An experimental study of the magneto-optical properties of ferromagnetic alloys

A N EXPERIMENTAL STUDY

OF THE MAGNETO-OPTICAL

PROPERTIES OF

FERROMAGNETIC ALLOYS

A N EXPERIMENTAL STUDY OF THE

MAGNETO-OPTICAL PROPERTIES OF

FERROMAGNETIC ALLOYS

1 INTRODUCTION 1

References 2 2 THE MAGNETO-OPTICAL K E R R E F F E C T 3

2.1 Description with the dielectric tensor 3 2.2 Short outline of previous experimental work 5

2.3 Microscopic models 6

23.1 Magnetic and non-local effects 6

2.3.2 Intraband transitions 7 2.3.3 Interband transitions 9

References 11 3 E X P E R I M E N T A L EQUIPMENT 13

3.1 Choice of the polar Kerr effect 13

3.2 Measuring principle 13 3.3 Optical path 15

3.3.1 Layout 15 3.3.2 Components 16 3.4 Automation 26

3.4.1 Logical equipment and interfacing 26

3.4.2 Measuring program 28

3.43 Data handling 29

3.5 Calibration and performance 30

3.5.1 Calibration 30 3.5.2 Correction and accuracy of the results 33

3.5.3 Discussion 35 3.6 A magneto-optical measuring apparatus with two lasers 37

3.7 Determination of the complex dielectric constant 38 3.8 X-ray diffraction and magnetic measuring methods 40

References 41 4 S A M P L E P R E P A R A T I O N 42

4.1 Crystalline samples 42 4.1.1 Preparation 42 4.1.2 Influence of the sample quality on the measurement results 43

4.2 Preparation of amorphous thin films 47

References 48 5 S U R V E Y OF T H E P O L A R K E R R ROTATION IN F E R R O M A G N E T I C

A L L O Y S AT TWO D I F F E R E N T W A V E L E N G T H S 49

5.1 Introduction 49 5.2 Crystalline Co- and Fe-based binary alloys 49

5.5 Crystalline ternary alloys 57

5.6 Conclusions 59 References 59 6 SPECTROSCOPIC RESULTS A N D DISCUSSION 61

6.1 Introduction 61 6.2 The pure metals N i , Co and Fe 61

6.3 Binary alloys 67

6.4 The Heusler alloys Co2YSn (Y=Ti,Zr,Hf) 82

6.5 Ternary alloys containing Si, Ge or Sn 86 6.6 PtMnSb and related compounds 91

References 98 7 CONCLUSIONS 100

S U M M A R Y 102 S A M E N V A T T I N G 103

1. INTRODUCTION

During the last few decades considerable attention has been given to the magneto-optical properties of ferromagnetic or ferrimagnetic substances. A n im-portant motivation for this interest stems from the possibility to use magneto-optical effects in various technological applications. Studies have been made of a number of magneto-optical devices, but most effort has been put into investigations regarding erasable information storage (1 - 5). In this application the information concerned has to be stored in thin films because a small film thickness favours a low writing threshold and a high recording density (2). Metallic magnetic materials, many of which have large Kerr and Faraday effects, therefore seem to be more appropriate as information carriers than non-metallic materials. On the other hand, there are several non-metallic materials, for instance Bi-containing garnets (6), which have a considerably higher magneto-optical figure of merit than the best metallic materials known, due to their small optical absorption. Although the feasibility of erasable magneto-optical recording has been demonstrated both in non-metals (7) and in metals (1 - 4), the most promising materials belong to the latter class because of the formerly mentioned reasons. Moreover, thin metal films that have the required magneto-optical and magnetic properties are more easily manufactured with sufficiently high optical quality.

With respect to writing and reading characteristics the performance of storage media based on thin rare earth — transition metal films is quite satisfactory (3, 4), but for high-frequency applications, such as video recording, an improved signal to noise ratio will be necessary. Although a number of electronic and optical

techniques have been found to enhance the signal to noise ratio (4, 5), there remains a need for alloys that have higher magneto-optical effects than the materials used so far. The purpose of the present study is to investigate the polar Kerr effect in various alloys at room-temperature in a systematic way, thereby dis-regarding the requirements imposed on the magnetic properties from the point of view of possible applications. The reason for this approach is that coherent informa-tion on the magneto-optical properties of magnetic metallic systems is lacking. Furthermore, to our knowledge no model exists that is able to predict magneto-optical properties from other physical data, in other words, there is no useful 'rule of thumb' that can be applied in the search for materials with a large magneto-optical Kerr effect.

As a result of this, the present investigation is necessarily an approach based on trial and error. The great majority of all crystalline alloys that are know from the literature to be ferromagnetic at room-temperature were prepared in polycrystalline form and the room-temperature values of the polar Kerr effect and the magnetiza-tion were determined. Where the alloys formed a continuous series within a certain composition range, representative members of such series were selected. Apart from crystalline materials some amorphous systems were investigated as well. In the present work the word 'alloy' is meant to apply not only to amorphous alloys and solid solutions, but also to intermetallics that have a well-defined crystal structure

The Kerr rotation of the investigated alloys was determined at the two wave-lengths 633 and 830 nm, which fairly well characterize the wavelength region of current practical interest. This was done because the necessary experimental set-up could be built in a relatively short time and because many different materials could be investigated in this way. The most interesting materials emerging from these experiments were also investigated spectroscopically in the wavelength region 280 - 2000 nm.

In contrast to previous magneto-optical studies on the ferromagnetic elements and alloys, in the present approach a large number of different materials has been investigated, in order to be able to compare the results directly. A possible short-coming of this approach is that the preparation and handling of each sample cannot be given that much attention as would have been possible in case only a few samples would have been investigated. The implication of the former with respect to the experimental accuracy will be discussed in a separate chapter. A n advantage of the present approach is the possibility to discern systematic trends with varying chemical composition, which may throw new light upon already existing models. Thus, apart from giving an answer to the practical question as to which Kerr effects can be expected to occur in various ferromagnetic alloys at room-temperature, the results of the present study can also be used as a basis for new insights into the microscopic mechanisms that are responsible for those effects.

References

1. B.R. Brown, Appl. Opt. 13, 761 (1974).

2. K. Egashira, A . Katsui and A. Shibukawa, Rev. Electr. Comm. Lab. 25, 163 (1977).

3. P. Hansen and M. Urnei-Wille, J. Appl. Phys. 50, 7471 (1979); S. Tanaka and N . Imamura, J. Magn. Magn. Mat. 35, 205 (1983).

4. J. Biaat and K. Schouhamer Immink (to be published).

5. D. Treves, J. Appl. Phys. 38, 1192 (1967); E. Jagei and U . Ropke, Phys. Stat. Sol. a 19, 529 (1973); M. Gomi, M . Abe and S. Nomura, Jpn. J. Appl. Phys. 20, L821 (1981); M . Mansuripur, G.A.N. Connell and J.W. Goodman, J. Appl. Phys. 53, 4485 (1982). 6. J.M. Robertson, P.K. Larsen and P.F. Bongers, IEEE Trans. Magn. MAG-11, 1112 (1975). 7. J.P. Krumme, H. Heitmann and K. Witter, Physica 89B, 273 (1977).

