Measurement and Interpretation of Magnetic Circular Dichroism and Magnetic Linear Dichroism Spectra BY J. BADOZ M. BILLARDON A. C. BOCCARA AND B . BRIAT Laboratoire d'Optique Physique,* E.P.C.T. 10 r w Vauquelin Paris V" Received 9th October 1969 This paper deals with three problems of ;t different nature. We first discus the conditions required to obtain reliable and usable magneto-optical and absorption data at any temperature down to that of liquid helium; this discussion includes the description of our cryostat and absorption device as well as a critical study of the optimization of the signal-to-noise ratio of the instruments. Secondly a new fitting procedure is proposed for the analysis of absorption and magnetic circular dichroism curves and the extraction of useful parameters.Finally the significance of these para-meters is examined for anisotropic centres isolated in an isotropic matrix ; the results thus obtained are illustrated by means of magneto-optical experiments on CaF2 +Nd3+ crystals. Magneto-optical studies have largely benefited from instrumental progress in the measurement of natural optical activity. Most results have been obtained through the measurement of magnetic circular dichroism (MCD) and to a less extent magneto-optical rotatory dispersion (MORD). More recently magnetic linear dichroism studies (MLD Voigt or Cotton-Mouton effect) have been demonstrated to be of interest for the investigation of some particular spectroscopic problems. All these techniques lead to the experimental determination of parameters which in one way or another are related to molecular data (mainly magnetic moments) to be checked against theoretical predictions.In this paper we make comments on three different topics. (i) The experimentalist has two major aims when performing MCD and MLD work. First he requires measurable or even eventually large signals ; this problem can be dealt with by considering the signal-to-noise ratio as a parameter to be optim-ized. Secondly he often needs well-resolved magneto-optical and absorption data at many temperatures down to that of liquid helium ; we here investigate the difficulties encountered with particular emphasis on the study of very small (1 mm2 for example) crystals at low temperatures. (ii) A new fitting procedure is proposed for the analysis of absorption and MCD curves without any assumption about the number of actual components within a given band.(iii) Finally the significance of the extracted para-meters is discussed in the particular case of anisotropic centres isolated in an isotropic matrix. Two pertinent examples are chosen among recent MCD and MLD experi-ment s. INSTRUMENTATION GENERAL CONSIDERATION Circular dichroism measurements have now become well established.2* We use a photoelastic modulator in our instrument rather than a Pockels cell. This type of a modulator requires a very low driving voltage and possesses a wide aperture thus * Equip de recherche no. 5 du C.N.R.S. 2 optimizing the signal-to-noise ratio. Secondly the use of a null-method increases the stability of our instrument thus allowing dichroic optical densities AD- to be detected using a 6 A spectral width and a time constant of a few Throughout this paper MCD is referred to as the difference in optical densities D+ - D- for B+ and cr- components.Linear dichroism (e.g. stress- or magnetically-induced) is defined as the difference D,- D in optical densities for two mutually perpendicular linear polarizations (see fig. 1). Its measurement can be performed by 5 6' 6' FIG. 1 .-Schematic diagram showing circular and linear polarization. c c coupling a circular dichrometer with a quarter-wave plate (e.g. a Fresnel rhomb 6). The two circularly-polarized components are thus alternatively transformed into x and y linearly polarized components. The compensating system still works properly and performances for MCD and linear dichroism (ADID ratio) are the same.Magnetic linear dichroism is now induced by orienting the magnetic field perpendicular to the direction of propagation of the light beam (along one of the x or y axes). We now comment on two problems which the instrumentalist has to deal with, viz. to optimize the signal to noise (s/n) ratio and to obtain good resolution. OPTIMIZATION OF s / n The signal-to-noise ratio of a dichrometer is proportional to the square root (40)* of the luminous flux going through it. 4o is dependent upon three factors the effective brightness of the system comprising the light source and some suitable optical device ; the light gathering power 5 of the apparatus ; and the spectral width of the monochromator.In this section emphasis is on the second factor only the last being discussed later. The light-gathering power is often limited by the size of the sample S and that of the polarizer P placed next to the modulator (see fig. 2a). If no lens is used between P and S { is (1) 5 = ApAs/L2 = A,Q, D M M 1 -4 L - 1 , FIG. 2.