Journal of Magnetism and Magnetic Materials 104-107 (1992) 1039-1040

North-Holland

Spatial distribution of magnetostatic modes in a thin YIG slab

Antonio Azevedo and Sergio M. Rezende

Depurtamento de Fisica, Unir,er.sidade Federul de Pernamhuco, 50739 Recife, Brazil

The spatial distribution of magnetostatic wave modes has been measured in a thin YIG slab using Brillouin light

scattering. A conventional microwave setup was used to excite the resonance modes while the sample position was scanned

in the laser beam. The spatial distribution of the modes shows a central confinement of the uniform mode and an effective

pinning of the rf magnetization at the two ends of the slab.

Brillouin light scattering has been used as a power- ful tool to investigate ferromagnetic resonance (FMR) phenomenon, providing information not available with conventional microwave techniques only [l]. In this paper WC report the use of the Brillouin light scattering technique to measure the spatial distribution of mag- nctostatic volume wave modes in a thin YIG slab.

The experimental setup consists of two independent parts: a microwave magnetic resonance spectrometer and an optical Brillouin scattering system. In the mi- crowave circuit the radiation from a frequency-stabi- lized X-band backward-wave-oscillator is modulated by a PIN-diode modulator, amplified by a travelling- wave-tube and directed by a circulator to a shorted waveguide where the rf field drives the sample reso- nanccs. The sample is located half-wavelength away from the waveguide short, where the rf magnetic field is maximum, placed in an applied dc field H,, parallel to the surface (z-direction). The variations in the re- flected microwave radiation are detected with a Schott- ky barrier diode at the output port of a circulator. The Brillouin light scattering part, in the forward geometry, consists of a 2 mW He-Ne laser (632.8 nm) beam (x-direction), focussed on the YIG sample and col- lected by a lens through holes on the wavcguide walls, as illustrated in fig. 1. After passing a crossed polarizer the scattered light is analyzed in a 3-pass piezoelectri- tally scanned Fabry-Perot interferometer (FPI), de- tected with a photomultiplier tube (PMT) and recorded with photon counting in a multichannel analyzer (MCA). The sample-waveguide structure is held to a XY translator driven by two stepper motors to allow its motion relative to the laser beam in the y and z directions.

Fig. 2 shows the spectrum of a conventional FMR experiment obtained at a frequency w/2~ = 9.4 GHz with incident microwave peak power of 20 mW. The various peaks of absorption are associated with the long wavelength magnetostatic-mode resonances. When the field H,, is tuned to any of the resonating modes, strong light side-bands are observed in the Brillouin spectrum [2], with intensities proportional to the rf magnetization m, squared. Following ref. [3] a time

Microwave

He Ne Laser

Fig. 1. Experimental arrangement showing the YIG sample in

the microwave waveguide and the Brillouin scattering setup

used for the optical detection of the rf component of the magnetization in the x direction.

t- : 2500 2550 2600 Ho(Oe)

Fig. 2. Microwave absorption spectrum in a thin YIG slab at

9.4 GHz. Insets show the spatial variations of the rf magneti-

zation squared for modes (101) and (103) measured with

Brillouin scattering.

0312~X853/92/$05.00 0 1992 - Elsevier Science Publishers B.V. All rights reserved

1040 A. Am,edo, S.M. Rezrnde / Magnetostatic modes in a thin YIG slab

gate pulse synchronous with the microwave pulse and the FPI sweep is used to suppress all PMT signals except the frequency shifted lines. Photon counting data are recorded as a function of the sample position with respect to the laser beam while H, is adjusted to track the maximum absorption of a selected mode. Space resolved data are obtained by scanning the MCA synchronously with the motion of the translation stage in the z direction. Data for successive scans at differ- ent positions along the y direction are transferred to a computer so that we obtain 3d plots of the light scatter- ing intensity throughout the sample. This intensity is proportional to the transverse rf magnetization squared

111. The insets in fig. 2 show the tridimensional plots for

two modes of the spectrum obtained with 180 mW microwave incident peak power. The sample dimen- sions are a = 0.03 mm, b = 3.0 mm, c = 5.4 mm, and the modes are denoted by (n,n,n,) representing the number of half-wavelengths of magnetic oscillation along the X, y and z directions respectively. Due to the finite sample size, a demagnetizing field produces a pinning effect in the rf magnetization near the edges perpendicular to the dc field (z = 0, cl.

In the magnetostatic mode resonances the exchange interaction is negligible compared to the classical dipole-dipole interaction. Under these conditions the problem is essentially a magnetostatic one and is gov- erned by the equation of motion for the magnetization, dM/dt = yM x (IS,, + h) together with Maxwell’s equation in the magnetostatic limit, V.(h + 4~rm) = 0 and 0 x h = 0. Linearization of these equations leads to the equation for the magnetic scalar potential $,(h

= -V$,),

--\-+T *+;;t_=o. a 2ax2 - I

The parameter (Y is given by cy* = [(w/y)’ - H,f]/[ H,f

+ 4~rA4H,, - (w/Y)~], where y is the gyromagnetic ra- tio, M is the saturation magnetization and o is the spin precession frequency. Many years ago, Damon and Eshbach [4] solved this problem for a infinite thin slab. Imposing the appropriate boundary conditions at x = fa/2 and using a$/ay = 0, solution for modes with odd variation along x is $(x, y, z) = sinh(cuk,x) cos(kZz) [5]. It can be shown that the transverse rf magnetization in the x-direction is given by m,, =Ah, = A &b/ax, where A is a constant. Thus the spatial variation of the magnetization for the (101) and (103) mode in z-direction arc described by cos k;z, where kZ = n,a/c (n, = 1, 3). The spatially rc- solved patterns in fig. 1 confirm the theoretical varia- tion of the magnetization for these magnetostatic-wave modes. This is the first time that the spatial variation of the rf magnetization has been measured quantita- tively for magnetostatic modes.

The authors acknowledge the support from CNPq, FINEP and FACEPE (Brazilian agencies).

References

[ll

[21

[31

[41

bl

W. Wettling and W. Jantz, J. Magn. Magn. Mater. 45 (1984) 364. J.T. Hanlon and J.F. Dillon Jr.. J. Appl. Phys. 36 (1965)

1269. W. Wettling, W.D. Wilber, P. Kabos and C.E. Patton.

Phys. Rev. Lett. 51 (1983) 1680.

R.W. Damon and J.R. Eshbach, J. Phys. Chem. Solids 19

(1961) 308.

SM. Rezende and Antonio Azevedo. Phya. Rev. B44

(1991) 7062.