SKIN DEPTH EFFECT IN THE RF COLLAPSE STUDIES

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SKIN DEPTH EFFECT IN THE RF COLLAPSE STUDIES

G. Karczewski, M. Kopcewicz, A. Kotlicki

To cite this version:

G. Karczewski, M. Kopcewicz, A. Kotlicki. SKIN DEPTH EFFECT IN THE RF COLLAPSE STUD- IES. Journal de Physique Colloques, 1980, 41 (C1), pp.C1-217-C1-218. �10.1051/jphyscol:1980169�.

�jpa-00219738�

JOURNAL Dl? PHYSIQUE

Colloque Cl , supplkment au no

1 ,

Tome 41, janvier 1980, page C1-217

SKIN DEPTH EFFECT I N THE RF COLLAPSE STUDIES

G. Karczewski, M. Kopcewicz and A. Kotlicki I n s t i t u t e of Experimental Physics, Warsaw Unive

In the M6ssbauer studies of

the r£

effects induced i n ferlomagnetic materials per£omed so f a r the skin depth problem was not discussed i n detail.

Especially when studying the r f collapse effect (see e.g./l

,

2, 3/) the discrepancy between the cal- culated skin depth

and the

observed changes i n the mssbauer spectra is evident. The skin depth is cal-

culated i n a conventional way according to the for-

a a :

6=L?ir,, p

^{( 1 )}

where p is the specific resistivity,

p

is the mg- netic permeability

and v

is the frequency. In the only paperr in which the skin depth effect was men- tioned in w m c t i o n with the r f iduced effects / I /

d

was calculated. using the s t a t i c value of

p .

The skin depth calculated for b a r f o i l a t 50 MHz using typical value of f' and s t a t i c value of

r

(?=I203

+

6000, /4/) varies from 0.2 to 0.5pm.

The thickness of the samples normally used i n Mijss-

bauer experinmts i s 10 to 20pm, so the skin depth calculated i n t h i s way i s

two

orders of magnitude d l e r than the thickness of the typical sample.

Since the external r f field decreases within the rretallic f o i l as:

HT = H,, exp (- 5)

⁽²⁾

where

H0

^is the r f field intensity a t the -1e surface,

then

the major part of the sample volume should m t be affected by the rf field. H m e r , the rf wllapsed spectra show / I , 2, 3/ that the whole volume of the sample is affected by the r f field even when the sample i s about 50 times thic- ker than the skin depth calculated according to the formula (1 ⁾ with the use of the s t a t i c value of

p .

TI

solve t h i s discrepancy we suggest that the strong frequency dependence of the magnetic permea- b i l i t y should be considered. It is well

known

/5/

that the effective magnetic permeability depends on the frequency of an applied magnetic field

and

de- creases markedly for high frequencies when a m p r e d w i t h the s t a t i c value typical for a given ferrcnnag- net. When one assumes that in the extreme cases of the r f collapsed spectrum

the

permeability decre- ases to the value of the order of 1 for the fre- quency of about 50?.PIz,

then

the skin depth calcu- lated with p(v)~l is of the order of 10

pm.

r s i t y , 00-681 Warszawa, Hoza 69, Poland

T h e present paper reports the results of an experiment &ere this assumption was veryfied. The rf collapse effect was studied for invar samples of the cornpsition: 37.00%Ni-61. 98%Fe-0.02%Mn, am3 the thicknesses

( d l :

12, 17, 30, 41, 46, 61 and 80 m.

The samples were prepared

ard

the experiment was

P

performed in the sane way as in /2/. The intensity of the 50 MHz r£ field applied varied from 3 to 11

oe.

The skin depth

4

calculated w i t h

pO&l ,

^V=50

-?¶Hz and

p

=9Op.kan is equal to 18pm. So, the sanp- l e thicknesses studied cover the range

from

l e s s

than

one skin depthd; (for I2pm) to 4 . 5 4 (for 80

pm)

-

Typical results obtained for the r f collapse effect as a function of the sample thickness are re- ported i n Figs.1 and 2. Figs. IA, IB, 1C an3 ID pre- sent the MBssbauer spectra obtained for

the

rf field intensity of 5.7 Oe for

the

sample thicknesses of 12, 17, 30 and 41 p m , respectively. Fig. 2 shows similar results obtained a t 7.5 Ce for the s a q l e s of 12, 17, 30, 41, 46, 61 and 80pm; spectra 1E and 2H were obtained for 41pm sample i n

the

absence of the r f field.

