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Figures of merit for magneto-optic materials
0022-3697(95)00119-O
Pergamon
FIGURES
OF MERIT
1. P/Iw. C/WI. Solids Vol. 56. No. I I. pp. 1499-1507. 1995 Ekvier Science Ltd Prmted in Great Britain. 0022-3697195 $9.50 + 0.00
FOR MAGNETO-OPTIC
WILLIAM
MATERIALS
A. CHALLENER
3M Information, Imaging, and Electronics Sector Laboratory, 3M Center Bldg 201-IN-34, St Paul, MN 55144-1000, U.S.A. (Received 7 April 1995; accepted I April 1995)
Abstract--In the development of magneto-optic (MO) materials for device applications it is important to be able to quickly and quantitatively compare the expected performance of new materials with others previously developed. Several ‘figures of merit’ are in common use for doing this. We consider their relative advantages and disadvantages. Kewords:
A. magnetic materials, A. multilayers, A. thin films, D. optical properties
1. INTRODUCTION First
generation
MO media
disks with 625 MBytes
on 5ain double-sided
of user data corresponds
to
In the near future media with four times this density will be available. Part of this increase in storage density has been due to a reduction in laser wavelength from 830 nm to 680 nm, with a corresponding reduction in the size of the diffraction-limited focused spot used to record and read the magnetic marks on the media. The availability of lasers, either semiconductor or frequency-doubled, with even shorter wavelengths are expected to enable further increases in storage density. Several different amorphous rare earth-transition metal (RE-TM) alloys have found extensive use in MO media. Examples include TbFe, TbFeCo, GdTbCo, and NdDyFeCo. TbFeCo is probably the most commonly used material and is generally considered the prototype against which other materials are compared. These materials have many desirable characteristics, such as perpendicular anisotropy, easily adjustable compensation and Curie points, low noise due to their amorphous structure, high coercivity, etc., as well as a few undesirable characteristics including rather small MO activity and high chemical reactivity. Fortuitously, the MO activity and these materials peaks in the near-infrared to red regions of the spectrum, make them suitable for use at standard semiconductor laser wavelengths. However, their MO activity tends to drop fairly quickly at shorter wavelengths [l], making their continued use in future higher density media problematic. As a result there is a keen interest in materials research aimed at developing new materials with improved MO properties. an approximate
area1 density
of 4 x IO7 bits/cm2.
New materials must undergo a wide variety of tests before they can be incorporated into a successful product. A dynamic performance test is always a critical part of this process for measuring such things as mark length jitter and background noise, laser power and magnetic field recording sensitivity, cycling stability, etc. Nevertheless, it is also important to be able to apply some criterion based on static measurements of optical and magnetic properties which may not guarantee a successful new material, but at least may quickly eliminate materials which have no hope of success from the time-consuming process of designing new media for dynamic performance testing. Hence we are led to the use of some form of ‘figure of merit’ (FOM) to distinguish between different MO materials and indicate those candidates for further testing and potential media design. Figures of merit in this sense are generally meant to correlate with the signal or perhaps the SNR that might be expected from a media designed using the MO material in question. The most general technique for assessing the MO properties of a new material is to determine its complete dielectric tensor at all wavelengths of interest, and then using a general computer model design a thin film stack with appropriate dielectric and metallic thin films in addition to the MO layer to optimize the film stack with respect to important optical parameters, such as reflectance, Kerr rotation, and Kerr ellipticity. Such models and optimization procedures have been described in the literature [2-91. Eventually either this process or a lengthy experimental process of trial-anderror, or some combination of the two must always be undertaken to optimize the MO media with the new MO material. Although optical media design is relatively straightforward for those who have the appropriate computer models, it is clearly useful to have a 1499
W. A. CHALLENER
1500
Fig. 1. Schematic of disk drive. PBS is a polarizing beamsplitter, and LPBS is a leaky polarizing beamsplitter. simpler FOM for judging MO materials which does not rely on the particular optical properties of any other material than the MO material, or on a particular film stack design. At this point it is useful to briefly review the operation of an MO disk drive. A schematic of an MO drive is shown in Fig. 1. Linearly polarized light is incident on the media, which is generally on the back surface of a transparent (glass or plastic) substrate. The light reflected from the thin film stack has a component polarized perpendicular to the incident polarization which may have an arbitrary phase shift with respect to the reflected parallel polarization component. The thin film stack of standard MO media is usually designed to make this phase shift as small as possible. This allows the optics of the disk drives to be matched to that of the disks for maximum signal and standardization. There are also noise considerations related to birefringence in the substrate that favor minimizing the phase shift [lo]. When the phase shift is zero, the reflected light is still linearly polarized but with a small rotation. A nonzero phase shift causes the reflected polarization to become elliptical. Kerr rotation and ellipticity both result from the different indices of refraction for the two circular polarizations in the MO material, and hence both rotation and ellipticity change sign when the magnetic moment is reversed. Therefore, both rotation and ellipticity carry information about the magnetic state of the recorded marks and in principle either can be used for signal detection. By compensating for the phase shift in the media by including a suitable retarder in the optics of the disk drive and employing a differential detection scheme, the maximum signal (to first-order in rotation and ellipticity) is proportional to [lo- 121 Signal=
amplifiers and servo systems for maintaining accurate focus and tracking control. Media noise arises in both the substrate and thin films. Birefringence in the substrate distorts the beam shape and polarization state of the light, affecting both recording and readback processes. Surface roughness in the substrate as well as irregularity in the groove profile give rise to noise. Irregularity in the edges and/or lengths of recorded marks due to domain wall dynamics in the MO layer also contributes to noise. If the MO material is not amorphous, microcrystallites with random orientations and optical properties cause increased noise. Some of these noise sources are well understood and easily characterized, while others are quite difficult [20] or impossible to describe in a simple analytic form suitable for a figure of merit. Detector shot noise is a physically unavoidable source of noise and so in some sense it provides the ultimate limit to the SNR. Because shot noise is proportional to the square root of the light intensity incident on the detectors [21,22], eqn (1) can be modified to SNR,,,,, cc dR(Q’ + E’) Unfortunately, the noise sources associated with the media thin films and substrate, not the shot noise, are usually dominant in the current generation of MO media, so a FOM based on shot noise limited SNR is somewhat questionable. Nevertheless, a useful figure of merit for comparison of different MO materials may be related to either eqn (1) or eqn (2). It should also be mentioned in Fig. 1 that the reflected light also provides feedback to the tracking and focus servos. While it has been suggested [23] that one can maximize the SNRsh,, by minimizing the reflected light intensity, this is really not an option in practical drive systems. In fact, the MO media is generally designed to have about 20% normal incidence reflectance from the inside (thin film) surface. In order to adjust reflectance and phase shift of the media, the quadrilayer film stack has been widely adopted in the industry as shown in Fig. 2.
(1)
where R is the reflectance of the media, eK is the Kerr rotation, and eK is the Kerr ellipticity. There are a variety of noise sources in MO recording/reading [13-191. Laser noise can affect both the recording and read-back process. There is shot noise in the detectors and electronic noise in both the
Fig. 2. Standard quadrilayer thin film stack for MO media.
1501
Figures of merit for magneto-optic materials Qualitatively speaking, the thickness and refractive index of the dielectric barrier are adjusted to give the desired reflectance, while the thickness and index of the dielectric spacer are adjusted to minimize Kerr ellipticity in the reflected light. The reflector is optically opaque to maximize the signal.
2. KERR ROTATION AND ELLIF’TICITY Measurement of the magneto-optic Kerr rotation and/or Kerr ellipticity is probably the most commonly used FOM for comparison between different MO materials [24-431. The FOM is FOM = BK
(3)
or FOM=&+t;.
