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ELEMENTARY AND NONLINEAR EXCITATIONS
IN A BLOCH WALL
L. Dedukh, V. Nikitenko, V. Synogach
To cite this version:
L. Dedukh, V. Nikitenko, V. Synogach.
ELEMENTARY AND NONLINEAR EXCITATIONS
JOURNAL DE PHYSIQUE
Colloque C8, SupplLment au no 12, Tome 49, decembre 1988
ELEMENTARY AND NONLINEAR EXCITATIONS IN A BLOCH WALL
L. M. Dedukh, V. I. Nikitenko and V. T. SynogachInstitute of Solid State Physics, Academy of Sciences of U.S.S.R., Chernogolovka, Moscow distr., 112432,
U.S.S.R.
Abstract. - Domain wall standing flexural waves in yttrium iron garnet single crystal plates are investigated by magne- tooptical method. A number of nonlinear changes of the wall excitation spectrum is found and qualitatively explained.
There are many theoretical studies of the spec- trum of spin waves localized in a magnetic domain wall
(DW) [I, 21. One of the main reason for this interest is to obtain information applicable to the interpreta- tion of numerous experiments in the DW dynamics and therefore in the magnetization process as a whole. Nevertheless the possibility of a direct experimental study both of the elementary and the nonlinear ex- citations in a DW has been found only in the recent works [3, 41. In this paper we present the results of the further investigations of the wall standing flexural waves discovered in [4].
The samples in the form of a rectangular yttrium iron garnet single crystal prisms alongated along [lli] axis with in-plane magnetization Mo contained only one or two 180' Bloch walls. The monopolar wall state was produced as in [4] and stabilized by a dc magnetic field Hz normal t o the sample plane (112). Wall vi- brations caused by an uniform ac drive magnetic field
H, // Mo were detected by photomultiplier tube from the change in the intensity of the light transmitted through a region of the sample which contained half of the wall width and a part of the neighboring do- main (see the inset in Fig. 1). Magnetooptical signal was measured using a spectrum analyser, the signal averaging and frequency sweeping being made by a computer.
Figure 1 shows the dependences of the wall vibration amplitude q on the drive field frequency u at various field amplitudes H:. A set of nearly equidistant reso- nant peaks on the q ( u ) is caused by the excitation of
the wall standing flexural waves with the wave vector k l M o [4]. This is confirmed by the invers proportion- ality between the peak frequencies up and the sample thickness d. Figure 2 shows the plots of up versus the peak number N. It is seen from figures 1 and 2 that the variation of the
HZ
gives rise to the substantial changes of the wall excitation spectrum: the first peak disap- pears whenHZ
2
0.4 mOe : the decrease of the field causes the frequencies up to grow, the high-frequency peaks are gradually suppressed at high drives (H: 225 mOe). It should be noted that at low frequencies
(v 0.1 to 4 MHz at
HZ
= 60 mOe) the processes of the creation, unidirectional motion and annihilation ofFig. 1. - The wall vibration amplitude q versus the ac drive field frequency u at various amplitudes (H:, mOe): 0.25 (I), 0.5 (2), 5 (3), 12.5 (4), 50 (5), 63 (6); Hz = 28 Oe. Inset-sketch of the sample and of the photometered area (dashed line).
Fig. 2. - The frequency of the peak, up, versus its number,
N . Hz = 28 Oe;
HE
= 0.25 mOe (I), 5 (2), 12.5 (3), 25 (4), 50 (5).C8 - 1888 JOURNAL DE PHYSIQUE
the nonlinear excitations of the wall structure already take place. They were revealed using a storage os- cilloscope as in reference 131. The detected resonances were susceptible t o the wall structure also at lower H:, when the processes of the dynamical conversion of the wall structure were not observed: in a "demagnetized1' DW, the Bloch lines are found to suppress the peaks [41.
We suppose here that all the flexural modes n = 0,1, 2, ... are excited. So the frequency gap, Ro, in the spec- trum is determined from the value of the first peak fre- quency ( N = 1)
,
while the phase velocity S- from the up (N) curve: v ~ + l - v j ~ = S/2d. The measured values of S = 77 m/s and Oo/27r = 0.4f 2.6 MHz (it depends on HZ) proved to be much smaller than those calcu- lated using Winter's theory 111. Only the damping pa- rameter found from ferromagnetic resonance linewidth ~ u ~ ~ ~ = 0 . 7 ~ 1 0 - ~ agrees well with that found from the DW resonance linewidth a ~ w = (0.6 f 0.2) x 1 0 - ~ .The nonlinearities characterizing the wall spectrum at low H: can be explained allowing for the magnetic after-effect caused by the interaction of the moving DW with the crystal defects. Their energy W depends on the local magnetization. As a result, the DW ex- periences the action of the effective force 151:
where r is the relaxation time of defects. Using the parabolic potential well approximation:
and substituting (1) and (2) into the equations of the DW motion [2] one obtains:
= ( 2 ~ R ; l n o ) (Ht + H I T ) (3)
- .
(27ry2~o)-1, A: = A/K,
s2
= ~ . I T A ~ ~ (1+
h),
h = K , O A O / ~ T M ~ , q = IC/KO, y is the gyromagnetic ratio,rco is the coefficient of the wall restoring force; A and K are the exchange and anisotropy constants, respec- tively; H is the drive field. From equation (3), both the dispersion law for DW free vibrations
(HZ
= 0) and the resonant frequencies w, of standing DW flexural waves (forced DW vibrations) can be obtained. Fig- ure 3 shows the results of the computer calculations forFig. 3. - Dispersion dependences w, (k,) calculated at Ro = 1.5 MHz; r = 70 ns; 0, = 0.2 MHz; q = 0 (I), 30 (2), 50 (3), 100 (4), 150 (5), 200 (6), 300 (7). Insets show the appropriate q; ( w ) curves at lc = k;.
the dispersion curves w, (Ic,) at various q ( r = const,
k, =nn/d). It is seen that the values w, increase when
q grows. At certain q (curves 3 t o 5), the values w, (at Ic = Ici) are absent because the qi (w) curves have the relaxation form (curve 3 in the inset in Fig. 3). The results of the calculation quailitatively explain the ex- perimental ones under assumption that the increase of
HZ
causes the decrease of the q value.As regards the high field nonlinearities (the limita- tion of the amplitude of high frequency peaks), we can say the following. The theory should take into account nonlinear processes of the dynamical conversion of the wall structure including the creation, motion and an- nihilation of the Bloch line and sbliton-like excitations as well as uniform Walker's precession [2] of the mag- netization within the wall.
[I] Winter, J. M., Phys. Rev. 124 (1961) 452. [2] Malozemoff, A. P., Slonczewski, 3. C., Mag-
netic domain walls in bubble materials (Academic Press, New-York etc.) 1979.
[3] Gornakov, V. S., Dedukh, L. M., Nikitenko, V. I.,
Zh. Eksp. Teor. Ftz. 86 (1984) 1505 [JETP 59
(1984) 8811.
[4] Dedukh, L. M., Nikitenko, V. I., Synogach, V. T., Pis'ma Zh. EIcsp. Teor. Fiz. 45 (1987) 386
[JETP Lett. 45 (1987) 4911.
