IEEE TRANSACTIONS ON MAGNETICS, VOL. 25, NO. 5 , SEPTEMBER 1989 3485

FERROMAGNETIC RESONANCE FOLDOVER AND SPIN-WAVE INSTABILITY IN SINGLE-CRYSTAL YIG FILMS

* ** M. Chen, C. E. Patton, G. Srinivasan, and Y. T. Zhang

Department of Physics, Colorado State University Fort Collins, CO 80523

Abstract

Foldover in ferromagnetic resonance (FMR) has been theoretically investigated. The objective of the work was to (1) calculate field shifts for the FMR shoulder associated with foldover, following the analysis of Schlomann, and (2) make a detailed comparison with perpendicular FMR data recently published by Zhang and co-workers. The observed shifts were somewhat smaller than predicted theoretically on the basis of a single low power FMR linewidth. However, the theory could be fitted to the data by allowing the effective resonance linewidth to increase with the microwave power level. Such an increase in the effective resonance linewidth is consistent with the increase in losses that is known to occur at high power levels.

Introduction

Foldover in ferromagnetic resonance (FMR) has been a continuing subject of study since the early work of Anderson and S u h l [ l ] , Weiss [ 2 ] , and Schlomann [ 3 ] . Anderson and S u h l established the basic physical interpretation of this phenomenon in terms of the nonlinear magnetization dynamics in the material. Weiss first reported observations of dis- torted FMR lineshapes and foldover effects at high power levels [ 2 ] . Schlomann has refined the second- order nonlinear theory and included anisotropy effects into the analysis [ 3 ] .

The subject of foldover in FMR was revived in recent years by McKinstry et al. [4], who observed FMR lineshape changes in single-crystal yttrium-iron- garnet (YIG). The basic high power effect, shown schematically in Fig. 1, is the appearance of an extended resonance response when sweeping the static magnetic field in one direction and a sharp cusp when sweeping in the other direction. It was initially believed that these observed foldover-like distortions of the FMR absorption profile were directly related to the nonlinear magnetization process predicted by the theory. However, detailed profile measurements under pulsed microwave excitation conditions showed that these distortions disappeared for low duty cycle conditions [ 5 ] . These results indicated that the observed foldover effects were mainly due to sample heating, not the theoretically suggested bistable-type foldover discussed above.

IOW power

cr:

STATIC MAGNETIC FIELD

Fig. 1. Schematic illustration of the FMR foldover response.

Quantitative data on foldover in single-crystal YIG films were recently reported by Zhang, et al. [ 6 ] , for which the experiment was performed under condi- tions of low duty cycle pulsed microwave power and the absorption profiles were measured by signal averaging techniques. Such experiments eliminated the foldover effects due to heating and made it possible to examine the linebroadening and foldover effects associated with high power nonlinear processes. For FMR with the static field in the film plane, no foldover was found. True foldover, in the Anderson-Suhl sense, was ob- served for FMR with the static field perpendicular to the film plane. A representative set of FMR profiles for this case is shown in Fig. 2.

z .

L L L I I I I I I , 4700 4740 4700

APPLIED STATIC FIELD (Oe)

Fig. 2. Upsweep and downsweep FMR absorption curves for different values of the peak microwave power incident on the single-crystal YIG film, f-or a fixed duty cycle of 1% under perpendicular pumping. The static field was out-of-plane. (After Zhang et al. [ 6 1 . )

The purpose of this work was to apply the analysis of Schlomann in Ref. 3 to the perpendicular field FMR foldover data of Ref. 6 . More specifically, the theory was used to calculate the field shifts for the downsweep and upsweep shoulders, indicated schematically in Fig. 1 as H and H2, as a function of the microwave field amplitide h These results on H and H were then compared to t6g'observed shoulder positions as a function of h for the YIG film data of Ref. 6 . The observed shiftgfwere somewhat smaller than predicted theoretically on the basis of a single low power FMR linewidth. However, the theory could be fitted to the data by allowing the effective resonance linewidth to increase with the microwave power level. Such an increase is consistent with the simultaneous occurrence of foldover and second-order spin-wave instability at high power levels.