(4)
The bulk Kerr rotation and ellipticity are not directly related to signal or SNR as given by eqns (1) and (2). To first order in terms of the dielectric tensor or index of refraction for an opaque film (see the Appendix for the appropriate definitions and conventions),
dielectric layer, so direct comparison to other materials is again questionable. One big disadvantage of using Kerr rotation alone as a FOM is that it has led to considerable confusion among some segments of the magneto-optics community. For example, thin film stacks have been ‘optimized’ to maximize the Kerr rotation without regard to the reflectance of the film stack [45-471. While it is true that by careful design of an antireflection film on top of the MO layer very large Kerr rotations can be obtained, such film stacks are of no use in practical MO media. The primary advantage of using Kerr rotation as a FOM is its simplicity of measurement or calculation from the dielectric tensor. However, Kerr rotation by itself is not useful for comparison of completely different MO materials. This can be illustrated by a simple example. Suppose the index of refraction for right and left circular polarizations of a hypothetical material is N* = (2 f 0.1) + i(4 F 0.1233)
(6)
which corresponds to the dielectric tensor -12 + i(16) E= +0.307 - i( 1.39) [
0
-0.307 + i( 1.39)
0
-12 + i( 16)
0
0
-12+i(16)
1 (7)
= 2[(-2nK)An
+ (n2 - K2 - l)AK]
(n2 - K2 - 1)2 + (2nK)2
Although Kerr rotation and ellipticity can be considered intrinsic magneto-optical properties of a bulk material, the interpretation of these properties in terms of underlying MO electronic transitions is not necessarily straightforward [44]. In the case of a thin film it is not justified in general to consider Kerr rotation and ellipticity as intrinsic properties, due to interference effects within the film from reflections at the interfaces which may either enhance or reduce the Kerr rotation and ellipticity over the bulk values. If Kerr rotation and/or ellipticity data are to be used as a FOM on thin films, then at the very least the measurements must be made on an optically opaque (thick) film to avoid these effects. Another difficulty arises when the materials are highly reactive, as in the case of the RE-TM alloys. In this case the Kerr rotation must either be measured in vacuum during deposition, or the films must be deposited on a transparent substrate or overcoated by a protective dielectric film. In either of the latter two cases the Kerr rotation and ellipticity are functions not only of the MO material but also of the thickness and refractive index of the substrate or
This material will actually exhibit zero Kerr rotation! Yet it obviously has a large off-diagonal MO component. In fact, it can be shown that an optimized thin film stack can be designed with such a material giving 20% reflectance and over 4” of Kerr rotation. More generally, from eqn (5) we see that whenever
the Kerr rotation is zero. Similarly. whenever AK=
(“-2f;-‘)An
(9)
the Kerr ellipticity is zero. Clearly Kerr rotation by itself can be a very misleading FOM. From eqn (5) we also find that both Kerr rotation and Kerr ellipticity can be simultaneously zero for an absorbing film only if the material is nonmagnetic (i.e., An, AK = 0). Therefore, from an experimental point of view, there is a definite advantage to making both rotation and ellipticity measurements. Even when Kerr rotation is used as a FOM for comparison of small variations of composition within a general alloy family, such as when RE-TM ratios are varied or when the alloys are doped by small quantities of an additional element, caution must be
1502
W. A. CHALLENER
used in interpreting the results. As can be seen from eqn (5), depending on the values of n, K, An, and AK, the addition of a dopant which causes 18~1to decrease may actually be due to an increase in IAn( or \AK(, and in an optimally designed thin film stack the doped material would exhibit a larger signal than the undoped material. An example will illustrate this more clearly. Suppose we have another hypothetical material with n = 2, An = +0.025, K = 4, and AK = -0.0125. The Kerr rotation of the bulk material would be -0.06”, and the Kerr rotation of an optimized film stack with 20% reflectance would be 0.8”. Now, if this material were doped in such a way that AK changed to -0.025, and all other indices remained the same, the bulk Kerr rotation would drop to -0.02”, but the Kerr rotation for the optimized film stack would increase to 1.O”! 3. KERR ROTATION
AND REFLECTANCE
To partially eliminate the disadvantages of the Kerr rotation FOM, another widely used FOM [48-501 is
or FOM = d-
(11)
These equations are only superficially similar to eqn (2), because they refer to the bulk MO properties, not the properties of an optimized thin film stack. If this FOM for the bulk properties of a particular material is greater than that of a typical MO media film stack (for which R % 20% and OK4 1”), then the material will of course have sufficient MO activity in an optimized stack as well. On the other hand, if this FOM is smaller than that for a typical MO media film stack, as is usually the case, then this FOM is not sufficient to indicate suitability of the material in an optimized MO media film stack. It has the advantage of being a simple FOM to measure, and is definitely preferable to the Kerr rotation FOM for the additional information it provides. but is still far from being an ideal FOM.
affect the results. Unlike Kerr rotation measurements, Faraday rotation measurements require measurement of the thickness of the film, and the presence of the substrate is unavoidable. As a result, the Kerr rotation FOM is usually preferable to the Faraday rotation FOM.
5. VOIGT PARAMETER Occasionally the Voigt parameter is used for comparison of different MO materials. The Voigt parameter, Q, is a complex number given by the ratio of the off-diagonal component of the dielectric tensor to the on-diagonal component. To first order 1
-iQ
0
iQ
1
0
[ 0
0
1I
E=E~
(12)
The Voigt parameter contains information directly related to the intrinsic magneto-optical activity of the material, and can be used to compare the relative MO activity of closely related alloys [56-591, i.e., materials for which the on-diagonal component of the dielectric tensor is approximately the same. It is a more accurate determination of the potential usefulness of a material in MO media than Kerr measurements alone, because it is truly an intrinsic property of the material. Nevertheless, because there is not a direct connection between the Voigt parameter and the MO signal in a disk drive, the Voigt parameter is not by itself useful for comparing MO materials of completely different classes. Another problem is the fact that it is a complex number, which means that both real and imaginary parts must be compared separately between different materials, so it is not really a single number FOM. A final problem with the Voigt parameter is that no standard sign convention has been adopted in the magneto-optic literature, making comparison between papers by different authors sometimes quite difficult [60]. However, if the Voigt parameter and the ondiagonal dielectric constant are both measured, then the MO properties of the material have been completely characterized.
6. POTENTIAL
KERR COEFFICIENT
4. FARADAY ROTATION
Faraday rotation is also used occasionally as a FOM [51-551. It is generally more appropriate for transparent MO materials than highly absorbing ones. As a FOM it has all the advantages and disadvantages of Kerr rotation. In addition, if thin films are used for Faraday rotation measurements, they must be sufficiently thick and/or absorbing that interference effects within the thin film do not significantly
For incident linearly polarized light on a thin film stack, the Kerr coefficient is the amplitude of the component of the reflected light which is polarized perpendicular to the incident polarization. The magnitude of the Kerr coefficient is Jkj = Ii(r+ - r_)l = Ir(-
eK + &)I = Jm (13)
1503
Figures of merit for magneto-optic materials By comparison with eqn (2) we see that Ikl is proportional to the shot-noise limited SNR. It can be shown [61-641 that for an MO layer in a thin film stack,
IkIm =q&++2+AK’).
(14)
The interesting feature about this equation is that it is expressed in terms of the index of refraction of the MO layer and the reflectance of the entire stack, which can be adjusted independently by dielectric layers between the incident light and the MO layer. By choosing appropriate dielectric layers to minimize R, we obtain a FOM for maximizing the shot-noise limited SNR,
maximize the result with respect to R.We find that the maximum signal occurs for R = 4. It has been suggested that depositing the MO material on top of a reflector with n and K small is the best way to optimize an MO media thin film stack [73-751. This can be more effectively accomplished by using dielectric/metallic bilayer structures for the reflector [76], and it has been further suggested that such a bilayer structure might enable one to exceed the potential Kerr coefficient FOM limit [77]. Our numerical calculations indicate that this is indeed an effective way to optimize the film stack, but it is easy to show following the procedure in Ref. [61] that the potential Kerr coefficient FOM limit in eqn (15) applies to this type of reflector as well.
7.MAXIMUM KERR ROTATION (15) This FOM has been used to compare garnets and RE-TM alloys [65]. It has also been compared to Kerr rotation measurements on a variety of RE-TM samples, and its clear advantages as a predictor of performance in MO media are exhibited [66]. We notice that the FOM becomes very large as either n or K get small. Small n can occur at a plasma resonance, where an enhanced Kerr effect is a now well-understood phenomenon [41, 67-721. When K = 0 the MO material is perfectly transparent, so the enhanced Kerr effect in this case corresponds to an infinitely thick MO layer with a reflector on the back. We also see from eqn (14) that An and AK in principle are of equal importance to the Kerr signal of an optimized thin film stack. From eqns ( 13) and (14) we can also determine the reflectance which maximizes the signal given by eqn (1) rather than the SNRshot. To obtain the maximum signal we must multiply eqn (14) by fi and then
Equations (13) and (14) may be combined to derive the maximum Kerr rotation for a thin film stack with a specific reflectance [78].
_
(16)
2vQ
Of the figures of merit considered in this paper. this one is probably the most useful for MO media design for which the film stack reflectance is usually a fixed parameter. We now use this FOM for a specific example. As previously stated, amorphous TbFeCo is the prototype alloy for present MO media designed for use at wavelengths of 680-830nm. Although the industry has not settled definitively yet on the MO material for use at shorter wavelengths, there is a great deal of interest in nanolayered PtCo. It has been shown [79] that such nanolayered structures can be represented by a single dielectric tensor. It is therefore
TbFeCoTa
TbFeCoTa
400500600700800 Wavelength
'400500600700800 Wavelength
(1 -R)
(nm)
Fig. 3. MO index of refraction
for TbFeCoTa
as a function
(nm)
of wavelength.