2. THE MAGNETO-OPTICAL K E R R E F F E C T 2.1 Description with the dielectric tensor

Magneto-optical effects are usually described by means of a dielectric tensor or, alternatively, a conductivity tensor. For a solid with the magnetization Maligned along an axis of threefold or higher symmetry the relative dielectric tensor has the 'gyrotropic' form

where the z-axis is defined as the direction of the magnetization vector. From symmetry arguments it follows (1) that the diagonal components have an even dependence on the magnetization while the off-diagonal elements must be odd in M . In the cubic metals N i and Fe the difference e ^ - f ^ , being caused by magneto-optical effects that are second order in the magnetization, was found to be very small relative to (1). It was also found that the equatorial Kerr effect in single crystals of Ni is practically independent of the direction of M with respect to the crystal axes (2). Yet in another investigation (3) concerning single crystals of N i , a small dependence of this nature actually was observed for both the diagonal and the off-diagonal elements of e. This dependence, however, only concerned spectral fine structures.

All crystalline solids investigated in the present study were prepared as poly-crystalline samples with random crystallite orientation. Thus, the measurements concerned a tensor that was averaged over all crystal directions. The majority of the solids investigated had cubic symmetry but a small fraction had a non-cubic crystal structure. It is assumed_that, for non-oriented, polycrystalline samples of cubic materials, the effective e tensor can still be written in the form of relation (2.1) and that the difference between and ez z can be neglected. Two complex constants

er and 5, defined by

= /er i 6 ° \

e = I-iS er o J , (2.2)

\ o o er /

will be used to represent the dielectric tensor. A n experimental verification of the correctness of this expression was obtained from measurements on non-oriented N i films, which showed no noticeable dependence of the longitudinal Kerr sprectrum upon the incident polarization (4). Moreover, it was found that relation (2.2) is still a reasonably good approximation in the case of non-oriented films of hexagonal Gd (4) and it will be assumed that this also holds for the non-cubic metals investi-gated in the present study. Although experimental evidence obtained on metals in relation to this subject is scarce, the results for N i (3, 5) and Gd (4) seem to

indicate that the gross spectral features are retained when unoriented, polycrystalline samples are used but that spectral fine structures do get lost.

Tensor (2.2) can be diagonalized by a transformation to circular coordinates. This means that the two circular polarizations are the eigenmodes of a light beam travelling in the z-direction. When the 'spinning' direction of the rotating electric field of a circularly polarized beam is parallel or antiparallel to M, the light wave experiences a dielectric constant e+ or e-, respectively. If time dependence is taken

as e- 1" * the following relations hold:

e± = er + S . (2.3)

For the polar configuration, where the magnetization and the optical wave vector are perpendicular to the reflecting surface, substitution of (2.3) into the well known expressions for the Fresnel coefficients leads to an equation that relates the Kerr effect to the dielectric properties:

1 + tg eK 1 - n+ 1 + n_

* e-2 i* k = , (2.4)

1 - tg eK 1 + n+ 1 - n

with n* = (e*)^ = ( er+ ô ) ^ . The signs of the Kerr rotation <^ and the Kerr

ellipticity ejr are most conveniently defined if the incident beam is assumed to be linearly polarized. In that case the value of is counted positive if the rotation vector that can be associated with the 'handedness' of the reflected polarization is parallel to M , while ^ is counted positive if the sense of the rotation that is experienced by the major polarization axis upon reflection is given by the direction o f M , t o o .

In order to calculate the value of 5 from the experimental data for <pj^, and er,

eq. (2.4) was solved to first order in ô. If the modulus of 5 appeared to be larger than 0.07 the method of successive approximations was used. The limiting form of eq. (2.4) for small values of i ^ , and S is

i5

* K + i eK = "IT • (2-5)

* r * C I - er)

Actually, it was found that eq. (2.5) would have been sufficiently accurate for the calculation of S, because the difference between the results obtained with eqs. (2.4) and (2.5) never amounted to more than a few percent and therefore was smaller than the experimental error in the value of er (chapter 4). The present Kerr effect

measurements were performed with slightly off-normal incidence, the mean angle of incidence being about 4.5° (chapter 3), which can be accounted for by a correction (6). This correction was not applied as according to numerical estimates it was always smaller than 1.5%.

Finally, a remark is made on substrate-incident measurements in thin films. When there is no interference, in eq. (2.5) both er and 6 n should be divided by

the refractive index n of the substrate in order to obtain the substrate-incident Kerr effect. Because tfie dielectric constant of metals is very much larger than unity in the red and infra-red parts of the spectrum, the relation

^ K S + i eK S = ns ^ K + i eK ) ' <2-6>

where and indicate substrate-incident values, is a good approximation for this wavelength region.

2.2 Short outline of previous experimental work

Previous experimental studies of magneto-optical effects in metallic materials that are ferromagnetic at room-temperature will be summarized here. Most investi-gations were concerned with one of the Kerr effects although some Faraday effect measurements in thin films have been reported also. Only the results that have been obtained on the polar Kerr effect at near normal incidence or on the value of 6 can be compared directly with the present work. References in this survey, however, pertain to any magneto-optical effect that is linear in the magnetization.

Spectroscopic investigations will be treated first. Most frequently the spectra of the elements Ni and, less often, Co and Fe have been measured. The results of Krinchik and Artem'ev (5) on these 3d transitions metals have by now been adopted as a basis for theoretical considerations. Binary Ni-, Co- or Fe-based systems of which one or more alloys have been investigated are given in table 2.1 with a

specifi-Alloy wavelength ref. AUoy wavelength ref.

system region (nm) system region (nm)

Ni 103-15000 2 , 5 , 7 Fe 207-18000 5,9 Ni-Cu 2 4 0 - 2480 8 Fe-B 4 6 0 - 1770 16 Ni-Mo 7 3 0 - 2480 8 Fe-C 4 3 5 - 680 17 Ni-Al 400-20000 9 Fe-Si 3 0 0 - 1000 17,18 Ni-Pd 420-16000 10 Fe-V 400-18000 9 Fe-Co 4 3 5 - 690 17 Co 207-20000 5,9 Fe-Ni 4 0 0 - 2200 17, 19 Co-Cr 4 2 0 - 800 11 Fe-Rh 400-10000 20 Co-Al 400-18000 9 Fe-Pt 3 4 0 - 1150 21 Co-Si 2 7 5 - 955 12 Fe-Ce 4 3 5 - 680 17 Co-Y 4 0 5 - 615 13 Fe-Gd 3 5 0 - 2480 15, 22 Co-Nd 4 0 0 - 650 13,14 Co-Sm 4 0 5 - 615 13 Co-Gd 3 2 0 - 2480 13,15

Table 2.1. Survey of binary Ni-, Co- and Fe-based alloy systems of which one or more alloys were investigated magneto-optically in the specified wavelength regions.

cation of the wavelength region that was covered. A few ternary and quaternary alloys based on Co or Fe, usually amorphous ones, have also been studied (17, 23).

Further spectroscopic studies have been made of the Cr- and Mn-based alloys given in table 2.II. Finally, the influence of some additions to MnSb (Cu, Sn, CoX32), to

Alloy wavelength

region (run)

ref. AUoy wavelength

region (run) ref. CrTe 550-1000 24 MnGaGe 400-1000 30 C r3T e4 4 0 5 - 615 25 MnCuBi 3 6 0 - 700 31 Mn-Cu-Al 4 4 0 - 655 17 alloy M ns G e3 400-1150 26 MnAs 4 5 0 - 950 27 M n4S n 4 3 5 - 675 17 MnSb 360-1150 17,18 MnBi 230-1000 17,29

Table 2. II. Survey of some Cr- and Mn-based alloys that were investigated magneto-optically in the specified wavelength regions.

