STANDING WAVES IN THE MICROWAVE SPECTRA OF Ni AND NiFe SINGLE CRYSTAL DENDRITES

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STANDING WAVES IN THE MICROWAVE SPECTRA OF Ni AND NiFe SINGLE CRYSTAL

DENDRITES

T. Phillips, L. Rupp, Jr, A. Yelon, R. Barker, C. Vittoria

To cite this version:

T. Phillips, L. Rupp, Jr, A. Yelon, R. Barker, et al.. STANDING WAVES IN THE MICROWAVE

SPECTRA OF Ni AND NiFe SINGLE CRYSTAL DENDRITES. Journal de Physique Colloques,

1971, 32 (C1), pp.C1-1162-C1-1164. �10.1051/jphyscol:19711416�. �jpa-00214458�

JOURNAL DE PHYSIQUE Colloque C I , supplkment au no 2-3, Tome 32, Fe'urier-Mars 1971, page C 1 - ¹¹⁶²

STANDING WAVES IN THE MICROWAVE SPECTRA OF Ni AND NiFe SINGLE CRYSTAL DENDRITES

by T. G . PHILLIPS a n d L. W. RUPP, J r

Bell Telephone Laboratories, Incorporated, Murray Hill, New Jersey and A. YELON, R. C. BARKER and C. VITTORIA (*)

Yale University (**) New Haven, Connecticut

Rhumb. - Nous avons effectue une experience de spectroscopic microsonde, 5 la temperature ambiante, aux frk- quences 12 et 24 GHz, sur des plaquettes monocristallines dendritiques de nickel et d'alliage fer-nickel. On observe clai- rement la formation d'ondes stationnaires dans les echantillons, par la presence dans le spectre de modes discrets. Des relations de dispersion et de la dependance angulaire de ces modes, on en deduit qu'ils sont surtout d'origine magneto- statique, tout au moins pour le cas des plaquettes de fer-nickel.

Abstract.

We have performed a room temperature microwave spectroscopy experiment, at frequencies of 12 and 24 GHz, on single crystal dendritic platelets of pure nickel and nickel-iron alloys. We observe clear evidence for the for- mation of standing waves in these specimens, in that the spectra of the platelets show many discrete modes. From the dispersion relations and angular dependence of these modes we are able to deduce that they are mainly of magnetostatic origin, at least for the case of the nickel-iron platelets.

This paper discusses a room temperature, micro- wave frequency, spectroscopic investigation of small single crystal dendritic platelets. The specimens of nickel and nominally 82 nickel-18 iron are grown by a vapor transport technique [ I , 21 and usually have a

< 100 > axis normal to the plate. Multiple modes are observed in the microwave spectra, and we present evidence indicating that these modes are mainly of a magnetostatic type, previously observed only for nonmetallic ferrimagnets [3, 41. The experiments are carried out a t frequencies of 12 G H z and 24 GHz, a n d in the geometry in which the D. C. magnetic field I& is either along the normal (n) (perpendicular resonance), o r in the plane of the platelet (parallel resonance). The microwave magnetic field is always normal to Ho.

We have examined spectra from samples of various shapes : squares, right triangles, long rectangular a n d triangular blades, and one long thin wedge.

Figure I shows examples of the mode spectra obtained from these metallic crystals. The spectra show mul- tiple standing waves whose intensities decrease steadily a s one moves away from the main resonance. For perpendicular resonar;ce the modes die out at a field of about 2 n M below the main resonance. The main resonance, itself, is found a t the usual field for ferromagnetic resonance for both parallel and perpen- dicular cases respectively [5].

A major feature t o be noted in figure l a for a nickel- iron platelet in perpendicular resonance is that the mode spacing decreases with increasing separation from the main resonance. The dispersion relation for

(*) Supported in part by the National Science Foundation.

(**) Present address : Naval Ordnance Laboratory, Washing- ton, D. C.

24GHz NiFe

M.850

n 11% ^Qb,. _{T p I} ^12GHz

A ,

^M

FIG. 1. - Parallel and perpendicular field spectra for : a. NiFe triangular blade, b. NiFe long thin wedgc,

Ni triangle. Note that a 2 degree change in ficld angle enhances the structure.

Intensity scales are arbitrary.

this sample is shown in figure 2 for both perpendicular a n d parallel resonance. This effect is also clearly

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19711416

STANDING WAVES IN THE MICROWAVE SPECTRA OF Ni A N D NiFe SINGLE CRYSTAL C 1 - 1163

-

Oe

H,,-H,,n Ni

5 ^M=83O

5 0 0 0 0

24 GHz

H,,

4000 -

"11-Yn

3000

mode theory ?or

= 28.7

n

FIG. 2. - Mode spacing analysis of the spectra of figure la.