-Illustration for calculation of the light gathering power (see text for description) J . BADOZ M . BILLARDON A . C . BOCCARA AND B . BRIAT 29 where A and As are the cross section area of P and S respectively and L is the distance between them. The solid angle Cl should be as large as possible and this requirement emphasizes the advantage of our photoelastic modulator with respect to the electro-optic one. Now in work on crystals very often their size is quite small (e.g.1 mm2, and in such cases we use a lens of section AL in front of the sample. 5 then becomes (2) (fig. 2b) c' = ApAL/L2 = ALAs/12. Since I is chosen to be much smaller than L the lens improves considerably the s/n ratio. However much care should be taken in the experimental work since a poor quality lens or improper orientation of the lens might result in drastic changes in the MCD curve. In practice in all cases a zero line is obtained in the absence of the magnetic field. We sometimes use an alternative technique for the study of micro-crystalline samples. The powder is immersed in an inactive liquid of which the refractive index is very accurately adjusted. This method has been checked by comparing the MCD and absorption spectra of a massive sample (Nd3+ doped glass) and of the same sample broken into very small pieces which were then immersed.The same results were obtained although the noise level was slightly higher in the latter experiment. It follows from eqn (1) that L has to be reduced as much as possible in order to increase the light gathering power. Magnetic field generators should thus be as small as possible and hence the use of an electromagnet is discarded. Superconducting magnets have now become available and these induce a high magnetic field (at least 50 kG) over a reasonably short path length. (Such equipment should undoubtedly be used when very small signals are to be detected or when a small amount of material is available (bio-compounds or organics).The same problem arises when the sample is rather insoluble or contains only few impurity centres (crystals) and must thus be studied using a longer path length in order to increase the signal. 3 1 i\ CsCl - Pb2+ 2 I FIG. 3.-Absorption (- - - -) and MCD (---) of Pb2+ in CsCl. Such an example is shown in fig. 3 for Pb2++ CsCI. The impurity did not enter the matrix very well and we obtained small optical densities even over a 2 cm path. Here it proved necessary to use a high field (50 kG) provided by means of an Oxford instrument superconducting magnet. However we have made important progres 30 MCD AN11 MLD SPECTRA in the design of permanent magnets. In our laboratory room temperature routine work is conducted with a 8 cm long magnet which provides fields up to 8 kG in a 5 mm air gap.CRYOGENIC AND ABSORPTION DEVICES MCD work particularly on inorganic compounds must include low temperature measurements whenever possible and MCD signals are generally increased when the temperature is decreased due to either the paramagnetism of the sample (C terms 9), or a narrowing of the bands and the observation of A terms ( e g rare earths). Actually we have found that magnetic fields of a few hundreds or of a few thousands gauss were sufficient to conduct most of our experiments. Further the orientation of crystals in the light beam proved to be very critical in many instances. Thus rather than use a classical optical cryostat or the low-temperature aperture in our super-conducting magnet we designed our own cryostat with a number of major aims a short path length in order to be placed and oriented between the pole pieces of a permanent magnet ; the possibility of quickly cooling the sample down to any temp-erature without perturbing the light beam ; low cost and ease of use.Our cryostat s He FIG. 4.