MnBi (Ti) (33) and to MnCuBi (Ni (34), Dy (35)) was investigated in spectral ranges between 400 and 900 nm.

Many experiments, often with a practical application in mind, were carried out at one or, in a few cases, at two wavelengths. These experiments primarily con-cerned binary or multi-component alloys, usually amorphous, that contain Fe or Co and at least one rare earth metal (36). Other materials were investigated at one wavelength and comprise the compound MnAlGe (37) and alloys of the systems Co-P (38), Co-Sn (17), Co-Pt (39), Mn-B and Mn-Fe (17), in so far as the systems were not already mentioned in this section.

2.3 Microscopic models

In general there are two mechanisms responsible for the occurrence of those magneto-optical effects that can be described by means of a dielectric tensor. These mechanisms are the intraband and interband electronic transitions. Before discussing electrical polarization or conduction processes, some remarks will be made on the influence of magnetic permeability.

2.3.1 Magnetic and non-local effects

Magneto-optical phenomena that occur in ferrites at microwave frequencies are known to be caused by a collective precession of the spins (40) and they

are described by means of a magnetic permeability tensor /J. As ferromagnetic and antiferromagnetic resonance frequencies, in practically all substances, are some orders of magnitude smaller (40-42) than the frequency of near infra-red light, the magnetic susceptibility is usually neglected when near infra-red light or electro-magnetic radiation of shorter wavelength is considered. Still, the possibility of dielectric and magnetic effects being present simultaneously was investigated experimentally in N i , Co and Fe with near infra-red and visible light by measuring both a reflective and the transmissive magneto-optical effect (43). It appeared that the effects could not both be explained by one and the same dielectric tensor and therefore an e- as well as a ju-tensor were used to give a consistent description. The underlying principle is most easily seen in ordinary optics where propagation properties are determined by the product and reflection properties by the ratio er/Mr

-Extraction of a gyrotropic /i-tensor from experimental data is also possible when the polar or, alternatively, the longitudinal Kerr effect is compared with the equatorial effect. Such experiments were also done (44) on the 3d transition metals in the same spectral region as in ref. 43. Here, too, substantial discrepancies were found when both effects were described with an e-tensor and therefore a significant role was attributed to the /i-tensor. However, the polar Kerr rotation data presented in refs. 43 and 44 clearly differ from Krinchik and Artem'ev's spectra (5), which will appear to agree quite well with the present and with other results (chapter 6). Moreover, in ref. 5 the equatorial spectrum was determined in addition to the polar spectrum, and in this case the differences are found to be rather small as can be seen by comparing Krinchik and Artem'ev's curves (see figs. 6.1-6.3). In fact, the difference seems to be within experimental accuracy, as will again be discussed in chapter 6. It should be mentioned that the equatorial spectrum of N i given in ref. 5 is also roughly confirmed by other work (2).

It was pointed out by Pershan (45) that a difference between reflective and transmissive properties may also be the result of non-local effects and can therefore be described by means of a wave vector dependence of the dielectric tensor. How-ever, it can be inferred from literature values (42,46) that non-local effects in metallic materials, which are related to the anomalous skin effect, are probably not very important at room-temperature in the neighbourhood of the visible region. In short, experimental evidence and the additional considerations mentioned above seem to indicate that a description with a local dielectric tensor alone is sufficiently accurate with regard to the magneto-optical effects studied in the course of the present investigation.

2.3.2 Intraband transitions

As was discussed, magneto-optical properties are primarily caused by interactions of the electric field component of a light wave with the electrons in a solid. Left-right asymmetry that is induced in electron orbits by static magnetic fields is several orders of magnitude too small to account for the magneto-optical effects that exist

in ferromagnets. Since Hulme (47) showed that left-right asymmetry induced by spin-orbit coupling does have the correct order of magnitude, spin-orbit effects have now been accepted as a basis for the theoretical description of magneto-optical effects in ferromagnetic media. This applies to both interband and intraband effects.

At low frequencies, intraband electronic transitions are the dominant mechanism. Erskine and Stern (4) presented a phenomenological intraband theory which deals with two processes, both being caused by spin-orbit effects: asymmetric scattering of electrons and intraband polarization currents that are normal to M and to the electron wave vector. The first process is characterized by a skew scattering life-time 1 /r, while the normal collision frequency is y. The second process dominates when the optical frequency cj is much larger than T and than y, while the first one dominates when oj has the same order of magnitude as T or 7, or when « is smaller.

Erskine and Stern (48) assume <J>r,y in Ni for near infra-red light, and in that limit their relation for the frequency dependence of the imaginary part of 5 reduces to

where the skew scattering term has been dropped. Only the imaginary, absorptive part of 5 will be treated in this section because it is, in general, more easily discussed in terms of microscopic concepts than the real part. Moreover, hardly any informa-tion is lost by this restricinforma-tion, because a causal relainforma-tionship exists between the real and imaginary parts. In view of eq. (2.7) experimental results are plotted as (hp)28

vs. photon energy, with v = co/(27r), in this work. Intraband polarization currents, if at all significant, then appear as a vertical offset in the spectra but do not con-tribute to spectral structures. This representation was also chosen because it facilitates direct comparison with other published data and because it tends to equalize the magnitude of extrema over the whole spectral region.

Voloshinskaya and Bolotin (2) performed a calculation of intraband effects which only took skew scattering processes into account. Their result for the frequency dependence of w2 Im(6) is

coaIm(8)a "ƒ . (2.8)

( o r +

7 )

This relation is equivalent to the limit of Erskine and Stern's skew scattering term for r ^ 7. The essential assumption made in ref. 2 is that the collision frequency y is comparable to the frequency of near infra-red light. According to eq. (2.8) the value of co2 Im(5) displays either a maximum or a minimum at co = 7.

For comparison with experiment the spectrum of (h^)2 Im(6) of Ni is reproduced

from ref. 5 in fig. 2.1. Experimental values in the low-energy range are also given in ref. 2, where the spectrum has approximately the same shape including the mini-mum and maximini-mum below 2 eV. Voloshinskaya et al (2) ascribe the low-energy maximum at about 1.5 eV to rapidly relaxing d electrons with minority spin, and attribute the minimum near 0.4 eV to more slowly relaxing sd electrons, also

Fig. 2.1. Value of(hu)2Im(8J vs. photon energy hv of Mas obtained by Krinchik and Artem 'ev. (5). The photon energy is related to the vacuum wavelength A accor-ding to the formula hv = 1.2398/X, if hv is expressed in eV and \ in pm.

with minority spin. Majority spin electrons are defined here as electrons with a spin magnetic moment in the same direction as M, while minority electrons have a spin magnetic moment in the opposite direction.

2.3.3 Interband transitions

A n alternative explanation for the spectrum of fig. 2.1 is based on interband transitions. For the discussion of these transitions it is useful to express the value of Im(5) in terms of optical transition matrix elements by means of the following relation (4,49):

co2Im(ô) = C S \\<#\n\a>\2

- |<pV|a>|H

a,0 ^

where C is a positive constant, 5J-J the familiar 8-function, the transition frequency, and where |o£> and |/3> represent the occupied and empty states, respec-tively. The operators tT" are defined by ir~ = 7rx ± w , if being equal to the sum of

the canonical momentum operator p" and a spin-orbit contribution. Wang and Callaway (50) showed from numerical estimates that the spin-orbit contribution to # is negligible in the case of N i , implying that 7? can be replaced by p in eq. (2.9). As regards the second term on the right hand side, it is known from standard theory that the operator p+ corresponds to the absorption of a circularly polarized photon

definitions given in section 2.1, such absorption gives a positive contribution to Im(e+) and, according to eq. (2.3), a negative one to Im(5), in agreement with

eq. (2.9). By analogy, the contribution to Im(6) from p'can be shown to be posi-tive.