1 2

Theory

The basic foldover effect addressed in Refs. 1 and 3 is due to the fact that a large amplitude uniform mode excitation of decreases the static mag- netization component in the applied field direction, perpendicular to the film plane. This, in turn, reduces the static demagnetizing field and results in

0018-9464/89/o900-3485$01 .WO 1989 IEEE

3486

downshift in the FMR field. In a downsweep (decreasing static field) trace of the FMR profile at high power, therefore, the resonance is essentially moving down in field ahead of the field scan. At some point, there is an abrupt drop in the signal as the field finally moves below the FMR peak position at the power level in operation. In upsweep mode, one gets an abrupt increase in signal at some other field. These effects are shown in both Fig. 1 and Fig. 2.

Reference 3 describes a canonical formalism for the nonlinear FMR response in ferrite materials. The operational foldover equation from this analysis, for the special case of a (111) YIG film magnetized per- pendicular to the plane, is given by

([2(H - Hres)/AR + p A2I2+ 1) A2 = 1. (1)

In Eq. (l), H is the applied static field, Hres is the low power FMR resonance field, AH is the low power FMR linewidth, B is a parameter which is proportional to the microwave power level, and A is a reduced FMR absorption parameter. The B-parameter for the case of interest here is given by

(2) 3 B - hZf[4aMs- f HAI/(mH) .

In Eq. (2). h denotes the linearly polarized micro- wave field ampfitude, 4aM is the saturation induction of the YIG film, and 'HA is the magnetocrystalline anisotropy field.

FMR profiles for very low power ( p = 0 ) and high power ( B - 20) conditions are shown in Fig. 3 . These curves were obtained with AH - 2 Oe, H = 53 Oe, and 4nM - 1750 G. Those are typical value$ for single crygtal YIG films at 9.18 GHz, the operating frequency in Ref. 6. A B-value of 20 corresponds to a hrf-value of about 330 mOe, which is comparable to the levels for the experimental foldover effects of Ref. 6, and shown in Fig. 2. The foldover character of the /3 - 20 curve is clearly evident. One would expect to see a sharp drop in absorption at (a) for downsweep FMR and a jump in absorption at (b) for upsweep FMR. Note that the horizontal axis is in terms of a reduced field shift relative to the low power FMR position and normalized to the low power linewidth.

over (see Fig. 1) can bi evaluated from eq. (1) as The field shifts H and H2 associated with fold-

t I I I I I I I I -30 -20 -10 0 IO

REDUCED APPLIED FIELD (H - Hres)/AH

Fig. 3 . Theoretical foldover curves for a slab magnet- ized perpendicular to its plane.

( 3 ) 9 2

H1 - 0.5 hZf[4aMs- 7 HA]/(AH) ,

and

H2 - 0 . 9 5 hf:3[4aMs- . (4)

These two expressions show that the downsweep shift scales quadr?F$cally with hr , while the upsweep shift scales as h It is afso noteworthy that the upsweep fol%ver shift H2 is independent of the FMR linewidth AH.

Results and Discussion

Figure 4 shows curves of the foldover downsweep field shift H as a function of the microwave field amplitude h fir three different values of the FMR linewidth &f The magnetic parameters (other than AH) are the same as given above. The data points (tri- angles) show the measured downsweep shoulder positions versus h from Ref. 6. These results show that the data andri!he theory yield fold-over shifts are roughly comparable. The results also show that it is not possible to fit the theory to the data for one unique choice of linewidth. The comparison in Fig. 4 indi- cates that a linewidth parameter which increases with hrf is needed in order to fit the theory to the ex- perimental points.

