Solid State Communications,Vol. S,pp.3l9322, 1967.
Pergamon Press Ltd. Printed In Great Britain
MAGNETOACOUSTIC EFFECTS IN RARE EARTH IRON GARNETS JudyR. Franz IBM Zurich Research Laboratory, Ruschlikon, Zurich, Switzerland and Bruno Luthi4 IBM Zurich Research Laboratory and Rutgers, The State University New Brunswick, New Jersey, U. S. A. (Received 5 January 1967 by E. Burstein)
Linear magnetoacoustic birefringence and transverse ferroacoustic resonance experiments were performed with rare earth iron garnet samples in the temperature range between 77 and 3000 K. The magnetoelastic coupling constant B 2 for Yb, Dy, Th and GdIron Garnet is compared with results from magnetostriction experiments. The preliminary damping results are discussed, applying the slow relaxation theory to the rare earth iron garnet system. WE HAVE used the techniques of linear magnetoacoustic birefringence 2 to measure 1 and transverse the realferroand acoustic imaginaryresonance parts of the index of refraction of soundwaves in the rare earth iron garnets (RIG). The birefringence experiment determines the magnetoelastic coupling constant B 2 and the effective magnetic field, whereas the transverse resonance enables one to measure damping effects.
temperature (296°K,298°K)were taken with two magnetization different samples. compensation For point TbIG below (242°K), the damping effects were large enough to Prevent us from getting any birefringence data (see Fig. 2). Some data for YbIG are also shown. No static magnetostriction data for this substance exist except for doped YbYIG (Yb0.3 Y2., Fe5 Oia)~ Extrapolated values for full Ybconcentration at T = 4°K give a magnetostriction constant Xm = 27. 5x10~,whereas a linear extrapolation of our results to 4°K gives X~ of about 25 x 10 in good agreement considering the approximated nature of the extrapolation. Finally, It should be pointed out that in our resonance experiments any terms responsible the soundwave for forced does not magnetostrictcouple to ion. These terms give an appreciable field dependent contribution in the static magnetostriction experiments ~ making such experiments difficult to interpret.
Figure 1 shows the RIG B2~values obtained from linear birefringence experiments. Our previous results for GdIG’ are plotted again to show the almost perfect agreement between our data and the most recent static 3 magnetostriction Our data for DyIGexperiments is in fair agreement on this substance. with the corresponding magnetostriction results. ~ For comparison we extrapolated the magnetostriction values4 to zero field. The agreement between our data and magnetostriction data for TbIG6 is not very good. It should be pointed out, however, that the two data points at room
~,
Figure 2 shows typical damping curves for the different RIGs. In GdIG one observes a well resolved resonance line in the temperature range where the effective field
The State University, New 319
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RARE EARTH IRON GARNETS
si
Vol.5, No. 5
I
[ergkc] 5010
x 100

FIG. 1
Magnetoelastic coupling constant 50
0

X ~
~
50
100
150
200
250
+
*
[ic] T
300
GdIG
(Clark et al.
DyIG
(—Clark et al. 6) Iith
TbIG
S YbIG
B3~
3) 4)
(....
TbIG29~K
YbIG 77°K
FIG. 2
GdIG2O2K
Transverse ferroacoustic resonance for RIG. Recorder plot of Integrated amplitudes of all the echos versus magnetic field. H
=
e
NM

I
1
2
3
4
5
6
7[KG] ~ 8
9
2K 1 M
1). (around Here N200°K, is the demagnetizing is small but not at roomfactor, temperature M the magnetization, and K 1 the first anisotropy constant. This resonance line is very similar to those observed In YIG and YGaIG. 2 In YbIG one observes a slightly broader line that is not resolved on the low magnetic field side because of the increased He. DyIG shows an even broader line than YbIG, and for TbIG the resonance line is very broad even at room temperature. Below the magnetization compensation point, the damping in ThIG is so strong
that one no longer can propagate any soundwave in the transverse ferroacoustic resonance geometry. In all cases with the exception of OdIG, from ordinary spinwavethe damping is spinwave stronger damping than one or would expect phonon conversion caused by spatial variation of the demagnetizing fields. The results in Figure 2, therefore, strongly indicate that the damping is due to some additional process, the likely one being the rare earth ion relaxation which is responsible for the analogous large linewldth effects in ferromagnetic resonance. To get a quantitative understanding of these damping effects and also to justify our
Vol.5, No.5
RARE EARTH IRON GARNETS
evaluation of the magnetoelastic coupling constants, which was done as in reference we applied the socalled slow relaxation theory 8 to our RIGsystem. This theory has been quite successful in explaining ferromagnetic resonance linewidths for dilute rare earth iron garnets. In contrast to the ferromagnetic resonance case, the relatively weak coupling between the spinwave and soundwave systems allows us in principle to study these llnewidth effects in concentrated samples. Our calculations followed closely the equation of motion method 8~ allowing however for a full rare earth sublattice magnetization and therefore also for optical spinwaves. In the equations of motion for the iron and rare earth sublattices, we used an isotropic exchange interation in the torque terms, since we are dealing‘su~~h long wavelength spinwaves and relatively high temperatures. The anisotropic exchange, vital for the slow relaxation theory, was taken into account in the single ion relaxation of the ferromagnetic rare earth ions.case, Thisbywas calculating done, asthe in the effective field acting on the iron due to the relaxing rare earth ions. 8 The soundwave couples to the iron and rare earth sublattices with individual magnetoelastic coupling constant BF and BR (B 2 = BF + BR). We obtain the following coupl ed dispersion equation for the soundwaves and spinwaves: 2 w2) k 2 re Urn ~22 (I) ~‘,
The magnetoelastic coupling constant, which for small 8 can be obtained using only the real part of wm, has already been discussed. For our specimens in the temperature region investigated we do not find an observable dynamic shift in the effective field He, and therefore we can use the small 8 approximation. This was confirmed both by a comparison of the measured linewidths with the imaginary part of equation (2) and also by an experimental determination of He in the linear birefringence experiment. Table 1 shows that the experimental values of He agree closely with those calculated from static anisotropy experiments. TABLE I Comparison of effective fields He = (K1/M)(4u N)M determined from linear birefringence experiments He (exp), 10and and magnetlzfrom static experiments ation anisotropy 11e (caic). 