When spin-orbit coupling is neglected, the matrix elements |<0|p+|a>|2 and

|<^|p"|ct>|2 are equal, leading to 5 = 0, even if there is exchange splitting. Upon

inclusion of spin-orbit effects these elements become unequal, but in the absence of exchange splitting one can still write |</3|p+|a>|2 = |</3'|p"|a'>|2, the primes

indica-ting time-reversed states. Because also u>a'p> = <*>an, summation then still leads to

5 = 0 . This illustrates that both spin-orbit and exchange coupling are needed in order to obtain a magneto-optical effect. Neglecting the spiorbit term in the n-vector, there are still two mechanisms (4) by which spin-orbit coupling gives rise to magneto-optical phenomena. The first mechanism is the splitting of degenerate levels; the second mechanism involves spin-orbit induced perturbation of the ground state wave functions |a> and |0>.

Erskine and Stern (4,48) have proposed an interband model, based upon eq. (2.9) and a number of additional assumptions, in order to give a qualitative inter-pretation of the (hi>)2 Im(6) spectrum of Ni shown in fig. 2.1. However, careful

application of this model leads to the result that the major features of the experi-mental spectrum are reproduced with the opposite sign. This contradicts the statement made by Erskine and Stern (48) that these features come out correctly, and it is concluded that the inherent assumptions of the model constitute an over-simplification. Still, some elements of this model seem to be useful and will presently be discussed.

Using the fact that magneto-optical effects in ferromagnets are based upon the presence of spin-orbit and exchange coupling, some remarks can be made about the transitions that are responsible for the interband magneto-optical polarization. In N i , the dependence on spin-polarization strongly favours the 3d states, which, moreover, have a much higher density than the s, p states. Because the 3d band is nearly filled, the interband effects will be mainly caused by d -*s, p transitions. Furthermore, the dependence on spin-orbit coupling, too, discriminates against transitions between conduction s and p states, even if these states exhibit some spin-polarization. In Erskine and Stern's model the four extrema in the (hv)2 Im(6)

spectrum of Ni are all ascribed to d -*p transitions. The low-energy minimum near 0.4 eV is attributed to transitions from the highest occupied states of the minority

3d band. The low-energy maximum occurring near 1.5 eV is assigned to transitions

from the top of the majority 3d band. The two extrema that occur at energies above 3 eV are attributed to transitions from the 3d band bottom.

Indeed, interband transitions involving minority d electrons may set in at a lower energy than those involving majority electrons, but the specific assignments that were mentioned above are doubtful in view of the erroneous sign. Excepting intra-band effects, it can only be stated that the low-energy part of the spectrum, e.g. the first two extrema, is probably the result of transitions involving the upper d levels, while the high-energy part can also be caused by transitions from d levels which are

closer to the bottom of the d band. It should be noted that transitions to empty minority d states cannot be entirely neglected and they may be responsible for some of the observed spectral structure.

Erskine and Stern (48) proposed the same model to explain the magneto-optical effects in Co and Fe, although the authors note that the structure due to d -> p transitions may be somewhat obscured by p -*-d transitions and by intraband effects because more empty d states are available. It will be apparent from inspection of Krinchik and Artem'ev's results (5) (see figs. 6.1 — 6.3) that the magneto-optical spectra of Co and Fe have some similarity to those of N i . However, the same doubts concerning the model exist in connection with its applicability to the magneto-optical spectra of Co and Fe.

Results for co2 Im(5) have been obtained from band structure calculations for

both N i and Fe. There was reasonable agreement (51) with experimental results, concerning the gross spectral features, in the case of Fe, while the calculations for Ni were only in very moderate agreement (50) or in complete disagreement (52) with experimental data.

In summary, several attempts have been made to explain the (hj>)2Im(5)

spectrum of N i . The gross spectral features below 2 eV are fairly well described by a four parameter model based on skew scattering processes within two separate minority bands (2). This model can also be applied to Co, Fe, and some binary alloys by means of parameter fitting (9, 10). A simple, convincing interband model, however, does not exist for these metals, while band structure calculations are only moderately successful. The upshot is that no reliable answer can be given to the question as to which mechanism is dominant at energies below 2—3 eV. Following other authors (2, 4,48) it will be assumed that intraband processes are no longer important at energies above 3 eV, although this cannot be stated with complete certainty as long as no reliable information is available on the collision time of d electrons.

References

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23. M . Urner-Wille, J. Magn. Magn. Mat. 15-18, 1339 (1980);G.S. Krinchik and L.S. Miio-nova, Fiz. Metal. Metalloved. 49, 1009 (1980).

24. R.L. Comstock and P.H. Lissberger, J. Appl. Phys. 41,1397 (1970). 25. R. Atkinson, Thin Solid Films 47,177 (1977).

26. E. Sawatzky, J. Appl. Phys. 42, 1706 (1971).

27. A . M . Stoffel and J . Schneider, J. Appl. Phys. 41, 1405 (1970). 28. E. Sawatzky and G.B. Street, IEEE Trans. Magn. MAG-7, 377 (1971).

29. D. Chen and R.L. Aagard, J. Appl. Phys. 41, 2530 (1970); K . Egashira and T. Yamada, J. Appl. Phys. 45, 3643 (1974).

30. E . Sawatzky and G.B. Street, J. Appl. Phys. 44,1789 (1973).

31. A . Shibukawa, A . Katsui and K . Egashira, Jpn. J. Appl. Phys. 15,1915 (1976). 32. M.S. Vijaraghavan and V . Sivaramakrishnan, Appl. Phys. Lett. 41, 686 (1982) and

references mentioned in this publication.

33. E . Feldtkeller, IEEE Trans. Magn. MAG-8, 481 (1972); K . Egashira, A . Katsui and A . Shibukawa, Rev. Electr. Comm. Lab. 25,163 (1977).

34. A . Katsui, A . Shibukawa, H. Terui and K . Egashira, J. Appl. Phys. 47, 5069 (1976). 35. A . Katsui, J. Appl. Phys. 47,4663 (1976).

36. Y . Mimura, N . Imamura and T. Kobayashi, Jpn. J . Appl. Phys. 17, 2007 (1978); B. E. Argyle, R.J. Gambino and K . Y . Ahn, AIP Conf. Proc. 24, 564 (1975). 37. K . Lee, E . Sawatzky and J.C. Suits, J. Appl. Phys. 44,1756 (1973).

38. J.H. Judy, K . Yokoyama and T. Fujiwara, IEEE Trans. Magn. MAG-7, 377 (1971). 39. D. Treves, J.T. Jacobs and E. Sawatzky, J. Appl. Phys. 46, 2760 (1975).

40. J . Smit and H.P.J. Wijn, 'Fetrites' (Wiley, New York, 1959).

41. A . H . Morrish, 'The Physical Principles of Magnetism' (Wiley, New York, 1965). 42. C. Kittel, 'Introduction to Solid State Physics' (Wiley, New York, 1976). 43. K . H . Clemens und J . Jaumann, Z . Physik 173,135 (1963).

44. H . Burkhard und J . Jaumann, Z . Physik 235, 1 (1970). 45. P.S. Pershan, J. Appl. Phys. 38, 1482 (1967).

46. F. Wooten, 'Optical Properties of Solids' (Academic Press, New York, 1972); M.A. Omar,

'Elementary Solid State Physics' (Addison-Wesley, Reading, 1975).