1504
W. A. CHALLENER Ptco
g -0.0 2 -0.0 $ 2
-0.0 -0.0 -0. 400500600700800
Wavelength
(nm)
Wavelength
(nm)
Fig. 4. MO index of refraction for PtCo as a function of wavelength. interesting to compare these two materials by means of the maximum Kerr rotation FOM. In order to determine the optical constants of TbFeCo, we prepared a trilayer film stack of Sic/ Tb0,20Feo,~sCoo,,oTao,oz/SiC with each layer about 13 nm thick on a glass substrate. This MO composition is typical of that used in the industry for MO media. The addition of a small amount ofTa improves the corrosion resistance of the film. The Sic films also prevent oxidation of the MO layer. All films were sputtered by a magnetron in a vacuum system with a typical base pressure < 1.O x lo-’ Torr. The MO layer was deposited at a 2 mTorr Ar pressure from an alloy target. Film thicknesses were determined by a stylus profilometer. The optical constants of the Sic were first determined independently by reflectance and transmittance measurements on an SIC film on a glass substrate, and then reflectance, transmittance, and Kerr rotation and ellipticity were measured on the trilayer stack to obtain the optical constants of the MO layer. In all cases, measurements were made from both sides of the sample, and a computer model was used which correctly accounts for the incoherently reflected waves within the substrate to determine the optical constants of the thin film. The results expressed in terms of n, K, An, and AK as a function of wavelength are shown in Fig. 3. Maxlmum
OKFOM
A nanolayered PtCo sample with periodicity of 8& 3A and total thickness of 20 nm was also deposited on a glass substrate by magnetron sputtering in a 5 mTorr Kr atmosphere. The film exhibited perpendicular anisotropy with a square hysteresis loop, although with a very small room temperature coercivity of 1800e. Although this particular film would not be suitable for MO media because of its low coercivity, the FOM computed for this film is representative of other PtCo films with properties better suited to MO media. The same set of optical measurements were used to determine the optical constants shown in Fig. 4. It is interesting to note that AK for this sample was found to have the opposite sign to that of TbFeCo, which apparently does not agree with other results in the literature [80] for reasons that are not understood, although sign conventions may be the issue. MO media is typically designed to have an inside surface reflectance of about 20%. Therefore, the figure of merit we have chosen for comparison of these two MO alloys is that given by eqn (16) with R = 0.2. The results are shown in Fig. 5. The FOM predicts a similar maximum Kerr signal for optimized thin film stacks of either TbFeCo or PtCo with 20% reflectance at the longer wavelengths. The FOM for the PtCo film increases at shorter wavelengths, while that of the TbFeCo film decreases, indicating the superiority of PtCo for maximizing signal at the shorter wavelengths. It is interesting, however, that the maximum Kerr rotation predicted for an optimized TbFeCo thin film stack at 400nm is actually quite reasonable for device applications. Depending on noise considerations and other factors, TbFeCo or a related RE-TM alloy may in fact be suitable for short wavelength recording.
8. CONCLUSIONS Wavelength
(nm)
Fig. 5. Comparison of the maximum Kerr rotation FOM for TbFeCoTa and PtCo as a function of wavelength.
Several different figures of merit found commonly in the MO literature have been described, including
Figures of merit for magneto-optic materials their advantages found
and disadvantages.
to be the most commonly
FOM, and easiest to measure,
Kerr rotation
but also one of the least
useful figures of merit for predicting obtainable Kerr
from an optimized
rotation
measurements
highly
misleading.
The
FOM
and closely
related
is
used and simplest the MO signal
thin film stack. In fact, by themselves
potential maximum
Kerr Kerr
can be
coefficient rotation
1505
5. Mansuripur M., J. Appl. Phys. 67,6466 (1990). 6. Challener W. A. and Grove S. L., Appl. Opt. 29, 3040 (1990). 7. Atkinson R., Salter I. W. and Xu J., J. Mugn. Magn. Mater. 102, 357 (1991). 8. Atkinson R., Salter I. W. and Xu J., J. Magn. Magn. Mater. 104-107, 1013 (1992). 9. Atkinson R., J. Magn. Mann. Mater. 124, 178 (1993). 10. Challener W. A. and Rinehart T. A., Appt. Opt. 26,3974
, , (*987’.
Chen’D., Appl. Opt. 13,767 (1974). 12. Bernstein P: and Guegnon C., IEEE ‘1.
FOM appear to be the best predictors mance in an optimized
of MO perfor-
thin film stack. These are also
more difficult figures of merit to obtain as they require
complete determination of the dielectric tensor of the material. Nevertheless, the additional effort is probably worthwhile in most cases. Several cautions applicable to all these figures of merit are in order. These figures of merit apply to normally incident plane waves upon a smooth surface. However, in standard MO disk drives the light is focused through a high N.A. lens onto the periodically grooved disk substrate. The typical quadrilayer film stack has been found to be particularly sensitive to high angle of incidence effects [81] and, therefore, may not perform as well as might be expected from a FOM calculation. In addition, the interference between various orders of the diffracted light can cause variations in the total reflected light intensity which are not accounted for by figures of merit calculated for a flat surface [ 151. Finally, and perhaps most importantly, none of these figures of merit take into account the potential sources of media noise from the MO layer due to nonuniform bit edges, microcrystallite scatterers, etc. Materials such as MnBi with a very large FOM nevertheless perform very poorly in MO media precisely because of the excess noise from grain boundary scattering. Using the maximum Kerr rotation FOM we have compared TbFeCo to PtCo, and find as expected that PtCo appears distinctly superior to TbFeCo for maximizing Kerr rotation at the shorter wavelengths. It remains to be seen, however, if PtCo or a RE-TM alloy or some other material will ultimately be successful in shorter wavelength MO media.
13. 14. 15. 16.
Trans.
Magn.
MAG-21, 1613 (1985). Brown B. R., IBM J. Res. Dev. 16, 19 (1972). Mansuripur M., Connell G. A. N. and Goodman J. W., J. Appt. Phys. 53,4485 (I 982). Dewey A. G., Proc. SPIE 695,72 (1986). Treves D. and Bloomberg D. S., Opt. Engng 25, 881
(1986). 17. Finkelstein B. I. and Williams W. C., Appl. Opt. 27, 703 (1988). 18. Dewey A. G., Proc. SPIE 1078,279 (1989). 19. Madison M. R.. J. Aool. Phvs. 73.5782 (1993) 20. McDaniel T. W’., Finkelstein B. 1: and Williams W. C., IEEE Trans. Magn. 24,2467 (1988). 21. Egashira K. and Yamada T., J. Appl. Phys. 45,3643 (1974). 22. Tang J. and Tang J., Appl. Opt. 29,2582 (1990). 23. Gamble R. and Lissberger P. H., J. Opt. Sot. Amer. A5,
1533 (1988). 24. Buschow K. H. J., van Engen P. G. and Jongebreur R., J. Magn. Magn. Muter. 38, 1 (1983). 25. Tsujimoto H., Shouji M. and Sakurai Y., IEEE Trans. Magn. MAG-19, 1757 (1983). 26. van Engen P. G., Buschow K. H. J. and Jongebreur R., Appl. Phys. Left. 42,202 (1983). 27. Masui S.. Kobavashi T.. Tsunashima S.. Uchivama S.. Sumiyama K. and Nakamura Y.. IEEE Trans. Magn.
MAG-20, 1036 (1984). 28. Imamura N., Tanaka S., Tanaka F. and Nagao Trans. Magn. MAG-21, 1607 (1985). 29. Reim W., Schoenes J., Hulliger F. and Vogt 0.. Mugn. Mater. 54-57, 1401 (1986). 30. Inukai T., Sugimoto N., Matsuoka M. and J. Magn. Sot. Jpn 11 (Supp. Sl), 217 (1987). 31. Ito H., Yamaguchi M. and Naoe M.. J. Appl. 5307 (1990).
Y., IEEE J. Magn. Ono K.. Phys. 67,
32. Kryder M. H., Shieh H.-P. and Hairston D. K., IEEE Trans. Mugn. MAG-23, 165 (1987). 33. Reim W.. Gambino R. J.. Ruf R. R. and Plaskett T. S.. J. Appl. ihys. 61,3349 (1987). 34. Suzuki T., Lin C.-J. and Bell A. E., ZEEE Trans. Mugn. 24,2452
(1988).
35. Honda S. and Yoshiyama M., Jpn. J. Appl. Phys. 27, 1687 (1988).
36. Weller D., Reim W. and Schrijner P., IEEE Mugn. 24,2554
Trans.
(1988).
37. Naoe M., Kitamura N. and Ito H., J. Appl. Phys. 63, would like to thank Dr W. C. Mitchell for the opportunity to attend the 1994 Conference on Magneto-optic Materials at Los Alamos, and for his suggestion for the topic of this paper. Acknowledgements--I
3850 (1988).