(c2
~
m
P(MF
+
8
2
y e (He
~
+
M 2 F MF+MR
2 (ut) 1+(wT)2

jut 1+(wt)2
~ n
~

T [°K]
He(exp) (Gauss]
He(ca1c~) [Gauss]
______________________________________ TbIG DyIG
274 188
—1380 480
YbIG
90
+
900
+
820
77
+
470
+
490
—
1450 620 —
NR)
where ‘~eis the effective gyromagnetic ratio, MFandMp aretheironandrareearthsublattice rnagnehzations, c and k are the sound wave velocity and wave number, p is the density, and ~ is the frequency of the acoustical spinwave mode. For we get:
m
321
.......a
~ ‘
where 8 is the complex susceptibility characteristic of the slow relaxation theory. ~ The spinwave frequency tum reduces to the one used in the dilute RIG case ~when MR = 0. The factor 8 contains the relaxation terms giving rise to a dynamic field shift and damping. From equation (1) one can calculate the real and imaginary parts of the soundwave refractive index and cornpare them with our experimental results.
The linewidths determined from the transverse ferroacoustic resonance for individual ultrasonic echos show these features: For YbIG at we get a linewldth of the sameextrapolorder as the 77° oneKfrom ferromagnetic resonance ated linearly to 100% Yb concentration. This indicates that the linewidth is proportional to the Ybion concentration over the whole concentrationrange. However, for ThIGat 300°K andfor DyIG at 190°K we get llnewldths which are of the same order as the ones from ferromagnetic resonance at 1% concentration. The single crystals used in this work were grown by Dr. E. A. Giess at the IBM Research Center. We thank Dr. Clark for making available to us prior to publication results of his magnetostriction experiments on GdIG. A very informative discussion with Dr. HartmannBoutron is gratefully acknowledged.
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References
1.
LUETHI B., J. Appl. Phys. 37, 990 (1966).
2.
LUETHI B. and OERTLE F., Phys. kondens. Materie 2, 99 (1964).
3.
CLARK A. E. and DE SAVAGE B. F., (to be published).
4.
CLARK A. E., DE SAVAGE B. F., TSUYA N. and KAWAKAMI S., J. Appi. Phys. 37, 1324 (1966).
5.
IIDA S., Physics Letters 6, 165 (1963).
6.
FLANDERS P.J., PEARSON R. F. and PAGE J. L., Brit. J. Appl. Phys. 17, 839 (1966).
7.
LUETHI B., App!. Phys. Letters 6, 234 (1965); ibid, 8, 107 (1966).
8.
HARTMANNBOUTRON F., Phys. kondens. Materie 2, 80(1964); VAN VLECK J.H. and ORBACH R., Phys. Rev. Letters 11, 65 (1963). —
9.
This assumption will be discussed further in a forthcoming paper.
10.
PEARSONR.F., J. Appl. Phys. 33, 1236 (1962).
Lineare magnetoakustische Doppelbrechungs  und transversale ferroakustische Resonanz Experiments wurden mit Seltenen Erden Eisen Granat Proben in Temperaturbereich zwischen 77°K and 300°K durchgeführt. Die magnet
oelastische Kopplungskonstante B2 für Yb, Dy, Tb und GdEisen Granate wird verglichen mit Resultaten von MagnetostriktionsExperimenten. Die vorlaufigen Dämpfungs resultate werden mit Hilfe der longitudinalen Relaxations Theorie, angewandt auf ths Seltene Erden Eisen Granat System, diskutiert.