47. H.R. Hulme, Proc. Royal Soc. A 135, 237 (1932).

48. J.L. Erskine and E.A. Stern, Phys. Rev. Lett. 30, 1329 (1973). 49. H.S. Bennett and E.A. Stern, Phys. Rev. 137, A448 (1965). 50. C S . Wang and J. Callaway, Phys. Rev. B 9,4897 (1974).

51. M. Singh, C S . Wang and J.CaUaway, Phys. Rev. B 11, 287 (1975). 52. N.V. Smith, R. Lässer and S. Chiang, Phys. Rev. B 25, 793 (1982).

3. EXPERIMENTAL EQUIPMENT 3.1 Choice of the polar Kerr effect

In our study of magneto-optical effects in metals we have chosen for measuring reflection rather than transmission properties. A n important reason was that for metals an experimental study of transmissive effects can only be done in thin films. Since one of the aims of the present work was to have a quantitative idea of the magneto-optical effect in virtually all alloys that are known to be ferromagnetic at room-temperature, a study of bulk samples has the advantage that these are more easily prepared than thin films. Another advantage of reflection studies relative to transmission studies is that no allowance has to be made for Faraday rotation and multiple reflections in the substrate and for discontinuous polarization changes at the interfaces. As a disadvantage we note that the effect in reflection is more sensitive to the specific properties of the surface like those that are caused by surface contamination. The significance of this problem will be discussed in the next chapter.

The polar configuration was chosen for several reasons. One of the reasons is contained in the fact that this configuration is optimal for producing large effects, the magnetization and the optical wave vector being directed along the same line. In addition, it follows from eq. (2.5) that for large values of er the polar effect is

proportional to er~3 / 2 , where both the longitudinal and the transversal effects are

proportional to e~2 (see for instance ref. 1). Because metals generally have large

dielectric constants this implies that the polar effect is the largest of the three. Moreover, the value of the off-diagonal tensor element i5, which is calculated from the Kerr effect and the dielectric constant, is somewhat less sensitive to experi-mental errors in the value of et- A numerical comparison between the polar and the

longitudinal effect showed that the latter is some 2 to 5 times smaller for the materials and the spectral range considered in this study.

A second advantage of the polar configuration is that it allows extension of the equipment with a transmission part in a relatively simple way. Last but not least, the application of magneto-optical recording is straightforwardly connected with the polar effect.

A disadvantage is the relatively high magnetic field that is required for proper alignment of the magnetization. It has, however, been possible to obtain sufficiently perpendicular alignment in practically all samples investigated.

3.2 Measuring principle

The polar Kerr effect can be measured in several ways. A n essential difference between the various possibilities is contained in the optical modulation method. The approach that was chosen in the present apparatus is sketched in fig. 3.1. The incident beam is linearly polarized by a fixed polarizer P. The orientation of the polarization ellipse (azimuthal direction) of the reflected beam is modulated by a Faraday modulator Mod. After passing through an electrically adjustable analyzer A ,

Fig. 3.1. Illustration of the measuring principle. P: fixed polarizer; R: linear phase retarder;Mod: Faraday modulator; A: electrically adjustable analyzer.

the light beam falls on to the detector. Phase-sensitive rectification of the output signal produces a voltage that is equal to zero when the analyzer is exactly crossed to the azimuthal direction of the reflected beam. This position of the analyzer is automatically found by an electronic system. Reversal of the sample magnetization causes a change in azimuthal direction, which is followed by the analyzer. The Kerr rotation is now determined as being equal to half the change in the crossed analyzer position upon magnetization reversal. This procedure is repeated with a phase retardation plate R introduced in front of the modulator. If R is an exact quarter wave plate, execution of the measuring procedure now results in the Kerr ellipticity instead of the rotation. If the phase retardation is not equivalent to a quarter wave, a linear combination of rotation and ellipticity is measured.

Various alternative modulation techniques have been used in ellipsometric measurements by several investigators. These alternatives often involve large modu-lation angles, as can be obtained by means of electro- (2) or piezo- (3) optical materials or by a rotating polarizer (4). This is attractive because analysis of the detector signal provides information on both the azimuth and the ellipticity from one measurement. Actually these are intensity measurements where both the DC component and the component at the modulation frequency or its second harmonic are concerned. Therefore the influence of uncorrelated fluctuations and long term variations in the system's response to these different components is more disturbing than with the zeroing method that is used in the present set-up. In practice the pros and cons seem to compensate each other fairly well, because a comparison of literature data on the various methods shows that no significant differences in performance exist. A system (5) that is based upon the same principle as the present one is reported to have 0.0006° resolution in the spectral range of optimal performance, using a 10 sec phase-detector integration time constant. Other systems, such as the one described by Aspnes et al (4) which is based upon a rotating

polarizer, perform equally well, or they are less sensitive, but also have a shorter response time (2). The present approach was chosen because of its directness. The use of two modulators (6) working at different frequencies or in quadrature would provide a way to measure azimuth and ellipticity simultaneously by means of a zeroing method. This possibility was discarded in order to keep the optical and the electronic parts of the system relatively simple.

For the spectroscopic measurements mirrors are used as collimating elements because they do not suffer from chromatic aberration. In the ultra-violet (UV), however, scattering due to surface roughness becomes significant and the reflection coefficient decreases, so here the advantage of the use of collimating mirrors is lost. Mirrors have the disadvantage, if placed between polarizing elements, that they disturb the polarization. To avoid this effect as much as possible, care was taken to use only near normal incidence and p- or s-polarization. In that case the influence of the mirrors on the state of polarization is not too serious, in particular because the Kerr effect is always relatively small. Moreover, by doing appropriate calibra-tion experiments one can make correccalibra-tions for effects like this, as will be shown in section 3.5.

In the following a description will first be given of the equipment used for spec-troscopic measurements. Afterwards the design of a simple measuring apparatus will be shown where two lasers, working at two different wavelengths, are used as light sources.

3.3 Optical path

3.3.1 Layout

In fig. 3.2 a diagram of the optical layout is shown with a list to explain the the symbols. The spherical mirror M l images the arc of the Xe lamp on to the

Fig. 3.2. Diagram of the optical layout of the Kerr spectrometer. L: Xe arc lamp; Ml - 10: mirrors; MC: monochromator; Fl, 2: optical filters; P: fixed polarizer; S: sample;R: linear phase retarders;Mod: modulators; A: analyzer, adjustable with stepper motor; SI: slit; D: detectors.

entrance slit of the monochromator. The purpose of the flat mirror M2 is to mini-mize the angle of incidence on M l . This is necessary to prevent light losses due to

geometrical aberration. The spherical mirrors M4, M6 and M9 image the mono-chromator exit slit, with the help of flat mirrors, on to the polarizer, sample and analyzer, respectively. The mean angle of incidence on these mirrors and on the sample is almost 4.5°, being slightly larger than half the aperture of 8.4°, which is determined by the monochromator. A l l spherical mirrors operate at unit magnifi-cation. The radius of the spherical mirrors was to be sufficiently large to keep the geometrical aberration within acceptable limits. A value of 75 cm was chosen as this allowed the dimensions of the set-up to be reasonably small. The images produced appeared to be of sufficient quality. The image of the bright spot of the Xe arc has an area of some 1.5 x 3 m m2, which is approximately equal to the spot size itself.