38. Kirby R. D., Shen J. X., Woollam J. A. and Sellmyer D. J., J. Appl. Phvs. 69,4574 (1991). 39. Gambino-R. J.,.Plaskett T. S., McGuire T. R. and McElfresh M. W.. J. AUDI. Phvs. 69.4750 (1991). 40. Shen J. X., Kirby R. D:,‘Sellmyer D: J. and Wang Y. J., J. Appl. Phys. 69,5984
REFERENCES Grove S. L. and Challener W. A., Jpn. J. Appt. Phys. 28, (Supp. 28-3), 51 (1989). Heavens 0. S., Optical Properties of Thin Solid Films. Dover Publications, New York (1991). Sprokel G. J., Appl. Opr. 23,3983 (1984). Balasubramanian K., Marathay A. S. and Macleod H. A., Thin Solid Films 164,391 (1988).
( 199 1).
41. Weller D., Brandle H., Gorman G., Lin C.-J. and Notarys H., Appl. Phvs. Letr. 61.2726 (1992). 42. Huang D., Zhang X: W., Luo C. P., Yang H. S. and Wane Y. J.. J. ADDI. Phvs. 75.6351 (1994). 43. Zhang Y., Rungk’A. P.: Shan Z. S. and Sellmyer D. J., J. Appl. Phys. 75,6354 (1994). 44. Feil H. and Haas C., Phys. Rev. Let/. 58, 65 (1987). 45. Sato R., Saito N. and Morishita T., IEEE Trans. Magn. 24,2458 (1988).
1506
W. A. CHALLENER
46. Kudo T., Johbetto H. and Ichiji K., J. Appl. Phys. 67, 4718 (1990). 47. Maeno Y., Kobayashi M., Oishi K. and Kawamura K., J. Appl. Phys. C&4325 (1990). 48. Suzuki T. and Katayama T., IEEE Trans. Magn. MAG-
22, 1230 (1986). 49. Iiyori H. and Takayama S., J. Appl. Phys. 69, 4161
Solid State Spectroscopy, pp. 245-248. North-Holland,
New York (1986). 85. Argyres P. N., Phys. Rev. 97,334 (1955). 86. Bennett H. S. and Stern E. A., Phys. Rev. 137, A448
(1965). 87. Connell G. A. N., Appl. Opr. 22, 3155 (1983).
(1991). 50.
Song K., Naoe M. and Ito H., J. Appl. Phys. 70, 6395
APPENDIX
(1991). 51. Gambino R. J. and McGuire T. R., J. Magn. Magn. Marer. 54-57, 1365 (1986). 52. Gambino R. J., McGuire T. R., Plaskett T. S. and Reim W., IEEE Trans. Magn. MAG-22, 1221(1986). 53. McGuire T. R., Gambino R. J., Plaskett T. S. and Reim W., J. Appl. Phys. 61, 3352 (1981). 54. Ostorero J., Guillot M. and Artinian M., IEEE Trans. Magn. 24, 2560 (1988). 55. LeGall H., Guillot M., Marchand A., Nomi Y., Artinian M. and Desvignes J. M., J. Magn. Sot. Jpn 11 (Suppl.
Sl), 235 (1981). 56. Prinz G. A., Krebs J. J., Forester D. W. and Maisch W. G., J. Magn. Magn. Mater. 1518,119 (1980). 57. Atkinson R., Salter I. W. and Xu J., J. Magn. Magn. Murer. 95, 35 (1991). 58. McGahan W. A., He P., Chen L., Bonafede S., Woollam J. A., Sequeda F., McDanielT. and Do H., J. Appl. Phys. 69,4568 (1991). 59. Carey R., Newman D. M., Snelling J. P. and Thomas B. W. J., J. Appl. Phys. 7S,JO8J (1994). 60. Atkinson R. and Lissberger P. H., Appl. Opt. 31, 6076 (1992). 61. Gamble R., Lissberger P. H. and Parker M. R., IEEE Trans. Magn. MAG-21, 1651 (1985). 62. Tomita Y. and Yoshino T., J. Opt. Sot. Amer. Al, 809
Because there are unfortunately a variety of different conventions in the literature [60] for definitions of refractive index, Voigt parameter, handedness of circular polarization, etc., we describe in this Appendix the conventions adopted in this paper. Following the traditional convention as described in Born and Wolf [82] the electric vector of right circular polarization (RCP) rotates clockwise when viewed so that the light is propagating towards the observer. RCP light has positive ellipticity. Similar, optical rotatory power is considered positive when the plane of polarization is rotated clockwise as seen by an observer looking back at the wave propagating towards him [83]. For MO rotation the same convention applies [84], but it is not complete without specifying the direction of magnetization of the sample. In the standard convention [85871 the sample is magnetized in the direction of propagation of the incident light. The dielectric tensor is
(1984). 63. Mansuripur M., Appl. Phys. Left. 49, 19 (1986). 64. Smith D. 0.. Out. Acra 12 (13). 193 (1965). 65. Bryant J. and Parker M. k.,‘J. Aipl. Phys. 67, 5313
(1990). 66. Atkinson R., Gamble R., Gu P. F. and Lissberger P. H., Thin Solid Films 162,89 (1988). 67. Feil H. and Haas C., Phys. Rev. Lett. S8,65 (1987). 68. Schoenes J. and Reim W., Phys. Rev. Left. 60, 1988
The dielectric constants for RCP and LCP polarizations are [84]
(1988). 69. Feil H. and Haas C., Phys. Rev. Letr. 60, 1989 (1988). JO. Katayama T., Suzuki Y., Awano H., Nishihara Y. and Koshizuka N., Phys. Rev. Let?. 60, 1426 (1988). 11. Reim W., Hfisser 0. E., Schoenes J., Kaldis E., Wachter P. and Seiler K., J. Appl. Phys. 55,2155 (1984). 72. Balasubramanian K., Macleod H. A. and Marathay A. S., Proc. SPIE 1078,214 (1989). 13. Reim W. and Weller D., IEEE Trans. Magn. 25, 3152 (1989). 74. Weller D. and Reim W., Appl. Phys. A49,599 (1989). 15. Reim W. and Weller D., Appl. Phys. Lett. 53, 2453
where we explicitly note the inverted ‘f’ sign. This differs from the convention proposed by Atkinson and Lissberger [60] in that it keeps the definition of positive rotation and ellipticity the same for both transmitted and reflected light. The indices of refraction for RCP and LCP are N+ = (n 2~An) + i(K & AK).
(198X). 16. Zhai H. R., Xu Y. B., Lu M. and Miao Y. Z., J. Magn. Magn. Mater. 104-107, 1021(1992). 11. Xu Y., Zhai H. and Lu M., J. Appl. Phys. 70, JO33 (1991). 18. Atkinson R., Grundy P. J., Hanratty C. M., Pollard R. J. and Salter I. W.. J. ADDI. Phvs. 75.6861 (1994). 79. Atkinson R., J. Magi.‘Magn. Ma&r. 95 (61), 89 (1991). 80. Hashimoto S., Ochiai Y. and Aso K., J. Appl. Phys. 67, 4429 (1990). 81. Deeter M. N., Ingle J. T. and Sarid D., Appl. Opt. 28,335
(1989). 82. Born M. and Wolf E., Principles of Optics, 5th edn, pp. 28-30. Pergamon Press, New York (1915). 83. Jenkins F. A. and White H. E., Fundamentals of Optics,
4th edn, p. 595. McGraw-Hill, New York (1976). 84. Wallis R. F. and Balkanski M., Many-Body Aspects of
(A.3)
This assumes a time dependence for the helds given by exp( -iwr). Therefore, to first order, E,~x =
n+iK=
(n* - K*) + i2nK
+{w d I,/-
(A.4)
Re(c)
2
+i
-We) +
2
(A 5)
Figures of merit for magneto-optic
c.~).= -2(KAn
+ nAK) + i2(nAn - KAK)
(A.6)
materials
1507
If the reflected electric field amplitudes RCP and LCP are
for incident
and An
+
iAK
=
rf = (r*l&
[nIm(E,.) - KWcyy)I 2(nZ + K*) _
Wm(~,.) + nRe(~,.)l~
(A.ll)
then the MO rotation and ellipticity are (A,7)
(A.12)
2(n2 + K*)
From the definition of the Voigt parameter in eqn (1 I), Q=?=
-2(nAn
+ KAK) + i2(KAn - nAK) n2+K?
(W
&+kK
=s,
(A.9)
and An + iAK = k [-nRe(Q) - i[KRe(Q)
+ KIm(Q)] + nIm(Q)].
(A.lO)
and eK = tan-’ (I;;!
+ I;;!).
(‘4.13)
Equation (A. 13) correctly accounts for the change in sign of the ellipticity upon reflection, i.e., due to the reversal in the direction of propagation LCP becomes RCP and vice versa.
