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CALCULATION OF MAGNETO-OPTICAL SPECTRA
IN COMPOSITIONALLY-MODULATED
MULTILAYERED FILMS
K. Sato, H. Kida
To cite this version:
K.
Sato,
H.
Kida.
CALCULATION
OF
MAGNETO-OPTICAL
SPECTRA
IN
JOURNAL DE PHYSIQUE
Colloque C8, Supplement au n° 12, Tome 49, decembre 1988
C8 - 1779
C A L C U L A T I O N O F M A G N E T O - O P T I C A L S P E C T R A I N C O M P O S I T I O N A L L Y - M O D U L A T E D M U L T I L A Y E R E D F I L M S
K. Sato and H. Kida1
Tokyo University of Agriculture and Technology, Koganei, Tokyo 184, Japan
A b s t r a c t . - Magneto-optical spectrum of compositionally modulated multilayered thin films (CMF) of transition metal/noble metal structure is calculated by using virtual optical constant method, by which most of the experimen-tal results are explained. The physical reasons of enhancement of magneto-optical effect are discussed.
Compositionally-modulated multilayered films (CMF) are of recent interest among researchers of new magnetic materials. Magneto-optical studies in those of transition metal/noble metal structure by Katayama el al. [1, 2] have gained much attention, as they first showed the possibility of controlling the magneto-optical Kerr effect (MOKE) by employing the CMF structure. One of their results is shown in fig-ure l a , in which an enhancement of MOKE in Fe/Cu CMF around the wavelength of the absorption edge of Cu is observed.
We have carried out a sitaulation of MOKE spec-trum in CMF with the same composition and thickness ratio in terms of the virtual optical constant method proposed by Ohta et al. [5] by using reported values of the diagonal and off-diagonal elements of the di-electric tensors in Fe and Cu [6, 7] with no adjustable parameters employed. The calculated virtual optical constants can be interpreted as the renormalization of the multiple reflection and interference effects into a single set of optical constants, which should converge to the value deduced from the averaged dielectric con-stant in the limit of the least modulation length. Most of the experimental MOKE spectra have been quan-titatively explained [3, 4] as shown in figure l b . The fact t h a t the multiple reflection plays an important role in the magneto-optical spectrum of CMF means t h a t consideration of the light-phase is important even in such a layer as order of magnitude thinner than the wavelength of light.
Next, we discuss on the physical meaning of the en-hancement of the MOKE in the transition metal/noble metal CMF's. In our previous papers [3, 4] we sug-gested that the enhancement of MOKE is caused by the reduction of dielectric constant due to the plasma resonance at the wavelength of the absorption edge in the noble metal. Strictly speaking, however, silver is the only one in the tttree noble metal species t h a t has a plasma edge at the absorption edge; i.e. the real part of the dielectric constant crosses zero only in Ag but remains negative in Au and Cu.
Fig. 1. - Spectra of polar Kerr rotation in Fe/Cu CMF's. Curves denoted as "Cu(Fe)-surface" are those with Cu(Fe) layer at the uppermost surface. Fe/Cu thickness ratio is kept constant (= 0.62) and modulation length is taken as a parameter. Kerr rotation spectrum in a Fe film is also shown in the figure, (a) Experiment [2], (b) calculation.
To clarify the nature of the enhancement of MOKE due t o plasma resonance, we have calculated MOKE spectra in Fe/noble metal CMF's with Fe at the sur-face, keeping the thickness ratio of Fe/noble metal con-stant ( = 0.62) and the modulation length D = 162 A. The results are shown in figure 2. A sharp and clear
Present address: Takenaka Komuten Ltd. Kobe, Japan.
C8 - 1780 JOURNAL DE PHYSIQUE
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3b0
460 5b0 6bo 760 E J ~ O WAVELENGTH ( n m )Fig. 2. - Spectra of polar Kerr rotation in Fe/Cu, Fe/Au and Fe/Ag CMF's calculated by the virtual optical constant method for Fe-surfaced case with Fe/Cu ratio = 0.62 and modulation length = 162 A.
peak of MOKE appears in the Fe/Ag CMF, while broad peaks are seen in Fe/Cu and Fe/Au. This ten- dency is consistent with that observed by the experi- ments [I].