The images of the exit slit also fitted well within the cross-sections of the polarizer and the analyzer. The mean angle of incidence on the last mirror M10 is higher than 4.5°, and this mirror also has a radius of only 50 cm as no more space is available. This is permissible because the final image is still smaller than the sensitive detector area.

The monochromator was placed directly behind the lamp and not in front of the detector. This was done to prevent high intensity U V radiation and ozone formed by this radiation from attacking the metal sample surface. A set of interchangeable order-sorting filters (F2) was placed in front of the detector, this being the position where maximum stray light reduction is obtained. Some interchangeable low-fluorescence filters ( F l ) were placed behind the monochromator to block high orders in the U V . This was thought advisable because U V light turned out to produce well detectable fluorescence in the various components. For measurements in the U V these filters are left out. In that case blocking of the fluorescent light is done by some interchangeable U V band filters that are incorporated in filter set F2.

3.3.2 Components

Lamp

A n Oriel 6262 Xe arc lamp is used as a light source. The lamp housing and the power supply were also obtained from Oriel under model numbers 6148 and 6102, respectively. The housing is provided with a spherical mirror at the rear of the lamp, which adds 25 — 30% to the lamp output power, according to the manufacturer. The Xe spectrum is rather smooth apart from some peaks at wavelengths between 800 and 1200 nm. Measurements in this wavelength range are performed at these peaks to give maximum signal to noise ratio.

Mirrors

Some flat mirrors were obtained from Spindler & Hoyer. The other mirrors were home-made. This was necessary because mirrors with a 75 cm radius are not readily available commercially and also because some mirrors, especially M7 and M8, have

dimensions that are not available either. These dimensions are imposed by the size of the reflected beam and by other light beams or components, between which these mirrors have to fit. A l l mirrors were made from aluminium, overcoated with a 30 to 40 nm thick M g F2 layer. This coating was intended to decrease considerably

the slow deterioration of U V reflectivity of A l surfaces in an atmospheric environ-ment. The coatings are sufficiently thick to be fully closed and sufficiently thin to preclude interference.

It was found that the surfaces of the mirrors M l and M2 were severely blemished by the high intensity radiation emanating from the Xe lamp. As this blemishing is likely to be stimulated by the presence of oxygen and ozone, two fresh mirrors were mounted and enclosed in a box that was fixed to the lamp housing and the monochromator and that was flushed with dry nitrogen gas. This box also served to intercept spurious light that would otherwise reach the detector. Upon inspection after a year of operation these mirrors again appeared to be blemished very severely at the parts that had been hit by the radiation. This also probably accounts for a slight gradual decrease in equipment performance that was observed during this year at wavelengths below 300 nm. This kind of surface deterioration is probably due to the M g F2 coating, as it is not observed on bare A l mirrors. It is therefore

expected that the wavelength range of the equipment will be extended towards shorter wavelengths when mirrors M l and M2 will be replaced by bare A l mirrors or mirrors with a better coating. Some blemishing, though much less severe, was also visible on the other mirrors.

Monochromator

The monochromator is a Spex 1702 spectrometer with 75 cm focal length. For measurements from the U V up to 1050 nm wavelength a 1200 gr/mm grating is used, blazed at 500 nm. Measurements in the infra-red (IR) above 1050 nm are done with a 600 gr/mm grating blazed at 1600 nm. This monochromator was chosen for several reasons. In the first place, gratings can be interchanged conveniently and in less than one minute. Secondly, this monochromator is provided with a stepper motor and an electronic drive unit which allow fast wavelength scanning (8 nm/sec) and ample facilities for automation. Thirdly, this model can be equipped with fairly large gratings (102 x 128 m m2) , providing good intensity at a given spectral width.

Spex also offers a similar model with 1 m focal length. The 75 cm version was chosen because very sharp peaks were not expected in the spectra of metals, so preference could be given to high optical intensity instead of ultimate resolution.

The slits are both set to a width of 1.5 mm when the 1200 gr/mm grating is in use, thus providing a spectral width of 1.6 nm. With the other grating the slits are set to their maximum width of 3 mm, corresponding to a spectral width of 5—7 nm. The spectral resolution AX/X now varies between 0.25 and 0.65% over the whole wavelength range.

Optical filters

The optical filters were partly obtained from Schott and partly from Oriel. Two low-fluorescence filters with cut-on wavelengths of 380 and 420 nm are used at wave-lengths above 400 nm for U V blocking. The filters are mounted one above the other in a metal frame that can contain up to five filters. The frame is suspended from a steel wire, the other end of which is fixed to a small spirally grooved cylinder. The cylinder is mounted directly on to the shaft of a stepper motor. Switching to an adjacent filter position is accomplished by applying a prescribed number of pulses to the stepper motor. When no filter is used the whole frame is pulled up to a position above the light beam.

A similar filter mount (F2) is used in front of the detector. This mount contains two order-sorting and three U V band filters. Another order-sorting filter was placed in the other mount ( F l ) together with a U V blocking filter at the same position, as all positions in front of the detector were occupied. The U V band filters cover the spectral range between 250 and 390 nm.

The order-sorting filters provide a high order blocking that is better than 0.001% for measurements in the spectral region below 1700 nm, apart from some small intervals where the high order intensity rises to 0.01%, or even to 0.3% in the inter-val 1280 - 1290 nm. The Kerr effect at high order wavelengths is attenuated by the same amount as the intensity, so the high order blocking is adequate in the above-mentioned wavelength region. From 1700 nm on the high order intensity gradually increases up to approximately 1% of the first order at wavelengths above 2000 nm. However, this is not a serious limitation as the accuracy in this region is usually determined by the signal to noise ratio.

Polarizer and analyzer

Two Glan-Thompson prism polarizers of calcite, made by Karl Lambrecht, type no. MUGTS10, are used as a polarizer and an analyzer. The prisms were delivered joined with a U V transmitting fluid. Because of the U V absorbance of calcite these

polarizers become less efficient at shorter wavelengths. At 275 nm the transmission has dropped to half the transmission for visible light. This is believed to be one of the factors that limit the spectral range of the equipment on the U V side to 280 nm. Quartz polarizers of another type show a higher transmission in the U V but are not used because they cannot accommodate the optical aperture of 8.4°.

The extinction ratio is 5.10"5 over the inner 6.6 x 6.6 m m2 of the cross-section.

The monochromator exit slit, which is at most 3 mm wide and is illuminated over 3 mm of its height, is imaged well within this area on to the polarizer. At the analyzer the light spot is approximately 7 x 6 m m2 in size, falling only slightly

outside the optimum area but still within the total analyzer cross-section of

1 0 x 1 0 m m2. The light spot at this position is rather large because two modulators

with different glass rods are used in order to cover the whole wavelength range. These glasses have different refractive indices, which results in a longitudinal shift

of the image plane over some 15 mm when the modulator is switched. The analyzer was placed between the two positions of the image plane.

The polarizer was adjusted to give a maximum degree of linear polarization at the location of the sample. This degree was measured with an analyzer at a number of wavelengths and the extinction ratio was found to be better than 10^*. The polarization was chosen in the p-direction because the grating reflects p-polarized light relatively better at longer wavelengths and s-polarized light at shorter wave-lengths. In this way more spectral range is gained as the system performance already drops rather sharply in the UV, due to other factors, but only gradually in the IR.

The analyzer is mounted in a tube that is driven by a stepper motor and a gear mechanism which produces a rotation of 0.001° per step. The relative accuracy, which may vary with the angular position, was designed to be at least 0.7%. There is an additional hysteresis of the order of 0.005°, but this is eliminated by always approaching the crossed analyzer position from the same side. The maximum rota-tion speed is 0.5° per sec.