Pergamon
FIGURES
OF MERIT
1. P/Iw. C/WI. Solids Vol. 56. No. I I. pp. 1499-1507. 1995 Ekvier Science Ltd Prmted in Great Britain. 0022-3697195 $9.50 + 0.00
FOR MAGNETO-OPTIC
WILLIAM
MATERIALS
A. CHALLENER
3M Information, Imaging, and Electronics Sector Laboratory, 3M Center Bldg 201-IN-34, St Paul, MN 55144-1000, U.S.A. (Received 7 April 1995; accepted I April 1995)
Abstract--In the development of magneto-optic (MO) materials for device applications it is important to be able to quickly and quantitatively compare the expected performance of new materials with others previously developed. Several ‘figures of merit’ are in common use for doing this. We consider their relative advantages and disadvantages. Kewords:
A. magnetic materials, A. multilayers, A. thin films, D. optical properties
1. INTRODUCTION First
generation
MO media
disks with 625 MBytes
on 5ain double-sided
of user data corresponds
to
In the near future media with four times this density will be available. Part of this increase in storage density has been due to a reduction in laser wavelength from 830 nm to 680 nm, with a corresponding reduction in the size of the diffraction-limited focused spot used to record and read the magnetic marks on the media. The availability of lasers, either semiconductor or frequency-doubled, with even shorter wavelengths are expected to enable further increases in storage density. Several different amorphous rare earth-transition metal (RE-TM) alloys have found extensive use in MO media. Examples include TbFe, TbFeCo, GdTbCo, and NdDyFeCo. TbFeCo is probably the most commonly used material and is generally considered the prototype against which other materials are compared. These materials have many desirable characteristics, such as perpendicular anisotropy, easily adjustable compensation and Curie points, low noise due to their amorphous structure, high coercivity, etc., as well as a few undesirable characteristics including rather small MO activity and high chemical reactivity. Fortuitously, the MO activity and these materials peaks in the near-infrared to red regions of the spectrum, make them suitable for use at standard semiconductor laser wavelengths. However, their MO activity tends to drop fairly quickly at shorter wavelengths [l], making their continued use in future higher density media problematic. As a result there is a keen interest in materials research aimed at developing new materials with improved MO properties. an approximate
area1 density
of 4 x IO7 bits/cm2.
New materials must undergo a wide variety of tests before they can be incorporated into a successful product. A dynamic performance test is always a critical part of this process for measuring such things as mark length jitter and background noise, laser power and magnetic field recording sensitivity, cycling stability, etc. Nevertheless, it is also important to be able to apply some criterion based on static measurements of optical and magnetic properties which may not guarantee a successful new material, but at least may quickly eliminate materials which have no hope of success from the time-consuming process of designing new media for dynamic performance testing. Hence we are led to the use of some form of ‘figure of merit’ (FOM) to distinguish between different MO materials and indicate those candidates for further testing and potential media design. Figures of merit in this sense are generally meant to correlate with the signal or perhaps the SNR that might be expected from a media designed using the MO material in question. The most general technique for assessing the MO properties of a new material is to determine its complete dielectric tensor at all wavelengths of interest, and then using a general computer model design a thin film stack with appropriate dielectric and metallic thin films in addition to the MO layer to optimize the film stack with respect to important optical parameters, such as reflectance, Kerr rotation, and Kerr ellipticity. Such models and optimization procedures have been described in the literature [2-91. Eventually either this process or a lengthy experimental process of trial-anderror, or some combination of the two must always be undertaken to optimize the MO media with the new MO material. Although optical media design is relatively straightforward for those who have the appropriate computer models, it is clearly useful to have a 1499
W. A. CHALLENER
1500
Fig. 1. Schematic of disk drive. PBS is a polarizing beamsplitter, and LPBS is a leaky polarizing beamsplitter. simpler FOM for judging MO materials which does not rely on the particular optical properties of any other material than the MO material, or on a particular film stack design. At this point it is useful to briefly review the operation of an MO disk drive. A schematic of an MO drive is shown in Fig. 1. Linearly polarized light is incident on the media, which is generally on the back surface of a transparent (glass or plastic) substrate. The light reflected from the thin film stack has a component polarized perpendicular to the incident polarization which may have an arbitrary phase shift with respect to the reflected parallel polarization component. The thin film stack of standard MO media is usually designed to make this phase shift as small as possible. This allows the optics of the disk drives to be matched to that of the disks for maximum signal and standardization. There are also noise considerations related to birefringence in the substrate that favor minimizing the phase shift [lo]. When the phase shift is zero, the reflected light is still linearly polarized but with a small rotation. A nonzero phase shift causes the reflected polarization to become elliptical. Kerr rotation and ellipticity both result from the different indices of refraction for the two circular polarizations in the MO material, and hence both rotation and ellipticity change sign when the magnetic moment is reversed. Therefore, both rotation and ellipticity carry information about the magnetic state of the recorded marks and in principle either can be used for signal detection. By compensating for the phase shift in the media by including a suitable retarder in the optics of the disk drive and employing a differential detection scheme, the maximum signal (to first-order in rotation and ellipticity) is proportional to [lo- 121 Signal=
amplifiers and servo systems for maintaining accurate focus and tracking control. Media noise arises in both the substrate and thin films. Birefringence in the substrate distorts the beam shape and polarization state of the light, affecting both recording and readback processes. Surface roughness in the substrate as well as irregularity in the groove profile give rise to noise. Irregularity in the edges and/or lengths of recorded marks due to domain wall dynamics in the MO layer also contributes to noise. If the MO material is not amorphous, microcrystallites with random orientations and optical properties cause increased noise. Some of these noise sources are well understood and easily characterized, while others are quite difficult [20] or impossible to describe in a simple analytic form suitable for a figure of merit. Detector shot noise is a physically unavoidable source of noise and so in some sense it provides the ultimate limit to the SNR. Because shot noise is proportional to the square root of the light intensity incident on the detectors [21,22], eqn (1) can be modified to SNR,,,,, cc dR(Q’ + E’) Unfortunately, the noise sources associated with the media thin films and substrate, not the shot noise, are usually dominant in the current generation of MO media, so a FOM based on shot noise limited SNR is somewhat questionable. Nevertheless, a useful figure of merit for comparison of different MO materials may be related to either eqn (1) or eqn (2). It should also be mentioned in Fig. 1 that the reflected light also provides feedback to the tracking and focus servos. While it has been suggested [23] that one can maximize the SNRsh,, by minimizing the reflected light intensity, this is really not an option in practical drive systems. In fact, the MO media is generally designed to have about 20% normal incidence reflectance from the inside (thin film) surface. In order to adjust reflectance and phase shift of the media, the quadrilayer film stack has been widely adopted in the industry as shown in Fig. 2.
(1)
where R is the reflectance of the media, eK is the Kerr rotation, and eK is the Kerr ellipticity. There are a variety of noise sources in MO recording/reading [13-191. Laser noise can affect both the recording and read-back process. There is shot noise in the detectors and electronic noise in both the
Fig. 2. Standard quadrilayer thin film stack for MO media.
1501
Figures of merit for magneto-optic materials Qualitatively speaking, the thickness and refractive index of the dielectric barrier are adjusted to give the desired reflectance, while the thickness and index of the dielectric spacer are adjusted to minimize Kerr ellipticity in the reflected light. The reflector is optically opaque to maximize the signal.
2. KERR ROTATION AND ELLIF’TICITY Measurement of the magneto-optic Kerr rotation and/or Kerr ellipticity is probably the most commonly used FOM for comparison between different MO materials [24-431. The FOM is FOM = BK
(3)
or FOM=&+t;.
