Direct observation of two-dimensional self-focusing of spin waves in magnetic films

Bauer, M.; Mathieu, C.; Demokritov, S. O.; Hillebrands, B.; Kolodin, P.A.; Sure, S.; Dötsch, H.; Grimalsky, V.; Rapoport, Yuriy; Slavin, A. N.

doi:10.1103/physrevb.56.r8483

Cited by 47 publications

(52 citation statements)

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“…Thus, plane BVMSW modes fulfill the Lighthill criterion [10] for modulational instability in both in-plane directions (SN , 0 and DN , 0), and the effects of self-modulation (leading to the formation of temporal envelope solitons) and self-focusing (leading to the formation of stationary spatial solitons) are allowed for these waves. Both of these effects have been separately observed in YIG films earlier [11][12][13][14].…”

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Observation of Spatiotemporal Self-Focusing of Spin Waves in Magnetic Films

et al. 1998

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The first observation of spatiotemporal self-focusing of spin waves is reported. The experimental results are obtained for dipolar spin waves in yttrium-iron-garnet films by means of a newly developed space-and time-resolved Brillouin light scattering technique. They demonstrate self-focusing of a moving wave pulse in two spatial dimensions, and formation of localized two-dimensional wave packets, the collapse of which is stopped by dissipation. Nonlinear self-focusing of wave beams and pulses is an important phenomenon in physics because it provides a mechanism for localization of wave energy in a small spatial region [1]. In a simple model based on the nonlinear Schrödinger equation with two or three spatial dimensions, self-focusing for certain initial conditions leads to the collapse of the initial wave packet, when the packet amplitude becomes infinite in a finite time [2]. In real physical experiments singularity is, of course, avoided, and the process of collapse is stopped by saturation of nonlinearity and/or by dissipation. The effects of strong self-focusing and of wave collapse have been observed thus far for light waves in nonlinear optics [3], and for nonlinear Langmuir waves in a plasma [4]. The possibility of "light bullets," i.e., stable optical wave pulses strongly localized in space and time by self-focusing, which is stabilized by saturation of nonlinearity at high wave amplitudes, has been suggested by Silberberg [5]. There exists, however, no experimental evidence for this effect in optics, likely because, in optical fibers, diffraction is much stronger than dispersion, and, therefore, both effects cannot be observed simultaneously.In this Letter we report the first experimental observation of spatiotemporal self-focusing of dipolar spin waves and formation of strongly localized two-dimensional wave packets (spin wave bullets) propagating in yttrium-irongarnet (YIG) films. Here the diffraction to dispersion ratio is much smaller than in optical fibers, which makes it possible to observe a simultaneous self-focusing of a propagating spin wave packet along both in-plane directions. The "spin wave bullets" in our experiments are formed as a result of a spatiotemporal self-focusing, similar to the self-focusing effect described in Ref.[5], as our two-dimensional input spin wave packets are self-focused along both in-plane directions (y and z), while propagating along one of them (z). We note, however, that selffocusing of dipolar spin waves in YIG films is stabilized by dissipation, rather than by saturation of nonlinearity, as was suggested for light bullets in Ref. [5].It is well-known [6,7], that, in the absence of dissipation, two-dimensional self-focusing of an input wave packet leads to a packet collapse only if the packet amplitude is sufficiently large for nonlinearity to overcome the effects of diffraction and dispersion. Thus, the twodimensional collapse is critical; i.e., it has an amplitude threshold even in a dissipationless medium.In the presence of dissipation, the amplitude of a ...

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Observation of Spatiotemporal Self-Focusing of Spin Waves in Magnetic Films

et al. 1998

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“…We show results obtained for propagating spin waves in yttrium iron garnet (YIG) films in the nonlinear regime [7,8,9,10]. Phenomena like self focusing [7], formation of solitons in a quasi-one-dimensional waveguide and so-called spin wave bullets in infinite films [9] are presented. A crucial test to identify nonlinear objects are experiments, in which such objects collide in a head-on collision configuration [10].…”

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confidence: 99%

“…The method opens new fields of investigations. First, nonlinear excitations, like, e.g., microwave driven spin waves with large precession amplitudes in a magnetic film, can be monitored as they propagate through the film [7,8,9,10]. Pulses of surface phonons can be studied as well, although this is not subject of this manuscript.…”

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Space- and time-resolved Brillouin light scattering from nonlinear spin-wave packets