Magnet

Alignment of the sample magnetization is accomplished with the help of a magnet of a design that is standard at our laboratories. A cross-sectional outline is shown in fig. 3.3, which also indicates the position of the sample. The magnet

036

<*80

Fig. 3.3. Cross-sectional outline of the magnet with some dimensions indicated in mm S: sample.

consists of six water-cooled coils and an iron core. The light beam passes through a hole in the front polepiece. This hole has the shape of a truncated pyramid the top of which, being a square with 12 mm sides, is located near the sample. The distance between the polepieces is rather large (26 mm) because the sample holder, being of a rugged construction, has a thickness of 20 mm. Moreover, the sample surface must preferably be positioned at some 5 mm from the front piece because the

magnetic field decreases at shorter distances due to the presence of the hole through which the light beam passes. Also some space is needed for sample alignment.

The maximum field is determined by core saturation and by heat development in the coils. It amounts to 1.2 T at 1.8 — 1.9 kW power dissipation. For fields above 0.75 T the measuring procedure is stopped for a short time after every measuring point to allow the magnet to cool down. These idle periods are increased at higher fields up to 40 sec at the maximum field of 1.2 T. Because the illuminated spot at the sample is never larger than 3 x 3 m m2, the hole in the polepiece might be

smaller than it is now. An increase of the maximum field to 1.4 T is expected when the conical end of the piece would be replaced by a new one with a smaller hole.

The magnet current is supplied by an Electronic Measurements power supply model SCR 160-30-20100. The current is regulated by means of a programming resistance. For checking purposes it can also be measured by means of a small series resistance in the magnet leads. Field switching is accomplished by means of a relay that is software protected against switching while the magnet is still under power, the magnet current being sensed through the series resistance. The magnetic field was calibrated against current with the help of an F.W. Bell magnetometer model 811A with Hall probe. This calibration is used during the magneto-optical measurements.

Sample holder

In fig. 3.4 the central part of the sample holder is shown. It consists of a hollow brass cylinder with 20 mm thickness and 25 mm inner diameter, which is closed

, 2 7 x 1 4

4 H

Fig. 3.4. Central part of sample holder; dimensions in mm. S: sample, cast into Technovite cylinder.

on one end. The sample is placed within the cylinder and firmly pressed by means of a ring that is screwed into the cylinder. This can be done very conveniently because the samples usually are cast into a cylinder of Technovite to facilitate surface polishing. Bare metal samples are embedded with the rear side in a ring with a conical hole.

ends of these rods have to be mounted in two adjusting mechanisms, which were built from Micro Controle mechanical adjusting elements (see also fig. 3.6). This construction allows sample positioning in three dimensions and orientation of the sample surface in the two angular directions. A t the same time the whole construc-tion is sufficiently rugged to the effect that not the slightest sample movement can be detected when the magnetic field is applied, even if a large sample of iron is present in the holder.

Phase retardation plates

A n important aspect of phase retardation plates is their sensitivity to non-normal incidence. In a uniaxial wave plate with refractive index n the relative retardation error for a slant ray with angle of incidence 7 can be shown to be of the order of 1 /2(7/n)2, for small values of the birefringence and 7. In the two halves of a

compound retarder these errors are additive. A quartz compensator, which has a retardation of at least 50 orders in each half, thus shows an error of at least 37° if n is put at 1.6 and 7 at 4.2°, being half the aperture of the light beam. Therefore a compensator would produce a very inhomogeneous retardation and would also be very sensitive to small alignment errors. These difficulties were avoided by choosing a number of single-order plates as linear retarders. This solution was preferred to the use of Fresnel rhombs or compound achromatic wave plates (7) as these, too, do not offer the possibility to span the entire spectral range with a single element and are also more sensitive to non-normal incidence.

Three mica single-order retarders are used for wavelengths above 350 nm. The nominal retardation is 90° at the wavelengths 490, 690 and 1450 nm, respectively. For wavelengths below 350 nm a compound zero-order quartz retarder (2—3 mm thickness) is used with 90° phase retardation at 320 nm. This is necessary because mica is too absorptive in the U V , while single-order quartz retarders are too thin to be practical and a multiple-order wave plate, though thinner than a compound retarder, is not usable over a broad wavelength range. A l l retardation plates were delivered by Steeg & Reuter.

The plates were mounted one above the other in a frame which can be raised by a stepper motor in much the same way as the optical filters. The frame is rather heavy because each plate is provided with a simple rotation facility which allows the axes to be aligned in the horizontal and vertical directions. The weight is adapted to the maximum motor torque by means of a two-wheel gear mechanism. The middle position in the frame is empty and is used during Kerr rotation measure-ments.

Modulators

Fig. 3.5 gives a cross-sectional view of one of the modulators. It consists of a glass rod surrounded by a cooling jacket and a solenoid. The construction material is perspex. In the set-up there are two modulators, placed one above the other. One

cooling

jacket

foam

plastic

Fig. 3.5. One of the Faraday modulators with some dimensions indicated in mm.

is used at wavelengths below 430 nm and contains Heraeus Suprasil I quartz as a modulator glass for its high U V transmittance. As quartz has a rather low Verdet constant, especially at longer wavelengths, the region above 430 nm is covered by the Schott glass SF59. This material was supplied as a replacement for the obsolete type SFS6, which is known to be a good modulator material (8) due to its high Verdet constant and low absorbance. A rough determination of the Verdet constant of SF59 at a number of wavelengths showed that its magnitude is comparable to that of the known Verdet constant of SFS6 (8).

A problem arises due to the existence of stress-induced birefringence in the glass rods. This problem was partly met by using two rods per modulator, each of half the total length, which were mutually oriented so as to provide maximum com-pensation. Then the two halves were rotated together to a position where the axes of the remaining phase retardation were horizontally and vertically directed. The residual effect was taken care of by means of calibration experiments (section 3.5). Thermal stress was minimized by packing the rods in a sheet of foam plastic in order to provide for thermal insulation and to accommodate thermally induced changes in the dimensions of the glass rods and the perspex holder. The total length of the glass rods in one modulator amounts to 100mm and the diameter is 40 mm.

The solenoid is wound with 636 turns of varnish-insulated copper wire with 1.5 mm core diameter. Adjacent layers are separated by a thin insulating sheet. The inner diameter of the solenoid is 60 mm, the outer diameter 100 mm, and the length 78 mm. The DC resistance amounts to 1.6Í2, the selfinductance to 18 mH, and the magnetic field at the centre to 7 mT/A. Each solenoid forms a resonant circuit with a series capacitor, thereby providing a reasonable adaptation to the 1Í2 output of a Philips 200 W audio amplifier model SQ4 LBB1104. Each capacitor is

constructed from four 10 /jF, 250 Vef f capacitors which are interconnected to

form one 10 iiF, 500 Vef f capacitor. One of the resonant circuits was trimmed by

means of a small capacitor parallel to the large one in order to obtain equal resonance frequencies, which amount to 383 Hz.

The modulator current amplitude is 2.6 A, corresponding to a magnetic field of 18 mT. Heat development in the solenoid is the limiting factor, as the amplifier is able to produce a current that is 3 to 3.5 times higher. This potential modulation amplitude has not yet been reached because connection of the cooling water supply has been delayed by some practical difficulties.