-Schematic diagram of the cryostat used in our experiments is shown in fig. 4. Cold nitrogen or helium gas is pumped up through I and evacuated through E by means of a vacuum pump. A thermocouple t allows the temperature of the sample to be measured. This temperature can be varied easily by adjusting the flow of gas. A double jacket is used to reduce the thermal loss. Silica windows W allow the light to pass through the sample ; they are sealed on copper sheets and do not contribute any stray birefringence.This device is only 2 cm length alon J . BADOZ M . BILLARUON A . C . BOCCARA A N D B . BRIAT 31 the light path and can be easily oriented between the pole pieces of the permanent magnet. The sample itself is further oriented with respect to the light beam by means of its holder S. The measured temperature is the actual one since the sample is placed in the cryogenic fluid. The operation is very easy since one has merely to plunge the T cylinder into the dewar and then pump. After 5-10 min temperatures down to 5 K can be obtained. Moreover any chosen temperature can be stabilized within kO.1 K by means of a flow-valve monitored by the thermometer. For low-temperature work we thought it was important to run MCD and absorption spectra under the very same experimental conditions such as position of the sample temp-erature and spectral width.The best way to achieve this is to record both spectra simultaneously on the same instrument. The device shown in fig. 5 has thus been FIG. 5.-Schematic diagram of our absorption attachment. added to our dichrometer. Two semi-reflecting plates L and L are used before and after the sample in order to direct part of the light on to two photomultipliers. Their readings are then equilibrated by means of a servo-mechanism monitoring a wedge W linear in optical density. The displacement of the wedge is thus recorded as a function of the wavelength. We have not yet considered the role of the slit width of the monochromator and t iiiis the resolution of the instrument.Actually except for lanthanides actinides (i.e. UClg- or UOZ-) and certain spin forbidden lines (ruby) the absorption com-ponents of most compounds are reasonably wide at room temperature and MCD and absorption spectra can be run on any commercial instrument. Low-temperature work on the other hand usually requires a much increased resolution. With a given ~iionochromator one has to reduce the slit width in order to gain resolution thus alter-ing the signal-to-noise-ratio. Using a very luminous grating monochromator (1 200 groves/mm (102 x 102) we have succeeded in detecting small signals optical density unit) with a 1 A spectral width. This resolution is insufficient in some cases and further improvement would be much appreciated. Even so reasonably accurate parameters can be extracted by means of a deconvolution of the experimental curves.ABSORPTION A N D MCD CURVES ANALYSIS ?‘HE PROBLEM We have now dealt with a number of devices which contribute to obtaining accur-ate and reliable experimental data. Unfortunately these data cannot as a general rule be used as such since significant parameters have first to be extracted from the curves before any detailed assignment can be attempted. We now comment on fitting procedures; it will be assumed throughout that the resolution of the apparatus is adequate but that absorption and MCD components are not fully resolved in the spectra due to the broadening of lines via any mechanism 32 MCD AND MLD SPECTRA An absorption curve is then considered as the sum of many unresolved compon-ents and one can write for the optical density* where Dm andf,(v) are the maximum optical density and shape function for the isolated ith component.Similarly one has (4) for the magnetic dichroic optical density (standardized to 1 G). As has been shown recently,l a description of an MLD curve requires generally a linear combination of the absorption curve and its first and second derivatives. The treatment given for both MCD and MLD assumes the Zeeman separations to be much smaller than both the line-width and kT as well as a rigid shift of the Zeeman lines. One way of fitting the curves is to assume a reasonable number of components as well as some standard (gaussian or lorentzian) line shape. A computer programme then allows the Dml ai bl and ci parameters to be determined.In simple cases, mere consideration of the shape of the curves and magnitude of the peaks can provide a reasonably accurate answer to be checked against rather crude theoretical calcula-tions. It has recently been argued lo that the method of moments can be profitably used in many instances. This is true as long as the actual number of components does not need to be known; on the other hand however it does not require any assumption about the rigid or non-rigid shift of the individual