- 50 1 8

40 v)

I E LO 30

9 Lu LL 20 0. Lu Lu

2 10 f B

0

MICROWAVE FIELD AMPLITUDE h,f (Oe)

Fig. 4. Foldover static field shift H1 vs. microwave field amplitude hrf.

The theory was fitted to the data, therefore, by adjusting AH to match H1 to the observed shift at each data point. The results of this fit are shown in Fig. 5 . The open triangles show the values of AH required for the fit; the solid triangle at hrf _ = 0 is the actual measured low power FMR linewldth, given by AH - 1.7 Oe. line- width which is needed to model the downsweep foldover increases linearly with hrf, and follows an operation- al equation

It appears that the effective FMR

+ 2.2 hrf] [Oe]. (5) AHeff [AH(low power) - = FMR

An increase in the effective F'MR linewidth at high power is not unreasonable. The increased line- broadening and decrease in the l o s s component of the microwave susceptibility with increasing power are well known. Both effects can be expressed in terms of an increase in the effective FMR linewidth. This effective FMR linewidth is not to be confused with the off-resonance effective linewidth discussed in the context of low power microwave losses [7].

3487

W I

MICROWAVE FIELD AMPLITUDE h,f (Oe)

Fig. 5. Effective FMR linewidth AH vs. microwave field amplitude h , obtained from fitting the theory to the data in Figft.

Finally, consider the upsweep field shift H versus h and the corresponding upsweep FNR shoulde? positiongf The data points and a single theoretical curve are shown in Fig. 6 . is expected be independent of AH; an array of s6rves for various AH values is not possible. It is clear that the upsweep shifts are generally larger than predicted from the theory, except at relatively low powers. It is also evident that there is no simple way to force a fit, for example, by increasing the linewidth.

Recall that H2 vs. h to

50 - - 8 N 40 r

* 30 5 n g 20

m I-

L

a W : 10 v)

n 3

MICROWAVE FIELD AMPLITUDE h,f (Oa)

A

0 0 0.2 0.4 0.6 0.8 IO

* Present address: Department of Physics, Oakland University, Rochester, MI 48309

** Present address: Department of Physics, Shanghai University of Science and Technology, Shanghai, China

References

P. W. Anderson and H. Suhl, "Instability in the Motion of Ferromagnets at High Microwave Power Levels," Phvs. Rev., vol. 100, pp. 1788-1789, 1955. M. T. Weiss, "Microwave and Low-Frequency Oscil- lation due to Resonance Instabilities in Ferrites," Phvs. Rev. Lett., vol. 1, ~ p . 239-241, 1958.

[3] E. Schlomann, "Ferromagnetic Resonar.ce at High Power Levels," Ratheon Tech. Rep. Nc,. R-48, 1959 (unpublished).

[4] K. D. McKinstry, C. P. Patton, and M. V. Kogekar, "Low Power Nonlinear Effects in the Ferromagnetic Resonance of Yttrium Iron Garnet," J.App1. Phvs., vol. 58, pp. 925-929, 1985.

[5] Y. T. Zhang, C. E. Patton and M. V. Kogekar, "Ferromagnetic Resonance Foldover in Single Crystal YIG Films - - Sample Heating or Suhl Instability," IEEE Trans. Maa., vol. 22, pp. 993- 995, 1986.

[6] Y. T. Zhang, C. E. Patton and G. Srinivasan, "The Second-Order Spin-Wave Instability Threshold in Single-Crystal Yttrium-Iron-Garnet Films under Perpendicular Pumping," J. Appl. Phys., vol. 63,

[7] See, for example, C. E. Patton, "Effective Line- width due to Porosity and Anisotropy in Poly- crystalline Yittrium Iron Garnet and Ca-V- Substituted Yittrium Iron Garnet at 10 GHz,"

pp. 5433-5438, 1988.

Rev,, vol. 179, pp. 352-358, 1969.

Fig. 6. Foldover static field shift H2 vs. microwave field amplitude hrf.