(4)
The bulk Kerr rotation and ellipticity are not directly related to signal or SNR as given by eqns (1) and (2). To first order in terms of the dielectric tensor or index of refraction for an opaque film (see the Appendix for the appropriate definitions and conventions),
dielectric layer, so direct comparison to other materials is again questionable. One big disadvantage of using Kerr rotation alone as a FOM is that it has led to considerable confusion among some segments of the magneto-optics community. For example, thin film stacks have been ‘optimized’ to maximize the Kerr rotation without regard to the reflectance of the film stack [45-471. While it is true that by careful design of an antireflection film on top of the MO layer very large Kerr rotations can be obtained, such film stacks are of no use in practical MO media. The primary advantage of using Kerr rotation as a FOM is its simplicity of measurement or calculation from the dielectric tensor. However, Kerr rotation by itself is not useful for comparison of completely different MO materials. This can be illustrated by a simple example. Suppose the index of refraction for right and left circular polarizations of a hypothetical material is N* = (2 f 0.1) + i(4 F 0.1233)
(6)
which corresponds to the dielectric tensor -12 + i(16) E= +0.307 - i( 1.39) [
0
-0.307 + i( 1.39)
0
-12 + i( 16)
0
0
-12+i(16)
1 (7)
= 2[(-2nK)An
+ (n2 - K2 - l)AK]
(n2 - K2 - 1)2 + (2nK)2
Although Kerr rotation and ellipticity can be considered intrinsic magneto-optical properties of a bulk material, the interpretation of these properties in terms of underlying MO electronic transitions is not necessarily straightforward [44]. In the case of a thin film it is not justified in general to consider Kerr rotation and ellipticity as intrinsic properties, due to interference effects within the film from reflections at the interfaces which may either enhance or reduce the Kerr rotation and ellipticity over the bulk values. If Kerr rotation and/or ellipticity data are to be used as a FOM on thin films, then at the very least the measurements must be made on an optically opaque (thick) film to avoid these effects. Another difficulty arises when the materials are highly reactive, as in the case of the RE-TM alloys. In this case the Kerr rotation must either be measured in vacuum during deposition, or the films must be deposited on a transparent substrate or overcoated by a protective dielectric film. In either of the latter two cases the Kerr rotation and ellipticity are functions not only of the MO material but also of the thickness and refractive index of the substrate or
This material will actually exhibit zero Kerr rotation! Yet it obviously has a large off-diagonal MO component. In fact, it can be shown that an optimized thin film stack can be designed with such a material giving 20% reflectance and over 4” of Kerr rotation. More generally, from eqn (5) we see that whenever
the Kerr rotation is zero. Similarly. whenever AK=
(“-2f;-‘)An
(9)
the Kerr ellipticity is zero. Clearly Kerr rotation by itself can be a very misleading FOM. From eqn (5) we also find that both Kerr rotation and Kerr ellipticity can be simultaneously zero for an absorbing film only if the material is nonmagnetic (i.e., An, AK = 0). Therefore, from an experimental point of view, there is a definite advantage to making both rotation and ellipticity measurements. Even when Kerr rotation is used as a FOM for comparison of small variations of composition within a general alloy family, such as when RE-TM ratios are varied or when the alloys are doped by small quantities of an additional element, caution must be
1502
W. A. CHALLENER
used in interpreting the results. As can be seen from eqn (5), depending on the values of n, K, An, and AK, the addition of a dopant which causes 18~1to decrease may actually be due to an increase in IAn( or \AK(, and in an optimally designed thin film stack the doped material would exhibit a larger signal than the undoped material. An example will illustrate this more clearly. Suppose we have another hypothetical material with n = 2, An = +0.025, K = 4, and AK = -0.0125. The Kerr rotation of the bulk material would be -0.06”, and the Kerr rotation of an optimized film stack with 20% reflectance would be 0.8”. Now, if this material were doped in such a way that AK changed to -0.025, and all other indices remained the same, the bulk Kerr rotation would drop to -0.02”, but the Kerr rotation for the optimized film stack would increase to 1.O”! 3. KERR ROTATION
AND REFLECTANCE
To partially eliminate the disadvantages of the Kerr rotation FOM, another widely used FOM [48-501 is
or FOM = d-
(11)
These equations are only superficially similar to eqn (2), because they refer to the bulk MO properties, not the properties of an optimized thin film stack. If this FOM for the bulk properties of a particular material is greater than that of a typical MO media film stack (for which R % 20% and OK4 1”), then the material will of course have sufficient MO activity in an optimized stack as well. On the other hand, if this FOM is smaller than that for a typical MO media film stack, as is usually the case, then this FOM is not sufficient to indicate suitability of the material in an optimized MO media film stack. It has the advantage of being a simple FOM to measure, and is definitely preferable to the Kerr rotation FOM for the additional information it provides. but is still far from being an ideal FOM.
affect the results. Unlike Kerr rotation measurements, Faraday rotation measurements require measurement of the thickness of the film, and the presence of the substrate is unavoidable. As a result, the Kerr rotation FOM is usually preferable to the Faraday rotation FOM.
5. VOIGT PARAMETER Occasionally the Voigt parameter is used for comparison of different MO materials. The Voigt parameter, Q, is a complex number given by the ratio of the off-diagonal component of the dielectric tensor to the on-diagonal component. To first order 1
-iQ
0
iQ
1
0
[ 0
0
1I
E=E~
(12)
The Voigt parameter contains information directly related to the intrinsic magneto-optical activity of the material, and can be used to compare the relative MO activity of closely related alloys [56-591, i.e., materials for which the on-diagonal component of the dielectric tensor is approximately the same. It is a more accurate determination of the potential usefulness of a material in MO media than Kerr measurements alone, because it is truly an intrinsic property of the material. Nevertheless, because there is not a direct connection between the Voigt parameter and the MO signal in a disk drive, the Voigt parameter is not by itself useful for comparing MO materials of completely different classes. Another problem is the fact that it is a complex number, which means that both real and imaginary parts must be compared separately between different materials, so it is not really a single number FOM. A final problem with the Voigt parameter is that no standard sign convention has been adopted in the magneto-optic literature, making comparison between papers by different authors sometimes quite difficult [60]. However, if the Voigt parameter and the ondiagonal dielectric constant are both measured, then the MO properties of the material have been completely characterized.
6. POTENTIAL
KERR COEFFICIENT
4. FARADAY ROTATION
Faraday rotation is also used occasionally as a FOM [51-551. It is generally more appropriate for transparent MO materials than highly absorbing ones. As a FOM it has all the advantages and disadvantages of Kerr rotation. In addition, if thin films are used for Faraday rotation measurements, they must be sufficiently thick and/or absorbing that interference effects within the thin film do not significantly
For incident linearly polarized light on a thin film stack, the Kerr coefficient is the amplitude of the component of the reflected light which is polarized perpendicular to the incident polarization. The magnitude of the Kerr coefficient is Jkj = Ii(r+ - r_)l = Ir(-
eK + &)I = Jm (13)
1503
Figures of merit for magneto-optic materials By comparison with eqn (2) we see that Ikl is proportional to the shot-noise limited SNR. It can be shown [61-641 that for an MO layer in a thin film stack,
IkIm =q&++2+AK’).
(14)
The interesting feature about this equation is that it is expressed in terms of the index of refraction of the MO layer and the reflectance of the entire stack, which can be adjusted independently by dielectric layers between the incident light and the MO layer. By choosing appropriate dielectric layers to minimize R, we obtain a FOM for maximizing the shot-noise limited SNR,
maximize the result with respect to R.We find that the maximum signal occurs for R = 4. It has been suggested that depositing the MO material on top of a reflector with n and K small is the best way to optimize an MO media thin film stack [73-751. This can be more effectively accomplished by using dielectric/metallic bilayer structures for the reflector [76], and it has been further suggested that such a bilayer structure might enable one to exceed the potential Kerr coefficient FOM limit [77]. Our numerical calculations indicate that this is indeed an effective way to optimize the film stack, but it is easy to show following the procedure in Ref. [61] that the potential Kerr coefficient FOM limit in eqn (15) applies to this type of reflector as well.
7.MAXIMUM KERR ROTATION (15) This FOM has been used to compare garnets and RE-TM alloys [65]. It has also been compared to Kerr rotation measurements on a variety of RE-TM samples, and its clear advantages as a predictor of performance in MO media are exhibited [66]. We notice that the FOM becomes very large as either n or K get small. Small n can occur at a plasma resonance, where an enhanced Kerr effect is a now well-understood phenomenon [41, 67-721. When K = 0 the MO material is perfectly transparent, so the enhanced Kerr effect in this case corresponds to an infinitely thick MO layer with a reflector on the back. We also see from eqn (14) that An and AK in principle are of equal importance to the Kerr signal of an optimized thin film stack. From eqns ( 13) and (14) we can also determine the reflectance which maximizes the signal given by eqn (1) rather than the SNRshot. To obtain the maximum signal we must multiply eqn (14) by fi and then
Equations (13) and (14) may be combined to derive the maximum Kerr rotation for a thin film stack with a specific reflectance [78].
_
(16)
2vQ
Of the figures of merit considered in this paper. this one is probably the most useful for MO media design for which the film stack reflectance is usually a fixed parameter. We now use this FOM for a specific example. As previously stated, amorphous TbFeCo is the prototype alloy for present MO media designed for use at wavelengths of 680-830nm. Although the industry has not settled definitively yet on the MO material for use at shorter wavelengths, there is a great deal of interest in nanolayered PtCo. It has been shown [79] that such nanolayered structures can be represented by a single dielectric tensor. It is therefore
TbFeCoTa
TbFeCoTa
400500600700800 Wavelength
'400500600700800 Wavelength
(1 -R)
(nm)
Fig. 3. MO index of refraction
for TbFeCoTa
as a function
(nm)
of wavelength.
