Macroscopic, layered onion shell like magnetic domain structure generated in YIG film using ultrashort, megagauss magnetic pulses

Study of the formation and evolution of large scale, ordered structures is an enduring theme in science. The generation, evolution and control of large sized magnetic domains are intriguing and challenging tasks, given the complex nature of competing interactions present in any magnetic system. Here, we demonstrate large scale non-coplanar ordering of spins, driven by picosecond, megagauss magnetic pulses derived from a high intensity, femtosecond laser. Our studies on a specially designed Yttrium Iron Garnet (YIG)/dielectric/metal film sandwich target, show the creation of complex, large, concentric, elliptical shaped magnetic domains which resemble the layered shell structure of an onion. The largest shell has a major axis of over hundreds of micrometers, in stark contrast to conventional sub micrometer scale polygonal, striped or bubble shaped magnetic domains found in magnetic materials, or the large dumbbell shaped domains produced in magnetic films irradiated with accelerator based relativistic electron beams. Through micromagnetic simulations, we show that the giant magnetic field pulses create ultrafast terahertz (THz) spin waves. A snapshot of these fast propagating spin waves is stored as the layered onion shell shaped domains in the YIG film. Typically, information transport via spin waves in magnonic devices occurs in the gigahertz (GHz) regime, where the devices are susceptible to thermal disturbances at room temperature. Our intense laser light pulse - YIG sandwich target combination, paves the way for room temperature table-top THz spin wave devices, which operate just above or in the range of the thermal noise floor. This dissipation-less device offers ultrafast control of spin information over distances of few hundreds of microns.

