencies can be controlled and reconfigured by the external magnetic [119][120][121] and electric 122,123 fields, and the same functionalities should therefore be inherited by the magnonic metamaterials.…”

“…In the case of the effective permeability of magnetic composites and metamaterials, the majority of analytical models employ the so-called macrospin approximation, in which each magnetic inclusion within a non-magnetic matrix is considered as a single giant spin and is therefore characterized by a single magnetic resonance. However, it is well known that the spin wave spectrum of magnetic nanostructures and nano-elements has a complex structure, featuring series of resonances due to spatially non-uniform spin wave modes [54][55][56]61,64,[67][68][69]71,[92][93][94][95][96][97][98][99]115,119 . Each of the resonances is expected to contribute to the susceptibility tensor of the magnetic constituents and correspondingly to the permeability tensor of the whole metamaterial.…”

Excitation of propagating spin waves with global uniform microwave fields

“…The other ends of the stripes are beyond the present study. 11 The interstripe spacing is large enough to neglect any interaction between them. Figure 1͑c͒ displays the part of the reflectivity image defining the boundary of the Kerr images shown later.…”

Spin wave non-reciprocity and beating in permalloy by the time-resolved magneto-optical Kerr effect

“…In this paper, we study the propagation of spin waves in thin permalloy (Ni 78 Fe 22 ) films by TRSKM, and report the presence of a low frequency beat-like interference pattern at the center of the stripe due to two distinct spin wave frequencies. We provide a simple mathematical model to explain our observations, and show good correlation between experimental and simulated data.…”

“…The finite size effect due to the lateral confinement of spin waves results in interference between spin wave modes revealing a spatial dependency of the spin wave intensity [14,16]. Time-resolved scanning Kerr microscopy (TRSKM) has a significantly higher temporal resolution (~20 ps) than BLS measurements, and this advantage has been used to explore the temporal characteristics of spin wave propagation [22][23][24][25][26]. Spin waves have been detected at distances up to 80 m away from a coplanar strip (CPS) line [23] in thin permalloy films using coplanar waveguides antennas.…”