The perpendicular field spectrum is matched with simple magne- tostatic mode theory.

seen in figure Ib for a sample of nickel-iron whose shape is that of a thin wedge. A second major feature of the nickel-iron spectra is that the modes for per- pendicular resonance are on the low field side of the main resonance, whereas the modes for parallel resonance are on the high field side. We have also noted that the nickel-iron platelet spectra vary some- what for different sample shapes. Typical dimensions for the nickel iron platelets are of the order of 20 microns thick and 1 mm in lateral dimension.

The case of the nickel platelets is not as well cha- racterized. The samples are somewhat thinner than the nickel-iron platelets and tend t o be triangular or rectangular in shape. Spectra at 12 Gc/s show a strong main resonance and sometimes weak, but distinct, multiple resonances (Fig. lc). The intensity of these modes shows a strong angular dependence close t o perpendicular resonance. Multiple resonances have not yet been observed in nickel platelets at 24 GHz.

For the geometry of a thin plate we may consider the available possibilities for multiple resonance modes. These would appear to be spin wave modes [6] and magnetostatic modes 131. The spin wave modes are characterized by a wave vector normal to the plate (k 11 n) and should show a quadratic disper- sion relation, with mode spacing increasing away from the main resonance. It is well known, of course, that this dispersion relation may show a distortion away from quadratic, at low mode numbers [7].

A second relevant feature of the spin wave modes is that they occur always on the low field side of the main resonance for both perpendicular and parallel resonance. They are generally observed for specimens of thickness of several thousand Angstroms. By

contrast the magnetostatic modes are characterized by a wave vector with a transverse component (k I n), but which is not large enough t o involve significant exchange energies. The mode spacing ^decreases with increasing separation from the main resonance, and for the geometry of a plate, the modes are expected to be on the low field side of the main resonance for perpendicular resonance, and on the high field side for parallel resonance [3]. In the case of dielectric ferrimagnets the modes have generally been observed when the thickness (dj to lateral dimension (L) ratio (aspect ratio) has been of the order lo-' t o lo-'.

The mode spacing is approximately proportional to the product of this ratio and the magnetization.

From the evidence of figure 1 and the dispersion curves of figure 2 it is clear that the nickel-iron plate- lets and wedge are showing modes of the magneto- static type. Although the aspect ratio of these samples is smaller, by about a factor of 3, than the samples of reference [3], the magnetization is larger by approxi- mately the same factor. However, the nickel samples spectra cannot yet be definitely characterized as either spin wave or magnetostatic.

There are several difficulties which prevent an immediate quantitative comparison between magne- tostatic mode theory and the spectra of the nickel- iron specimens. The usual theories of magnetostatic modes are for cases of simple shapes such as circular discs, square or rectangular plates. The initial observa- tions presented here have been made on awkward or irregular geometric shapes, however, it is clear from the nature of magnetostatic modes and the calculations which have already been carried out, that this wiil not change the qualitative conclusions that we have been able to draw.

An example of such a qualitative comparison is given for the specimen of figure la. We take the simple relation for magnetostatic modes in a rectangular insulating sample.

where o is the microwave angular frequency, y the gyromagnetic ratio, n the mode number,

and M is the magnetization. Figure 2 shows the fit of the data to this expression with M = 850 e. m. u.

and for a ratio L/d = 28.7 which is the best fit to the lowest mode spacings. This approximate aspect ratio is typical for these samples.

A further difficulty for comparison between experi- ment and present theory lies in the metallic nature of the samples. We expect that this will not drastically change the magnetostatic mode solutions obtained for dielectric materials, but the probIem is somewhat more complicated and the modes will certainly be broa- dened by eddy current damping effects.

In conclusion we believe that we have demonstrated

C 1 - 1164 T. G . PHILLIPS A N D L. W. RUPP, J A N D A. YELON, R. C. BARKER A N D C. VITTORRIA

that the initial observation of standing wave spectra the nickel-iron platelets. The pure nickel platelet in single crystal metal dendrites presented here is an spectra show weaker modes which we have not yet indication of magnetostatic mode effects, at least for been able to characterize.

References

[I] DEBLOIS (R. W.), J. Appl. Phys., 1965, 36, 1647. [4] DILLON (J. F.), J. Appl. Phys., 1960, 31, 1605.

[2] BRENNER (S. S.), Acta Met., 1956, 4 , 62. [5] RODBELL (D. S.), Physics, 1965, 1, 279.

[3] SPARKS (M.), TIITMAN (B. R.), MEE (J. E.) and NEW- [6] KITTEL (C.), Phys. Rev., 1958, 110, 1295.

KIRK (C.), J . Appl. Phys., 1969; 40,1518. [7] PHILLIPS (T. G.), Proc. Roy. SOC., 1966, A 292, 224.