1504
W. A. CHALLENER Ptco
g -0.0 2 -0.0 $ 2
-0.0 -0.0 -0. 400500600700800
Wavelength
(nm)
Wavelength
(nm)
Fig. 4. MO index of refraction for PtCo as a function of wavelength. interesting to compare these two materials by means of the maximum Kerr rotation FOM. In order to determine the optical constants of TbFeCo, we prepared a trilayer film stack of Sic/ Tb0,20Feo,~sCoo,,oTao,oz/SiC with each layer about 13 nm thick on a glass substrate. This MO composition is typical of that used in the industry for MO media. The addition of a small amount ofTa improves the corrosion resistance of the film. The Sic films also prevent oxidation of the MO layer. All films were sputtered by a magnetron in a vacuum system with a typical base pressure < 1.O x lo-’ Torr. The MO layer was deposited at a 2 mTorr Ar pressure from an alloy target. Film thicknesses were determined by a stylus profilometer. The optical constants of the Sic were first determined independently by reflectance and transmittance measurements on an SIC film on a glass substrate, and then reflectance, transmittance, and Kerr rotation and ellipticity were measured on the trilayer stack to obtain the optical constants of the MO layer. In all cases, measurements were made from both sides of the sample, and a computer model was used which correctly accounts for the incoherently reflected waves within the substrate to determine the optical constants of the thin film. The results expressed in terms of n, K, An, and AK as a function of wavelength are shown in Fig. 3. Maxlmum
OKFOM
A nanolayered PtCo sample with periodicity of 8& 3A and total thickness of 20 nm was also deposited on a glass substrate by magnetron sputtering in a 5 mTorr Kr atmosphere. The film exhibited perpendicular anisotropy with a square hysteresis loop, although with a very small room temperature coercivity of 1800e. Although this particular film would not be suitable for MO media because of its low coercivity, the FOM computed for this film is representative of other PtCo films with properties better suited to MO media. The same set of optical measurements were used to determine the optical constants shown in Fig. 4. It is interesting to note that AK for this sample was found to have the opposite sign to that of TbFeCo, which apparently does not agree with other results in the literature [80] for reasons that are not understood, although sign conventions may be the issue. MO media is typically designed to have an inside surface reflectance of about 20%. Therefore, the figure of merit we have chosen for comparison of these two MO alloys is that given by eqn (16) with R = 0.2. The results are shown in Fig. 5. The FOM predicts a similar maximum Kerr signal for optimized thin film stacks of either TbFeCo or PtCo with 20% reflectance at the longer wavelengths. The FOM for the PtCo film increases at shorter wavelengths, while that of the TbFeCo film decreases, indicating the superiority of PtCo for maximizing signal at the shorter wavelengths. It is interesting, however, that the maximum Kerr rotation predicted for an optimized TbFeCo thin film stack at 400nm is actually quite reasonable for device applications. Depending on noise considerations and other factors, TbFeCo or a related RE-TM alloy may in fact be suitable for short wavelength recording.
8. CONCLUSIONS Wavelength
(nm)
Fig. 5. Comparison of the maximum Kerr rotation FOM for TbFeCoTa and PtCo as a function of wavelength.
Several different figures of merit found commonly in the MO literature have been described, including
Figures of merit for magneto-optic materials their advantages found
and disadvantages.
to be the most commonly
FOM, and easiest to measure,
Kerr rotation
but also one of the least
useful figures of merit for predicting obtainable Kerr
from an optimized
rotation
measurements
highly
misleading.
The
FOM
and closely
related
is
used and simplest the MO signal
thin film stack. In fact, by themselves
potential maximum
Kerr Kerr
can be
coefficient rotation
1505
5. Mansuripur M., J. Appl. Phys. 67,6466 (1990). 6. Challener W. A. and Grove S. L., Appl. Opt. 29, 3040 (1990). 7. Atkinson R., Salter I. W. and Xu J., J. Mugn. Magn. Mater. 102, 357 (1991). 8. Atkinson R., Salter I. W. and Xu J., J. Magn. Magn. Mater. 104-107, 1013 (1992). 9. Atkinson R., J. Magn. Mann. Mater. 124, 178 (1993). 10. Challener W. A. and Rinehart T. A., Appt. Opt. 26,3974
, , (*987’.
Chen’D., Appl. Opt. 13,767 (1974). 12. Bernstein P: and Guegnon C., IEEE ‘1.
FOM appear to be the best predictors mance in an optimized
of MO perfor-
thin film stack. These are also
more difficult figures of merit to obtain as they require
complete determination of the dielectric tensor of the material. Nevertheless, the additional effort is probably worthwhile in most cases. Several cautions applicable to all these figures of merit are in order. These figures of merit apply to normally incident plane waves upon a smooth surface. However, in standard MO disk drives the light is focused through a high N.A. lens onto the periodically grooved disk substrate. The typical quadrilayer film stack has been found to be particularly sensitive to high angle of incidence effects [81] and, therefore, may not perform as well as might be expected from a FOM calculation. In addition, the interference between various orders of the diffracted light can cause variations in the total reflected light intensity which are not accounted for by figures of merit calculated for a flat surface [ 151. Finally, and perhaps most importantly, none of these figures of merit take into account the potential sources of media noise from the MO layer due to nonuniform bit edges, microcrystallite scatterers, etc. Materials such as MnBi with a very large FOM nevertheless perform very poorly in MO media precisely because of the excess noise from grain boundary scattering. Using the maximum Kerr rotation FOM we have compared TbFeCo to PtCo, and find as expected that PtCo appears distinctly superior to TbFeCo for maximizing Kerr rotation at the shorter wavelengths. It remains to be seen, however, if PtCo or a RE-TM alloy or some other material will ultimately be successful in shorter wavelength MO media.
13. 14. 15. 16.
Trans.
Magn.
MAG-21, 1613 (1985). Brown B. R., IBM J. Res. Dev. 16, 19 (1972). Mansuripur M., Connell G. A. N. and Goodman J. W., J. Appt. Phys. 53,4485 (I 982). Dewey A. G., Proc. SPIE 695,72 (1986). Treves D. and Bloomberg D. S., Opt. Engng 25, 881
(1986). 17. Finkelstein B. I. and Williams W. C., Appl. Opt. 27, 703 (1988). 18. Dewey A. G., Proc. SPIE 1078,279 (1989). 19. Madison M. R.. J. Aool. Phvs. 73.5782 (1993) 20. McDaniel T. W’., Finkelstein B. 1: and Williams W. C., IEEE Trans. Magn. 24,2467 (1988). 21. Egashira K. and Yamada T., J. Appl. Phys. 45,3643 (1974). 22. Tang J. and Tang J., Appl. Opt. 29,2582 (1990). 23. Gamble R. and Lissberger P. H., J. Opt. Sot. Amer. A5,
1533 (1988). 24. Buschow K. H. J., van Engen P. G. and Jongebreur R., J. Magn. Magn. Muter. 38, 1 (1983). 25. Tsujimoto H., Shouji M. and Sakurai Y., IEEE Trans. Magn. MAG-19, 1757 (1983). 26. van Engen P. G., Buschow K. H. J. and Jongebreur R., Appl. Phys. Left. 42,202 (1983). 27. Masui S.. Kobavashi T.. Tsunashima S.. Uchivama S.. Sumiyama K. and Nakamura Y.. IEEE Trans. Magn.
MAG-20, 1036 (1984). 28. Imamura N., Tanaka S., Tanaka F. and Nagao Trans. Magn. MAG-21, 1607 (1985). 29. Reim W., Schoenes J., Hulliger F. and Vogt 0.. Mugn. Mater. 54-57, 1401 (1986). 30. Inukai T., Sugimoto N., Matsuoka M. and J. Magn. Sot. Jpn 11 (Supp. Sl), 217 (1987). 31. Ito H., Yamaguchi M. and Naoe M.. J. Appl. 5307 (1990).
Y., IEEE J. Magn. Ono K.. Phys. 67,
32. Kryder M. H., Shieh H.-P. and Hairston D. K., IEEE Trans. Mugn. MAG-23, 165 (1987). 33. Reim W.. Gambino R. J.. Ruf R. R. and Plaskett T. S.. J. Appl. ihys. 61,3349 (1987). 34. Suzuki T., Lin C.-J. and Bell A. E., ZEEE Trans. Mugn. 24,2452
(1988).
35. Honda S. and Yoshiyama M., Jpn. J. Appl. Phys. 27, 1687 (1988).
36. Weller D., Reim W. and Schrijner P., IEEE Mugn. 24,2554
Trans.
(1988).
37. Naoe M., Kitamura N. and Ito H., J. Appl. Phys. 63, would like to thank Dr W. C. Mitchell for the opportunity to attend the 1994 Conference on Magneto-optic Materials at Los Alamos, and for his suggestion for the topic of this paper. Acknowledgements--I
3850 (1988).