Zeeman lines. which does not require any assumption about the number of components and which gives good results when the accuracy of the experimental data is sufficient. We have developed a different graphical method ANALYSIS OF ABSORPTION CURVES For simplicity only Gaussian components are considered although the method can be generalized to say Lorentzian components.A Gaussian curve can be repre-sented by Y = Di = Dmi exp { -[(v-vr)/6,12>, where vi and ai are the central frequency and half-width at l/e of the maximum of the ith line. Now it is easily shown that a plot of Y’ dDJdv 2 - -- { - -+v-vi) Y Di ai as a function of the frequency is a straight line ; the abscissa for Y’/ Y = 0 gives vi and the slope provides the band width. The method applies as well when curves are recorded in terms of wave length. The procedure is only slightly more complicated when the absorption curve contains many unresolved components. A plot of Y’/ Y = f(1) shows those fre-quency ranges where one of the ith lines gives a predominant contribution.This is illustrated for a theoretical example in fig. 6a where Do is the computed sum of two gaussian components of different intensities that are widely separated. Y’/ Y = f(A) is linear on the left-hand side of the figure and R1 = 3 OOOA and 6 = 160A are * D is used here for absorbance (A) since this last parameter (A) is widely used in the description of MCD data J . BADOZ M . BILLARDON A . C . BOCCARA A N D B . BRIAT 33 extracted for the major component which turns out to be identical to D1. The difference Do- D1 gives a curve 0; which is then analyzed in the same way. Only one component is obtained and its characteristic parameters are the same as those of 0 2 -I- a A FIG. 6.-Analysis of absorption nd MCD curves (see text for comments).We applied this method to a number of practical cases.ll* l2 We thus showed that the first excited state of d10s2 ions (3P1 in cubic symmetry) to have its degeneracy completely lifted and to give rise to three b terms. We also obtained interesting results for tetrahedral complexes of the 3d transitions metals. An example is illus-trated below. ANALYSIS OF MCD CURVES The procedure for MCD curves can be derived from eqn (4). We assume first a single absorption band and obtain Thus a plot of [AD]JDi against v (or A) is again a straight line. The ordinate for v = i t i gives (b,+c,/kT) and the slope provides the a parameter. This is illustrated in fig. 66. When absorption and MCD curves are both complex the absorption curve analysis is first carried out and the data thus obtained allow accurate MCD parameters to be extracted from the analysis of the experimental curve.The example of the CuC1:- ion is worked out here to illustrate (fig. 7-8) this procedure. The experimental absorption curve is shown in fig. 7a. Its analysis over the 395-415 nm and 276-295 nm regions shows that there are two gaussian curves located at 410 nm (I) and 294 nm (11) respectively (fig. 7b). These components are in turn subtracted from the experimental curve and one finds two residues R I and R 11. The analysis of R I does not show any linear relationship between Y'/ Y and v whatever the assump-tion on the shape of the component is ; this might indicate that a number of forbidden lines are indeed present under the long red tail of R I.On the other hand the analysis of R I1 clearly demonstrates the presence of two gaussian components at 347 and 318 nm respectively. With this information the MCD curve (fig. 8a) analysis can be S3-34 a 300 400 50 0 b FIG. 7.-Analysis of the absorption curve of CuC1:- (a) experimental curve ; (b) resolved components. FIG. 8 .-Analysis 2 0 - -2 Q s 2 2 0 - 2 -4 of the MCD curve of CuCIi-; (a) experimental curve ; (b) resolved a components J . BADOZ M . BILLARDON A . C . BOCCARA A N D B . BRlAT 35 carried out easily. The results obtained are shown in fig. 8b. Bands I and I1 both give a and (b + c/kT) terms while band I1 only shows a (b + c/kT) term and band IV does not contribute appreciably. The parameters obtained are given e1sewhere.l SIGNIFICANCE OF THE PARAMETERS ISOTROPIC OR ORIENTED MOLECULES We have not commented so far on the exact significance of the parameters a b and c obtained through the analysis of MCD curves.For an isotropic or oriented molecule in a longitudinal magnetic field H along the +z axis it is easy to relate a b and c to the &’ 98 %? and 9 parameters * proposed by Buckingham and Stephens.’ For any line-shape function one has where (5) Here Yg and Ye stand for the spectroscopic splitting factors of the ground and excited states respectively and /? is the Bohr magneton. If the ground state is doubly degener-ate one has for example I Yg ] = 2 I { + ] Lz+2Sz 1 +)I if ] +) is one of the doublet’s sublevels. Both procedures lead to the same physical quantity viz. the diagonal and off-diagonal matrix elements of the magnetic dipole moment operator.However, there are some differences in their use. On the one hand d/9 and %/9 can theo-retically be expressed from group theoretical arguments in terms of reduced matrix elements of the magnetic dipole moment operator. These in turn can be calculated in particular situations once approximate zero magnetic field wave functions have been evaluated. This mathematical approach is specially fruitful if associated with Griffith‘s irreducible tensor method l4 for the evaluation of matrix elements. It has now been widely used for fully allowed charge transfer bands of octahedral and tetra-hedral l2 complexes of the transition metals. On the other hand eqn (4) and ( 5 ) are derived assuming a separation =Yg/IH and 9’$H between the extreme components of the ground and excited states respectively, and expressing the difference in absorption between components for + and - circu-larly polarized lights.For an absorption transition atO one has for example,? AD-N+f(v,v+) I ( a I m+ I 0) I -N-f(v,v-) I ( a I m- I 0) 1 where m+ = nix. im is the electric dipole moment operator for circularly polarized light ; f(v,v+) andf(v,v-) are the shape functions for the individual lines ; N+ and N-the respective populations of the ground-state sublevels from which the o+ and o-lines start. This practice provides a more phenomenological approach to some MCD prob-lems and avoids theoretical complications when they are unnecessary. It is simple when one considers singlet or doublet states but requires more care when dealing with triplet or quartet states.The method has been widely used for rare-earths lS when * Cursive letters are used here in agreement with ref. (10) in order to differentiate between the optical density D and the dipole strength 9. t This expression leads to the now widely accepted sign convention for [AD] namely that say, [.AD] (or the molar ellipticity [el,) is positive within the 420 nm absorption band of potassium fcrricyanide and the Verdet constant of water is negative within the visible spectral range 36 MCD A N D MLD SPECTRA only singlet and doublet states are encountered. The procedure can be summarized as follows. Eqn (4) and ( 5 ) are general providing a sign convention is used 9 is positive when the a+ line starts from the lowest sub-level of the ground state and Ye is positive if the same polarization is allowed to the highest sub-level of the excited state.The experiment thus provides the parameters together with their signs. Using this sign convention it is then possible to derive the levels and the polarizations of the transitions between the various sub-levels of the ground and excited states. The selection rules are known from the literature and it is thus easy to assign to each sub-level its representation in the proper group to which the molecule or ion under con-sideration belongs. ANISOTROPIC CENTRES So far our remarks have been relevant to isotropic or properly oriented systems. Examples of this kind are found with octahedral or tetrahedral inorganic ions in solution or in crystals and divalent rare-earth ions in fluorite type crystals (iso-tropic t) or in tripositive rare-earth ions in oriented uniaxial calcium tungstate.A case frequently encountered however is that of an anisotropic centre in an isotropic (or eventually anisotropic) matrix. This is the rule when the impurity ion replaces ions with different valences such as tripositive rare-earth ions in fluorite. In that case the local symmetry of the centre is determined first by its structure i.e. by the positions of the nearest ions i.e. among those ions which compensate the excess charge (e.g. 02- F- in CaF,). In cubic crystals it is now agreed that impurity centres are statistically uniformly oriented along one or another of the equivalent directions which are symmetry axes of the lattice (3C4 4C3 or 6C2) so that the crystal preserves its optical isotropy.The microscopic anisotropy of the individual centres is hidden due to the ensemble averaging. In conclusion we comment on the suitability of magneto-optics for detecting hidden anisotropic centres. Emphasis will be on the problem of an anisotropic centre in an