The modulation angle amplitude was roughly estimated from the form of the detector output signal. The difference of the two analyzer positions where the characteristic dip in the output signal, being due to the second harmonic of the modulation frequency, disappears, was taken as the double amplitude. For the quartz modulator the amplitude decreases from 1.2° at 310 nm to 0.45° at 430 nm. It could not be determined in this way at shorter wavelengths. For the SF59 glass the modulation angle is limited to 2.1° at wavelengths below 510 nm and from there on it decreases to 0.6° at 1 /mi- Assuming the dispersion of SFS6 (8), it should be near 0.17° at 2 jum wavelength.

The amplitude is limited to 2.1° in order to minimize the influence of modulator birefringence. Besides, the signal to noise ratio is not increased in this spectral range by an increase in modulation amplitude, because both the signal and the noise are

proportional to the amplitude, the noise being dominated either by source fluctua-tions or by shot noise from the component in the optical intensity that is propor-tional to the square of the modulation amplitude. The amplitude is adjusted by means of a Philips programmable frequency synthesizer, model PM5190, which drives the power amplifier.

The first experiments, which comprise many of the measurements described in this study, were carried out with a slightly different electrical modulator circuit and a 40% lower modulation amplitude. The angular resolution during these measure-ments was somewhat less than it is now for wavelengths above 1050 nm, indicating that the noise in this spectral region is dominated by other components than those that were mentioned earlier (probably 1/f noise, see description of the detectors). In the U V below 310 nm the lower amplitude was just noticeable in the resolution, but it made no difference at all at the other wavelengths.

The modulators are switched by means of compressed air because of their rela-tively large weight. The compressed air is regulated by electrically powered valves. A relay, hardware protected from operating when the modulator is under power, switches the modulator current.

Slit

A vertical 3 mm wide slit is used as a field stop in the horizontal direction to block environmental light. Vertical blocking is performed by a simple circular diaphragm

placed close to the slit. The detector is positioned behind the slit at such a distance that the sensitive area is almost filled. Thus the detector serves as an aperture stop.

Detectors

The wavelength region below 1050 nm is covered by three Oriel photomultipliers with a built-in resistor divider network; their type designations are 7060, 7062 and 7066. The multiplier no. 7060 is used at wavelengths below 430 nm together with the quartz modulator because modulator switching causes a slight horizontal shift of the optical beam, which is met by this detector having a slightly different hori-zontal position. The wavelength range between 430 and 670 nm is covered by the 7062 and the range from 670 to 1050 nm by the 7066 multiplier. Above 1050 nm a Philips 62SV lead sulphide detector is used together with the IR monochromator grating because the optimum wavelengths for grating switching and detector switching approximately coincide. The detectors are placed one above the other in a metal frame that is positioned by means of a stepper motor and a two-wheel gear mechanism in the same way as the phase retardation plates.

The photomultipliers are powered by a Kepco 80P 1000M high voltage supply, which is programmed by means of an analog input voltage. The detector supply voltage, which varies between 200 and 900 V , is chosen according to wavelength from a table that was constructed to give maximum signal to noise ratio with a con-stant sensitivity setting of the lock-in amplifier. A t the same time, the table was constructed so as to avoid amplifier overload. This approach was preferred to a rather time consuming automatic procedure for optimum voltage setting and was possible because the signal to noise ratio does not depend strongly on the supply voltage, as long as the voltage is not too far removed from the optimum value. This implies that different samples with appreciable differences in reflectivity can be measured with the same detector supply voltage.

The PbS detector is operated via a 1 MS2 series resistance from a Delta Elektro-nika E0300-0.1 voltage supply, because the Kepco supply picks up too much spurious signal at the modulation frequency when used with the PbS detector. The voltage is fixed to 225 V as this unit is not programmable. Therefore the sensitivity of the system is adapted by decreasing the modulation amplitude at the few wave-lengths above 1050 nm where this is required.

When, during a measuring series, a multiplier is replaced by another one the high voltage line is switched to the new detector by means of two relays, after the voltage has first been returned to zero. The relays are hardware protected against switching when the voltage is still present. Switching to or from the PbS detector requires operator intervention, but this is not a limitation as it occurs at the same wavelength where the grating and the monochromator slit settings are changed, which operations are also manually performed.

A P A R 121 lock-in amplifier takes care of the phase-sensitive rectification of the detector output signal. The reference signal is taken from a separate output at the frequency synthesizer. A switching relay in the signal lines introduced a large

Fig. 3.6. The Kerr spectrometer. In the foreground are the magnet and part of the sample holder with its adjusting mechanism. Also shown are the polarizer, the phase retardation plates, the detectors and a part of the electronics. The modulators are just visible behind the retardation plates.

spurious signal at the modulator frequency, which could not be screened off in a simple manner. Therefore the three multiplier signal lines are connected in parallel. This causes a signal reduction of 20% and no noise increase. The signal line from the PbS cell is switched manually with the line from the multipliers.

The noise is dominated by shot noise or by source fluctuations in the wavelength region between 310 and 1000 nm. Owing to the decreasing optical intensity, the noise at wavelengths below 310 nm mainly stems from dark current; this is easily

verfied by interrupting the light beam and is also in agreement with the dependence of the angular resolution on the modulation amplitude (see above). In the same way the noise at wavelengths higher than 1000 nm is also found to be independent of the optical intensity. In the case of the PbS cell this kind of noise predominantly consists of 1/f noise according to the manufacturer's specifications.

3.4 Automation

3.4.1 Logical equipment and interfacing

The experimental set-up is controlled by an Apple II desk top computer, which also serves for processing the raw measuring data. The various signal paths are out-lined in fig. 3.7. Data storage and retrieval are performed by means of two mini floppy disk drives. A Philips P2123 printer is connected for program listing and numerical data output. The computer has a few digital T T L inputs and outputs, which can be operated by means of appropriately addressed microprocessor com-mands (pP comcom-mands). One digital output is used to switch off the lamp at the end of a measuring series, if required, thereby increasing the effective lamp life. Two outputs are in control of all stepper motors: one output provides the direction level, while the other output delivers the pulses. These two outputs can be connected to up to eight different stepper motors by means of a home-made 16-fold relay card, which is mounted in the computer.

A l l other communication is done by way of an IEC-625 interface card, which is also mounted in the computer. To the IEC bus are connected a Hewlett Packard digital plotter HP 9872A, a Hewlett Packard multiprogrammer HP6940B, which communicates via a separate IEC bus interface HP59500A, the Philips frequency synthesizer PM5190, and a Philips digital voltmeter PM2441.

The voltmeter input is switched by a 12-fold relay card in the multiprogrammer, which thus provides six input channels. The voltmeter is primarily used for moni-toring the lock-in amplifier output. Secondly, it is used for the determination of the magnet current. Sometimes the analog output of the magnetometer is monitored.

Most other functions are performed by the multiprogrammer. It controls the magnet power supply and the high voltage supply for the photomultipliers. It also switches the compressed air for the modulators, the modulator current, the high voltage line, and the polarity of the magnet current, and it senses the states of the end switches of most individual stepper motors. As mentioned, the modulation amplitude is controlled directly by means of the frequency synthesizer.

Each time a stepper motor (except the one in the monochromator) has been used, the state of its end switches is checked by the computer. Because the analyzer is rotated very often, the state of the analyzer's end switches is transferred to the computer by way of one of its own digital inputs (see above), which operate much faster than the combination of multiprogrammer and IEC bus interface. The four lower end switches under the phase retardation plates, the detectors, and the two filter sets are also used as position references when the measuring program is started.