38. Kirby R. D., Shen J. X., Woollam J. A. and Sellmyer D. J., J. Appl. Phvs. 69,4574 (1991). 39. Gambino-R. J.,.Plaskett T. S., McGuire T. R. and McElfresh M. W.. J. AUDI. Phvs. 69.4750 (1991). 40. Shen J. X., Kirby R. D:,‘Sellmyer D: J. and Wang Y. J., J. Appl. Phys. 69,5984
REFERENCES Grove S. L. and Challener W. A., Jpn. J. Appt. Phys. 28, (Supp. 28-3), 51 (1989). Heavens 0. S., Optical Properties of Thin Solid Films. Dover Publications, New York (1991). Sprokel G. J., Appl. Opr. 23,3983 (1984). Balasubramanian K., Marathay A. S. and Macleod H. A., Thin Solid Films 164,391 (1988).
( 199 1).
41. Weller D., Brandle H., Gorman G., Lin C.-J. and Notarys H., Appl. Phvs. Letr. 61.2726 (1992). 42. Huang D., Zhang X: W., Luo C. P., Yang H. S. and Wane Y. J.. J. ADDI. Phvs. 75.6351 (1994). 43. Zhang Y., Rungk’A. P.: Shan Z. S. and Sellmyer D. J., J. Appl. Phys. 75,6354 (1994). 44. Feil H. and Haas C., Phys. Rev. Let/. 58, 65 (1987). 45. Sato R., Saito N. and Morishita T., IEEE Trans. Magn. 24,2458 (1988).
1506
W. A. CHALLENER
46. Kudo T., Johbetto H. and Ichiji K., J. Appl. Phys. 67, 4718 (1990). 47. Maeno Y., Kobayashi M., Oishi K. and Kawamura K., J. Appl. Phys. C&4325 (1990). 48. Suzuki T. and Katayama T., IEEE Trans. Magn. MAG-
22, 1230 (1986). 49. Iiyori H. and Takayama S., J. Appl. Phys. 69, 4161
Solid State Spectroscopy, pp. 245-248. North-Holland,
New York (1986). 85. Argyres P. N., Phys. Rev. 97,334 (1955). 86. Bennett H. S. and Stern E. A., Phys. Rev. 137, A448
(1965). 87. Connell G. A. N., Appl. Opr. 22, 3155 (1983).
(1991). 50.
Song K., Naoe M. and Ito H., J. Appl. Phys. 70, 6395
APPENDIX
(1991). 51. Gambino R. J. and McGuire T. R., J. Magn. Magn. Marer. 54-57, 1365 (1986). 52. Gambino R. J., McGuire T. R., Plaskett T. S. and Reim W., IEEE Trans. Magn. MAG-22, 1221(1986). 53. McGuire T. R., Gambino R. J., Plaskett T. S. and Reim W., J. Appl. Phys. 61, 3352 (1981). 54. Ostorero J., Guillot M. and Artinian M., IEEE Trans. Magn. 24, 2560 (1988). 55. LeGall H., Guillot M., Marchand A., Nomi Y., Artinian M. and Desvignes J. M., J. Magn. Sot. Jpn 11 (Suppl.
Sl), 235 (1981). 56. Prinz G. A., Krebs J. J., Forester D. W. and Maisch W. G., J. Magn. Magn. Mater. 1518,119 (1980). 57. Atkinson R., Salter I. W. and Xu J., J. Magn. Magn. Murer. 95, 35 (1991). 58. McGahan W. A., He P., Chen L., Bonafede S., Woollam J. A., Sequeda F., McDanielT. and Do H., J. Appl. Phys. 69,4568 (1991). 59. Carey R., Newman D. M., Snelling J. P. and Thomas B. W. J., J. Appl. Phys. 7S,JO8J (1994). 60. Atkinson R. and Lissberger P. H., Appl. Opt. 31, 6076 (1992). 61. Gamble R., Lissberger P. H. and Parker M. R., IEEE Trans. Magn. MAG-21, 1651 (1985). 62. Tomita Y. and Yoshino T., J. Opt. Sot. Amer. Al, 809
Because there are unfortunately a variety of different conventions in the literature [60] for definitions of refractive index, Voigt parameter, handedness of circular polarization, etc., we describe in this Appendix the conventions adopted in this paper. Following the traditional convention as described in Born and Wolf [82] the electric vector of right circular polarization (RCP) rotates clockwise when viewed so that the light is propagating towards the observer. RCP light has positive ellipticity. Similar, optical rotatory power is considered positive when the plane of polarization is rotated clockwise as seen by an observer looking back at the wave propagating towards him [83]. For MO rotation the same convention applies [84], but it is not complete without specifying the direction of magnetization of the sample. In the standard convention [85871 the sample is magnetized in the direction of propagation of the incident light. The dielectric tensor is
(1984). 63. Mansuripur M., Appl. Phys. Left. 49, 19 (1986). 64. Smith D. 0.. Out. Acra 12 (13). 193 (1965). 65. Bryant J. and Parker M. k.,‘J. Aipl. Phys. 67, 5313
(1990). 66. Atkinson R., Gamble R., Gu P. F. and Lissberger P. H., Thin Solid Films 162,89 (1988). 67. Feil H. and Haas C., Phys. Rev. Lett. S8,65 (1987). 68. Schoenes J. and Reim W., Phys. Rev. Left. 60, 1988
The dielectric constants for RCP and LCP polarizations are [84]
(1988). 69. Feil H. and Haas C., Phys. Rev. Letr. 60, 1989 (1988). JO. Katayama T., Suzuki Y., Awano H., Nishihara Y. and Koshizuka N., Phys. Rev. Let?. 60, 1426 (1988). 11. Reim W., Hfisser 0. E., Schoenes J., Kaldis E., Wachter P. and Seiler K., J. Appl. Phys. 55,2155 (1984). 72. Balasubramanian K., Macleod H. A. and Marathay A. S., Proc. SPIE 1078,214 (1989). 13. Reim W. and Weller D., IEEE Trans. Magn. 25, 3152 (1989). 74. Weller D. and Reim W., Appl. Phys. A49,599 (1989). 15. Reim W. and Weller D., Appl. Phys. Lett. 53, 2453
where we explicitly note the inverted ‘f’ sign. This differs from the convention proposed by Atkinson and Lissberger [60] in that it keeps the definition of positive rotation and ellipticity the same for both transmitted and reflected light. The indices of refraction for RCP and LCP are N+ = (n 2~An) + i(K & AK).
(198X). 16. Zhai H. R., Xu Y. B., Lu M. and Miao Y. Z., J. Magn. Magn. Mater. 104-107, 1021(1992). 11. Xu Y., Zhai H. and Lu M., J. Appl. Phys. 70, JO33 (1991). 18. Atkinson R., Grundy P. J., Hanratty C. M., Pollard R. J. and Salter I. W.. J. ADDI. Phvs. 75.6861 (1994). 79. Atkinson R., J. Magi.‘Magn. Ma&r. 95 (61), 89 (1991). 80. Hashimoto S., Ochiai Y. and Aso K., J. Appl. Phys. 67, 4429 (1990). 81. Deeter M. N., Ingle J. T. and Sarid D., Appl. Opt. 28,335
(1989). 82. Born M. and Wolf E., Principles of Optics, 5th edn, pp. 28-30. Pergamon Press, New York (1915). 83. Jenkins F. A. and White H. E., Fundamentals of Optics,
4th edn, p. 595. McGraw-Hill, New York (1976). 84. Wallis R. F. and Balkanski M., Many-Body Aspects of
(A.3)
This assumes a time dependence for the helds given by exp( -iwr). Therefore, to first order, E,~x =
n+iK=
(n* - K*) + i2nK
+{w d I,/-
(A.4)
Re(c)
2
+i
-We) +
2
(A 5)
Figures of merit for magneto-optic
c.~).= -2(KAn
+ nAK) + i2(nAn - KAK)
(A.6)
materials
1507
If the reflected electric field amplitudes RCP and LCP are
for incident
and An
+
iAK
=
rf = (r*l&
[nIm(E,.) - KWcyy)I 2(nZ + K*) _
Wm(~,.) + nRe(~,.)l~
(A.ll)
then the MO rotation and ellipticity are (A,7)
(A.12)
2(n2 + K*)
From the definition of the Voigt parameter in eqn (1 I), Q=?=
-2(nAn
+ KAK) + i2(KAn - nAK) n2+K?
(W
&+kK
=s,
(A.9)
and An + iAK = k [-nRe(Q) - i[KRe(Q)
+ KIm(Q)] + nIm(Q)].
(A.lO)
and eK = tan-’ (I;;!
+ I;;!).
(‘4.13)
Equation (A. 13) correctly accounts for the change in sign of the ellipticity upon reflection, i.e., due to the reversal in the direction of propagation LCP becomes RCP and vice versa.