isotropic matrix although we have also developed some methods for anisotropic centres randomly oriented in a glassy matrix. Two examples will be chosen among recent MCD and MLD experiments. First we consider the absorp-tion and MCD of a tetragonal centre in a cubic matrix. The question arises whether the absorption and MCD spectra will be changed when the common direction of the magnetic field and Poynting vector are along e.g.a C or C3 axis of the cube. We further assume that only a polarized transitions are allowed and that the perpendicular splitting factors of the various states is zero. We first suppose the light wave to be propagated along a C4 axis ; it will encounter three distinct successive centres oriented along the three four-fold axes. Only one centre of three will have its axis properly oriented with regards to H and thus give rise to MCD ; on the other hand however, absorption corresponds to that of two centres having their axes in a plane perpendicu-lar to the electric field vector. The [AD]/& ratio will thus be 3 that which it would have if the three centres were all oriented with their axis parallel to [IOO]. Suppose now the light propagates along a three-fold axis and H is also parallel to [ 1 I I].Fol-lowing Merle d'Aubigne and Duval,16 a+ light propagating along [11 I] is split up as aa +pa- +p along the three four-fold axes. It can then be shown that a absorption for each centre is a2 + p 2 = 3 of that which it would be if the centres were all aligned along the axis of propagation (the " uniaxial " case). On the other hand the MCD is reduced by 3. Altogether considering the three centres the [AD]/Dm ratio is again 3 of that which would be in the uniaxial case. t except for I's quadruplets J . BADOZ M . B I L L A R D O N A . C . BOCCARA AND B . B R I A T 37 The above arguments thus lead 11s to the following important conclusion u tetragonal centre in a cubic matrix behaves as if it were isotropic when absorption or MCD experiments are performed ; absorption and MCD are merely 3 and 3 respec-tively of that which they would be in the uniaxial case.Our conclusion is essentially unchanged (i.e. same reduction factors) when one considers the MCD of a trigonal centre or the MORD of either tetragonal or trigonal centres. We confirmed the above ideas experimentally for the Nd3+ ion in CaF,. We had two crystals each containing mainly tetragonal (pink) and trigonal (blue) centres. H was oriented along [loo] and then [l 1 I] for each specimen. Within 5 % (experi-mental errors) we found no difference among the results for absorption and MCD or MORD for the two types of centres when the field was oriented along one of the particular axes. These results are in some respects disappointing since it would have been interesting to be able to differentiate between different types of anisotropic centres through magneto-optical experiments.These results are also in serious disagreement with previous predictions l7 for anisotropic centres. Actually stress-induced linear dichroism measurements or Cotton-Mouton experiments are likely to provide a more valuable approach to the problem.l* In conclusion we report on this latter point in connection with some recent experiments performed in our laboratory. It will be shown that the temperature-independent MLD is anisotropic for impurity centres possessing tetragonal or trigonal local symmetry. We assume throughout a transition between two doublets and lines allowed with cr light only.Now the spin Hamiltonian for each doublet can be written as t*-;) where 911 and 9,- are the parallel and perpendicular spectroscopic splitting factors res-pectively ; (b and 8 are the polar angles of the direction of H in a centre-fixed axes system. Fig. 9 shows the eigenvalues and eigenfunctions of the Hamiltonian. The FIG. 9.-Eigenvalues and eigenfunctions of the hamiltonian used in the calculation of the magnetic linear dichroism 38 MCD AND MLD SPECTRA latter are expressed as linear combinations of the basis functions 1 g,pT) and I Z,p*) diagonal in p (magnetic dipole moment operator). We further assume that the transitions [ g,p,)-+ [ e,p*) are Q+ polarized when H is directed along the axis of the centre. When the direction of the magnetic field is different each of the four transitions I g,-t-)+ I e,i-) is both allowed with Q+ and Q- polarization.We call FIG. 10.4rientation of the Poynting vector (112) and magnetic field (IlX) in a space fixed axes system. XYZ the space-fixed axes (see fig. lo) propagate light along 2 and apply the mag-netic field along X. The calculation of MLD is carried out by evaluating I (e I nTX I g) I 2 - I ( e [ my I g) [ for each individual transition in terms of the matrix elements of m and my in the centre-fixed axes system. The calculation is tedious but not difficult and one finally finds 2YIeYIg sin2 2@ cos2 o- Yil,Yil sin4 w cos2 cos 2@)82~2 + cos 24D jP2H2. 