Büttner¹,

Bauer²,

Rueff³

et al. 2000

Ultrasonics

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We have constructed a new Brillouin light scattering apparatus, based on the Sandercock multipass tandem interferometer design, for space and time resolved investigations of nonlinear wave packets in thin films. We have applied the method to studies of nonlinear spin wave pulse propagation in yttrium iron garnet (YIG) films. Spatial resolution is achieved by scanning the laser spot across the YIG film surface, and temporal resolution is obtained by measuring the elapsed time between the launch of spin wave pulses by an applied microwave pulse and the arrival of the respective inelastically scattered photons at the detector. We report the observation of nonlinear self-focusing of wave beams and pulses in one and two dimensions, the formation of one-dimensional envelope solitons, and of strongly localized, two-dimensional wave packets, "spin wave bullets", analogous to "light bullets" predicted in nonlinear optics. By generating two counterpropagating wave pulses, pulse collision experiments were performed. We show that quasi-one-dimensional envelope solitons formed in narrow film stripes ("waveguides") retain their shapes after collision, while twodimensional spin wave packets formed in wide YIG films are destroyed in collision. IntroductionBrillouin light scattering (BLS) has developed to a very versatile tool to investigate thermally driven excitations, like phonons and spin waves, on surfaces and in films in the wavevector regime 0-10 5 cm -1 [1]. Light is inelastically scattered from these excitations, and by the determination of the frequency shift of the Doppler shifted light for a preset transferred wavevector, determined by the scattering geometry, the dispersion relation of the excitation is obtained.Of particular advantage of BLS are its high sensitivity, high spatial resolution determined by the diameter of the light focus on the sample surface (≈40 µm), high frequency resolution in the sub-GHz regime, high contrast and moderate costs of equipment. For surface and thin-film excitations, in particular in opaque materials, the tandem Fabry-Perot interferometer designed by Sandercock is now widely used as a fairly standard solution [2,3,4,5,6]. Here we report the extension of a tandem interferometer towards spatial and temporal resolution, enabling the investigation of the details of the propagation of travelling pulses of excitation. The method opens new fields of investigations. First, nonlinear excitations, like, e.g., microwave driven spin waves with large precession amplitudes in a magnetic film, can be monitored as they propagate through the film [7,8,9,10]. Pulses of surface phonons can be studied as well, although this is not subject of this manuscript. We are able to study the formation of spin waves in the vicinity of the exciting antenna, to determine the decay properties, reflection of spin waves at film boundaries, and the formation of waveguide patterns in laterally confined films. If the microwave field is large in amplitude, the excited spin waves are nonlinear, and nonlinear effects like,...

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“…The antenna is connected to a high speed switcher for the pulsed measurements which allows microwave pulses of a time duration T ≥ 10 ns. The switcher in turn is connected to a generator / network analyzer / amplifier unit, which provides a microwave input power of up to 1 W. Evidence of nonlinear self-focusing of dipolar spin wave beams was presented in our previous short paper [17], where spectrally narrow BVMSW beams in a narrow waveguide (width 2 mm) were studied. One of the results was the appearance of a snake-like structure in the data which is caused by the interaction of transverse waveguide modes [18].…”

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“…To exclude the effect of boundaries in the measurements of self-focusing presented here, a wide Lu 0.96 Bi 2.04 Fe 5 O 12 (BIG) sample (width 10 mm) was used. The sample was cut out of the same BIG disc from which the sample in [17] was made. In this experiment the static magnetic field was H = 2090 Oe, the carrier frequency was f 0 = 8450 MHz, and the resulting carrier wavevector was k 0z = 300 cm -1 .…”

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Spatial and spatiotemporal self-focusing of spin waves in garnet films observed by space- and time-resolved Brillouin light scattering

Büttner

Bauer

Demokritov

et al. 2000

Journal of Applied Physics

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A new advanced space-and time-resolved Brillouin light scattering technique is used to study diffraction of two-dimensional beams and pulses of dipolar spin waves excited by strip-line antennas in tangentially magnetized garnet films. The technique is an effective tool for investigations of two-dimensional spin wave propagation with high spatial and temporal resolution. Nonlinear effects such as stationary and nonstationary self-focusing are investigated in detail. It is shown, that nonlinear diffraction of a stationary backward volume magnetostatic wave (BVMSW) beam, having a finite transverse aperture, leads to selffocusing of the beam at one spatial point. Diffraction of a finite-duration (non-stationary) BVMSW pulse leads to space-time self-focusing and formation of a strongly localized two-dimensional wave packet (spin wave bullet).Magnetostatic spin waves in yttrium-iron garnet (YIG) films provide a superb testing ground to study linear and nonlinear wave processes in dispersive, diffractive, and anisotropic media with relatively low dissipation [1,2]. The threshold of nonlinearity determined by the dissipation parameter is so low that a wide variety of nonlinear wave effects, like formation of envelope solitons [3], modulational [4], decay and kinetic [5] instabilities, can be observed for input microwave powers below 1 W. In films the wave process is easily accessible from the surface. Inductive probes [6,7], thermooptical methods [8], and Faraday rotation measurements [9] were used to study magnetostatic wave processes in YIG films. It is, however, the recently developed method of space-and time-resolved Brillouin light scattering (BLS) [10,11,12], which provides a major leap in this field due to its high temporal and spatial resolution, sensitivity, dynamic range and stability. Using this method it is now possible not only to reproduce all the results obtained previously for stationary wave processes, but also to investigate non-stationary nonlinear wave processes like propagation of intensive wave packets of finite duration and finite transverse aperture (pulse-beams) that are simultaneously affected by dispersion, diffraction, nonlinearity and dissipation [13]. In this paper we present the results of our investigations of nonlinear diffraction of dipolar spin waves propagating in tangentially magnetized YIG films. We show that our method allows to observe and investigate in detail new nonlinear effects such as the stationary one-dimensional selffocusing effect of microwave excited backward volume magnetostatic wave (BVMSW) beams leading to the formation of spatial spin wave solitons, and the non-stationary spatio-temporal self-focusing effect of two-dimensional propagating wave packets leading to the formation of highly localized quasi-stable wave pulses -spin wave bullets. The last effect was predicted in optics [14], but the first experimental observation of this effect has been reported for the system of magnetostatic spin waves propagating in a YIG film [13].The most interesting case to study two...

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Direct observation of two-dimensional self-focusing of spin waves in magnetic films

Cited by 47 publications

References 7 publications

Observation of Spatiotemporal Self-Focusing of Spin Waves in Magnetic Films

Observation of Spatiotemporal Self-Focusing of Spin Waves in Magnetic Films

Space- and time-resolved Brillouin light scattering from nonlinear spin-wave packets

Spatial and spatiotemporal self-focusing of spin waves in garnet films observed by space- and time-resolved Brillouin light scattering

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