skrymions (4). These domains arise out of a competition between different magnetic exchange and magnetostatic energies (5,6). Over the past few decades, a great deal of effort has gone into using light for probing different aspects of condensed matter physics (7,8,9,10,11,12). Effects of light interacting with magnetism have been primarily studied with low intensity (I ~ 10 5 -10 6 Wcm -2 ) femtosecond (fs) lasers (7,8,9,10) for exploring demagnetization processes occurring on time scales of a few picoseconds (ps) (10,13,14,15). Recently, optical coupling of angular momentum of light with spins in magnetizable media has been shown to create micron-sized domains on fs timescales (8,16,17,18). The use of high intensity femtosecond laser pulses (I~ 10 14 -10 18 Wcm -2 ) for such studies has however not been attempted so far. This may be attributed to the apprehension that the enormous energy scale associated with such excitation would overwhelm the spin -spin interaction energy scale and the thermal damage induced by such intense laser pulse would obliterate the possibility of seeing any ordered spin configuration.
Indeed, direct irradiation with such intense pulses typically ablates the material creating a high temperature plasma. However, interaction of an intense fs laser pulse with the plasma is interesting as it is known to produce giant megagauss (MG) magnetic field pulses of picosecond duration (19,20,21,22,23). It is therefore worthwhile studying the response of magnetic materials to such intense magnetic pulses. In this paper, with an innovative target design and careful control of experimental conditions, we demonstrate the creation of novel, unusual spin structures created by this magnetic pulse.
Here we study the response of Yttrium Iron Garnet (YIG) film subjected to megagauss magnetic field pulses produced by the interaction of a few hundred petawatt/cm 2 intensity, 30 fs laser pulse with a solid target. YIG is a well-known ferrimagnetic insulator film with very low damping, which in recent times has become an attractive material for studying magnon dynamics (24,25,26) (magnons are quasi particles associated with spin waves). Low damping of magnetization dynamics coupled with large magnon diffusion lengths reaching several microns (27), make YIG an important material for applications in magnonics (28,29,30), spin caloritronics (31,32,33) and magnon-based microwave applications (34,35). A careful target design is however, crucial for eliminating the ablative degradation of YIG due to laser induced ionization and subsequent heating. We therefore implement a novel sandwich target geometry of metal film (Al)-dielectric-YIG (Fig. 1A), where the laser irradiates the top Al layer, leaving the lower YIG layer unaffected by the laser induced damage. Magneto-optical microscopy (MOM) of the YIG samples exposed to the laser generated giant magnetic field shows the creation of novel, large, concentric, elliptically shaped magnetic domains extending up to a few hundreds of microns from the projected irradiation location. The shape resembles layered shells of an onion. Furthermore, we see that the local magnetic field direction flips up and down periodically across these elliptical domain structures and its magnitude also has a periodic variation with distance from the center of the irradiation. Micromagnetic simulation of a YIG film subjected to megagauss field pulse shows the excitation of ripples of spin waves travelling across the low damping YIG film, a few picoseconds after the pulse. The spin waves cause moments to gradually rotate out of the film plane periodically resulting in the observed behavior of the measured local field. These fast spin waves diffuse up to a few hundreds of microns in the YIG film from the projected laser irradiation site, giving rise to a non-collinear spin configuration, which in turn we propose, gives rise to an additional Dzyloshinskii-Moriya type interaction contribution to the magnetic energy of YIG. This interaction together with pinning effects, results in the spin waves getting stored as the layered onion shell like magnetic domain structure in YIG.
Each target (Fig. 1A) consists of a 16 m thick Al film suspended over a GGG (Gallium Gadolinium Garnet) substrate in a sandwich configuration. The lower side of the GGG substrate has a Bismuth doped YIG film grown on it (36,37). We use single pulses of 25 femtosecond (fs) laser (p-polarized, center wavelength 800 nm) having 20 m beam diameter to irradiate identical points at different locations on the Al layer at an angle of incidence of 45. The laser intensities used are between 3 × 10 17 to 1 × 10 18 Wcm -2 (details of setup in Supplementary section). The YIG film is isolated from the optical field of the intense laser as well the heating effects it generates.
The sandwich configuration provides a two level protection to the YIG film. Firstly, it eliminates laser induced ionization of the YIG film and the resulting thermal heat load that could lead to direct damage of the film, since the intense laser pulse ablates the sacrificial Al layer which takes away these deleterious effects. Secondly, the magnetic YIG layer has additional shielding from the heating effects provided by the intervening 200 m thick dielectric air gap and the GGG layer present between Al and YIG film layer. The YIG film was devoid of any micron sized magnetic domains prior to irradiation. As late as four days after irradiation, the irradiated region is imaged using a high sensitivity magneto-optic microscope (MOM setup details in Supplementary information and Ref. 23). The magneto-optical intensity is  2 z B , where B z is the component of local field perpendicular to the surface. The B z (x,y) distribution is determined from the MOM intensity distribution by suitable calibration (23) (the x and y axes are in the film plane while z axis is perpendicular to the film). . The smaller upper domain structure is more circular than the one below. Also seen is a defect in the YIG film which was present before irradiation. (G) MOM image of the region same as that in (F), imaged after 10 days of laser irradiation, with the black defect as the identifier. Here we see layered onion shell like magnetic domain patterns have disappeared. It is well established in intense laser-solid interaction studies that a high intensity, ppolarized femtosecond laser pulse incident on a target at a non-normal angle sets up electron waves in the generated plasma, which grow to large amplitude before breaking. This breaking unleashes a giant current pulse (~mega-ampere) that travels normally into the planar target and the entire process is known as resonance absorption (RA) (22,38). The current pulse is due to RA generated single or multiple collimated relativistic electron jets (39). These jets generate giant, azimuthal magnetic fields (B  ), having peak pulse height of few hundreds of Megagauss with typical pulse widths of a few ps (19)(20)(21)  To explore the effect of these RA generated giant magnetic field pulses on YIG films, we model the temporal evolution of in-plane local magnetization M in the YIG film under the influence of a magnetic field pulse (refer Fig. 2A The first term on the right in eqn.1 is the torque on M due to the effective magnetic field ( where  is the gyromagnetic ratio. The in-plane azimuthal field pulse (see Fig. 2A) is where  is the azimuthal unit vector in film plane. The second term is a damping term with to flip out of the film plane by an angle  0 due to a torque, There appears to be only one other group that has studied the influence of ultra-strong, ultrashort magnetic pulses on magnetic films (43,44) and it is therefore interesting to make a comparison with their results. Their studies subjected films of high  spin waves excited by the field pulse which propagate across the YIG film. Also note that for YIG, K u = 6.1 x 10 -4 MJ m -3 is nearly two orders smaller compared to the strong magnetic anisotropy material used at SLAC (43,44), hence the domains formed in YIG are more symmetrical compared to the asymmetrical dumbbell pattern found in the SLAC study. It is also important to mention the differences in the methods used to generate the field pulses in both cases. Our intense laser generated field pulses are essentially magnetic while both B  and E  pulses are generated by the relativistic e-bunches in the SLAC experiments (43). The electron beam in the SLAC study traverses the film and causes film damage, while such a deleterious effect is completely avoided in our study. Lastly, our B  pulse is larger by at least an order of magnitude (19,20) (~ 100 T) compared to that in the SLAC study ( ~ 10 T) (43).
For our simulation, the azimuthal magnetic field distribution experienced by the YIG film is approximated using an expression similar to that for the field distribution at positions located away from the relativistic electron bunch (45) Fig. 1F. By reducing the spacing between the field pulses down to 18 m we observe (Fig. 3C) a single rippling structure produced by the overlap of two spin wave ripples. The resulting ripple is not circular but elliptical in shape.
It is these elliptical shapes that we observe in our experiments (Fig. 1). The multi-peaked field structure may result from multiple closely spaced e-jets generated during RA process as shown in the schematic of Fig. 3A. From our simulations, we determine the phase velocity (v p ) of the spin waves generated by the giant field pulse, as the ratio of the distance covered by the crest of a ripple to the time taken. The v p turns out to be in the range of ~ 10 7 m s -1 which is four orders of magnitude greater than the typical limit of domain wall velocity (~ 1000 ms -1 ) reported for YIG films (47 We show that one to two order of magnitude higher THz frequency spin waves can be excited using our intense laser and the novel metal/dielectric/YIG film sandwich target combination. ). We also re-emphasize that our design for launching spin waves has multiple advantages compared to doing the same with an accelerator based relativistic electron beam (43,44). We have a much more compact table top design, less complexity in operation and the strength of the field pulses and pulse durations can be conveniently controlled by varying the laser intensity, the target design and the interaction geometries.