1 1 [cOs:-l 2(1,2 + 12,)(cos2 o - 1) cos 2 0 + This result can now be applied to the trigonal centres oriented along the four three-fold axes of a cubic matrix.Let us assume first that the light propagates along [loo]. Then cos w = 1 / J3 and the MLD is obtained by summing up the contributions of the individual centres = @; (D2 = CD+n/2; m3 = @+n; (D4 = @+371/2). One finally gets AD - q(Yle91g( 1 + cos 0) cos 2@ + 4YL,YLg cos o sin2 2@ - 8 dv We were able to check this expression experimentally by measuring the MLD through the 584 nm line of a blue CaF + Nd3+ crystal (mainly trigonal centres). The light was propagating along one C axis and we recorded a signal proportional to the absorption curve second derivative for a given position of the crystal. The crystal was then rotated around C4 through successive angles CD and fig. 11 was obtained where the amplitude is plotted against @.It is clear from the figure that the ordinate varies as expected from eqn (6). If we now assume that the light is propagating along [ 1 1 11 the MLD is easily shown to remain constant when @ varies ; this again has been checked experimentally within instrumental errors. The above calculation and experiment J . B A D O Z M. B I L L A R D O N A . C . ROCCARA A N D B . B R I A T 39 demonstrate that one must be careful in performing MLD experiments and attempting to explain the data since orientational problems are of prime importance here. Further a similar derivation can be made for tetragonal centres in a cubic matrix when the light is propagated along [ 1001 or [ 1 1 13 ; essentially similar conclusions are reached. i.e. AD varies according to cos2 2 0 in the former case and remains invariant in the latter.An unambiguous-identification of trigonal or tetragonal centres from a) (deg.1 FIG. 11 .-Magnetic linear dichroism of trigonal Nd3+ centres in CaF (see text for comments). just two MLD experiments within one absorption band is thus again unexpected (as from MCD work) when all 9’ factors are non-zero. It can be expected however, that more useful conclusions are likely to be obtained for paramagnetic centres with an even number of electrons where Y1 splitting factors are zero and the term pro-portional to sin2 2@ in eqn (6) vanishes. Experimental investigations along these lines are under way in our laboratory. We thank Prof. Chapelle (Fac. des Sciences Orsay) and Dr. Toledano (CNET, Issy-les-Moulineaux) for kindly providing the crystals used in our experiments.The assistance of Mrs. Lenain (D6partement de Recherches Physiques Facult6 des Sciences Paris) for polishing and orienting the crystals was greatly appreciated. Some of the results described here would not have been obtained without the skilful help of MM. Ferre and Rivoal. la A. C. Boccara J. Ferre B. Briar M. Billardon and J. P. Badoz J. Chem. Phys. 1969,50,2716. ‘ b A. C. Boccara Compt. rend. 1969 268 62. M. Grosjean and M. Legrand Compt. rend. 1960,251,2150. M. Billardon and J. Badoz Compt. rend. 1966,263,139. M. Billardon and J. Badoz Compt. rend. 1966 262 1672. M. Billardon J. C. Rivoal and J. Badoz Rev. Phys. Appl. 1969,4,353. Such a CD attachment is manufactured by FICA Le Mesnil Daint Denis France. G. Barth E. Bunnenberg and C. Djerassi Chem. Comm. 1969 1246. * A. C. Boccara P. Roubeau and J. Badoz Compt. rend. 1967,265,513. P. J. Stephens W. Suetaka and P. N. Schatz J. Chem. Phys. 1966 44,4592. lo P. J. Stephens Chem. Phys. Letters 1968 2,241 l 1 M. Billardon F. Sicart and J. Badoz J. Phys. 1970 31 219. l 2 (a) B. Briat J. C. Rivoal and R. H. Petit J. Chim. Phys. 1970 67,462. B. D. Bird B. Briat, l 3 A. D. Buckingham and P. J. Stephens Ann. Rev. Phys. Chem. 1966. 17 399. l4 J. S. Griffith The Irreducible Tensor Method for Molecular Symmetry Groups (Prentice-Hall, l5 see e.g., P. Day and J. C. Rivoal this Discussion. Inc. Englewood Cliffs N. J. 1962). (a) A. C. Boccara and B. Briat J. Phys. 1969 30,445. (b) L. A. Alekseyeva N. V. Starostin and P. P. Feofilov Opt. Spectr. 1967 23 140. L. A. Alekseyeva and P. P. Feofilov Sou. Phys. Solid State 1968 10 1397. J. Duran Compt. rend. 1969 269 540. l6 Y. Merle d’Aubigne et P. Duval J. Phys. 1968 29 896