When D is increased the MOKE peak shifts to longer wavelength in both Fe/Cu and Fe/Ag CMF's as shown in figures 3a and b. For large D
(N
1 000 A),
the plasma-enhanced peak is broadened in both
0;1, 4b0 €60 800 ldo0 1200 W A V E L E N G T H ( n m )
0 I I
200 400 600 800 1000 1200
WAVELENGTH (nm)
Fig. 3. - Variation of MOKE spectra with the modulation length in (a) Fe/Cu CMF's and (b) Fe/Ag CMF's. CMF's, and gross features in the spectral dependence of the MOKE seems to be independent of the noble metal species. Since the penetration depth of the light is limitted to no more than 1 or 2 layers for such a large D , the noble metal simply behaves as a reflecting mirror in the back of the magneto-optical layer. En- hancement of MOKE due t o the interference between Kerr (reflection) and Faraday (transmission) effects oc- curs in this case. The tendency is consistent with the experimental Kerr spectrum in bi-layered films [8].
Although most of the calculated results can ac- count for the experimental results quantitatively, they
showed substantial disagreement in the small D limit: the experimental value of peak Kerr rotation decreases rapidly as D becomes smaller than 50
A,
while the cab culated rotation tends t o a finite value as D goes tozero. The discrepancy seems to result from the devia- tion from an ideal Fe/Cu structure: The tendency has been explained by assuming that single atomic layer (about 2
A)
at both interfaces of the Fe-layer loses magneto-optical effect [3]. We tentatively attribute the loss of magneto-optical effect to slight alloying be- tween Fe and noble metal, although Fe and Cu are not alloy-making pair in equilibrium. On the contrary, in the case of the Fe/Ge CMF's, where Fe and Ge are alloy-making pair in equilibrium condition, experimen- tal MOKE spectra could hardly been explained by the simple optical theory [9]. Alloying effect seems to be essential in the latter case.In summary, the enhancement mechanism of MOKE in CMF of Fe/noble metal structures can be classi- fied in two categories: (1) small D limit, in which the plasma enhancement is significant and (2) large D limit, in which the reflector effect by the noble metal works. We have, thus, become able to predict and design the MOKE spectra in CMF's of transition metal/noble metal structure provided that no alloying effects occur.
Acknowledgments
Authors are very grateful to Dr. T. Katayama for kind discussions. This work has been partly supported by the Grant-in-Aid for Special Project Research from the Ministry of Education, Science and Culture of Japan.
[l] Katayama, T., Awano, H. and Koshizuka, N., J.
Phys. Soc. Jpn 55 (1986) 2539.
[2] Katayama, T., Awano, H., Nishihara, Y. and Koshizuka, N., IEEE Trans. Magn. MAG-23
(1987) 2949.
[3] Sato, K., Kida, H. and ~ a t a ~ a m a , T., Jpn J. Appl. Phys. 27 (1988) L237.
[4] Sato, K. and Kida, H., J. Magn. Soc. Jpn 12
(1988) 329. (In Japanese; English translation will appear in IEEE TJMJ).
[5] Ohta, K., Takahashi, A., Deguchi, T., Hyuga, T., Kobayashi, S. and Yamaoka, H., SPIE 382 (1983)
252.
[6] Landolt-Bornstein, New Ser. 111-15b (Springer) 1980, p. 210.
[7] Krinchik, G. S. and Artemjev, V. A., Sou. Phys. JETP (Engl. trans.) 26 (1968) 1080.
[8] Katayama, T., Suzuki, Y., Awano, H., Nishihara, Y. and Koshizuka, N., Phys.
Rev.
Lett. 60 (1988) 1426.[9] Yazawa, M., Iwata, S. and Uchiyama, S., J. Magn. Soc. Jpn 12 (1988) 311-315 (In Japanese; English