Conclusions
We   . The smaller upper domain structure is more circular than the one below. Also seen is a defect in the YIG film which was present before irradiation. (G) MOM image of the region same as that in (F), imaged after 10 days of laser irradiation, with the black defect as the identifier. Here we see layered onion shell like magnetic domain patterns have disappeared.

Experimental set-up
The laser irradiation experiments are performed in experimental chamber with base vacuum of 10 -5 mbar. The experimental schematic is shown in Fig. S1 (a). To irradiate a fresh portion of sample every laser shot, the sample is mounted on precise X-Y-Z-θ stage assembly. P-polarized 25 fs, 800 nm laser pulses were focused to 20 µm diameter spot by off-axis parabolic mirror (OAP) on to a sample to create a plasma. The intensity on the sample is varied from 10 17 to 10 18 Wcm -2 , by changing the laser energy appropriately. The angle of incidence on sample is maintained to 45 o to maximize resonance absorption (RA) (discussed later). The laser irradiated samples are imaged by high sensitivity magneto-optical imaging technique, which is based on the principle of Faraday effect. Figure S1

Resonance absorption
We give a short summary of the generation and effects of magnetic fields as a result of resonance absorption (RA) in laser-matter interaction. During the RA process, the incoming p-polarized (Efield in the plane of incidence) high intensity laser pulse impinges on the sample at oblique incidence and generates dense plasma. The preformed plasma created by the laser pre-pulse expands away from the target surface as shown in the schematic (Fig. S2)   A comparison of material parameters between YIG and the material studied in Ref.

Material Parameters YIG Co 70 Fe 30
Magneto-crystalline Anisotropy (K u ) 6.10 × 10 2 J.m -3 7.6 × 10 4 J.m -3 Damping Constant (α) 0.0005 0.015 A comparison from the above table shows that the K u and  of the Co 70 Fe 30 films used in the SLAC study [i] is two orders of magnitude larger than those in YIG.
YIG has a cubic lattice with lattice parameter of a = 12.37 A, magnetic moment of  = 40  B per unit cell [ii]. The Zeeman energy density of YIG associated with giant magnetic field pulses, B  ~ 7.5 MG can be written as, 3 14296 B a    MJ.m -3 . This Zeeman energy (E z ), generated either by the relativistic electron bunch at SLAC [43] or via intense FS laser pulses, overwhelm the magnetic anisotropy energy barrier of materials (for YIG E z ~ 14296 MJ.m -3 >> its magnetic anisotropy energy, K u = 6.10 x 10 2 J.m -3 ).

Shape of domains formed in YIG after a long time (~ 100 ms after field pulse)
In YIG, the equilibrium (100 msecs after B  pulse) domain configuration is rectangular shaped, which minimizes the free energy (Fig. S4). These are the natural equilibrium shapes of the domains in YIG which minimize the free energy of the domains. Note the layered onion shell like magnetic domains in YIG film ( Fig. 1 of our main MS) are completely different from these equilibrium rectangular shaped domains. The layered onion shell like magnetic domain structure is a snapshot of a rippling spin wave excited in YIG film by the intense fs laser pulse.