The results obtained suggest that the rf col- lapse effect depends strongly on

the

sanple thick- ness when the frequency and the intensity of

the

r f field are fixed. A s can be seen from Fig. 1 the 5.7 Oe rf field is large enough to collapse the spectrum to a single broad line for the 12

pm

s a m ple (Fig. 1A)

.

m e other spectra are less narnmcd, and

the

spectrum of the 41

pm

sample is only slight- l y affected by the rf field (Fig. ID) ., In this case the r f field is considerably reduced due to the skih effect

and is too

d l to force the magnetization reversal f a s t enough t o collapse

the h£

spectrum.

In Fig. 2 the skin depth effect i s much n-ore dis- tinguish. For

tkin

samples (12

-

30pm) the spec- t r a are c a p l e t e l y collapsed

to

a single narrow li- ne which .is accompanied by

r£

sidebands. ?hickne- sses of these samples ake still smaller

than

26;.

With the increase of

the

sample thickness the spec t r a still consisting of a single l i r e are conside- rably broader,Figs. 2D

-

^2F. Skin depth effect

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1980169

C l - 2 1 8 JOURNAL DE PHYSIQUE

which reduces (-)0 starts to be important for the sam- ple thickness comparable to 2 fA . For the thickest sample studied (Fig. 2G) the spectrum obtained con- sists of partly resolved hf lines. In this case the thickness of the sample is about 4.5 of , so the skin depth effect very strongly reduces H© field which is then too small to force fast enough rela- xation of the hf field to average it to zero.

"a 3 8 9 f - r r f - ^ V M * ^ rfWVA-V'- 1 5 0j L « B ;,

c5 375!- ** c I w

0 , 8

i

D

| . - ,

j£ ^ * " \ / ^ ^ ' " * ^x 235 » W M ^ S A W * - ^ * ^

if

E

T 1 V

Q 213 (W*!** "W*»* « < w vi MM, v l 5 1

Www ?f—-\/-—^

- 8 - 4 0 4 8 Vi33*p- * E ,f

VELOCITY Cmm/s) §"'" f — ^ ' - S s ~"""""

"4 V

f

,-.

Fig. 1 4 , 0-

!00r V V T H , 213 W * * ^ » « « . •"WW-****"*

Www

I I I I I - 8 - 4 0 * 6

VEI OCITY [ m m f e l

Fig. 2

Basing on the spectra obtained it is possible to evaluate the skin depth from the experiment. It is assumed that in thick samples the rf field which is responsible for the collapse effect is equal to the average value of the rf field applied. To cal- culate the average value of Hj* field the formula (2) was integrated in the limit of 0 to -i where <JL is the thickness of the sample. The average rf field acting within the sample is then:

Hr

^f

=H

⁰

^[^-expC~^)] (3)

Since H0 and d. are known it is possible to calcula- te H « for all the samples with tne skin depth a as a parameter. In order to estimate (T the Mossbauer spectra with the same full width at half depth ob- tained for different sample thicknesses clj, and rf fields M0were assumed to be equivalent (see e.g.

Fig. 1B and 2F, etc.). Hence the set of equations with o as a parameter was found:

H

ⁿ

tH.

^l

,Ae;= HrfCHJ^j) (4)

The number of equations is equal to the number of pairs of thr spectra with similar full widths at half depth. The parameter cT was calculated numeri- cally to fulfill the set of equations (4). The skin depth found in this way varied from about 10 urn to about 40pm. Since this method of evaluation of the skin depth is not very accurate the agreement of the experimentally estimated $ and the calcula- ted value with the assumption that yjy)-*} is quite good.

The experiment described shows that the skin depth effect can not be treated in a conventional way when interpreting the rf induced effects, and that the strong frequency dependence of the magne- tic permeability should be taken into account.

Acknowledgements. The authors are indepted to Dr. I. Sosnowska for her interest in this study.

One of the authors (MK) is deeply grateful to Professor U. Gonser for fruitful discussions.

Thanks are due to Mr. S. Fijalkowski for the con- struction of the rf generator and technical assis- tance.

References

1. L. Pfeiffer, in "Mosshauer Effect Methodology", ed. I. J. Gruverman, Plenum Press, New York 1972, vol. 7, p. 263.

2. M. Kopcewicz, J. Physique Coll. 37 (1976) 109, and Phys. Stat. Sol. (a) 46_ (1978) 265.

3. J. V. Baldokhin, V. A. Makarov, E. F. Makarov, V. A. Povitskii, Phys. Stat. Sol. (a) Tj_ (1975)

265.

4. K. Hoselitz, "Ferromagnetic Properties of Me- tals and Alloys", Plenum Press, New York 1952, p. 263.

5. S. W. Wbnsowskij, "Magnetizm", Nauka, Moskwa 1971, p. 881.