Orientation effects in soft X-ray magnetic circular dichroism

Journal of Electron Spectroscopy and Related Phenomena 86 (1997) 93–106

Orientation effects in soft X-ray magnetic circular dichroism J. van Elp a,*, B.G. Searle b a

ISA, Institute of Physics and Astronomy, University of Aarhus, DK-8000 Aarhus C, Denmark b Daresbury Laboratory, Daresbury, Warrington WA4 4AD, UK

Abstract The orientation dependence of magnetic circular dichroism (MCD) at soft X-ray absorption edges is discussed for paramagnetic 3d transition metal systems using ligand-field atomic multiplet calculations. Previous calculations have used a magnetic orientation along the z axis of the transition metal site. In the present work, three orientation directions are calculated: [001], [110] and [111]. Also an at-random spectrum is calculated which represents the actual situation for 3d transition metals in metalloproteins. The systems investigated can be divided into three classes based on the difference between the MCD effect for the different orientations. The first class contains spherical systems like, for instance, Fe 3+ (d 5) systems in O h and T d symmetries and Ni 2+ in O h symmetry. The differences between different orientations in these systems are small, or even absent. The second class contains first-class systems with a distorted local symmetry like Fe 3+ in D 2d symmetry and Ni 2+ in D 4h symmetry. The differences between the different orientations can be quite strong and result from differences in polarization for the left and right circularly polarized absorption spectra. The third-class systems exhibit relatively large zero-field splittings. The differences are very strong and are a result of the interaction between the zero-field splittings and the applied magnetic field. An example is Fe 2+ in D 2d symmetry. q 1997 Elsevier Science B.V. Keywords: X-ray absorption spectroscopy; Magnetic circular dichroism; Paramagnetism

1. Introduction Soft X-ray magnetic circular dichroism (MCD) measures differences in the absorption coefficient between circularly polarized X-rays at inner-shell absorption edges. The technique can provide element and, with large enough chemical shifts, oxidation-state specific information. It has attracted considerable attention, in particular at the L 2,3 (2p) edges of the 3d transition metals due to the recent availability of high flux and resolution and a high degree of circular polarization, using synchrotron radiation beamlines. Strong soft X-ray magnetic linear dichroism [1] was predicted theoretically for the rare earth M 4,5 edges using atomic multiplet * Corresponding author.

calculations. Shortly afterwards, a linear dichroism effect [2] was observed at the terbium M 5 edge in a terbium iron garnet. Soft X-ray MCD effects were observed at the L 2,3 edges of Ni [3]. The magnetic ordering in ferromagnetic and ferrimagnetic oxides [4,5] was studied using MCD spectra at Fe and Gd edges. Powerful sum rules based on the soft X-ray MCD response of a core level have been derived, which allows one to determine the orbital [6] and spin [7] moment in the ground state. Soft X-ray MCD was also recently observed in a paramagnetic system. A strong MCD effect was observed at the L 2,3 edges of a single Fe atom in the metalloprotein Pyrococcus furiosus rubredoxin [8]. Compared with a ferromagnetic or a ferrimagnetic system, a paramagnetic system requires a strong magnetic field and very low temperatures. The

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orientation of the magnetic moment is achieved by preferentially occupying the lowest level of the Zeeman split ground state. The magnetic fields and temperatures used are as high as 6 T and as low as 1.5 K [8]. After the first experiments on the oxidized form of Pyrococcus furiosus rubredoxin, a moderate effect was observed on the reduced form (Fe 2+) and a small effect on a Co- substituted form of the same protein [9]. The last single-site system investigated to date is Cu 2+ [10] in the blue copper protein plastocyanin. As we will show later, the intensities of the observed MCD effects (especially in the Cu system) were not always fully understood. The question we want to address in this paper is the orientation dependence of the MCD signal. It has always been assumed in our ligand-field atomic multiplet calculations [8,9] and also in the work by van der Laan and Thole [11] that the magnetic field is oriented along the z axis of the transition metal site. In a metalloprotein sample this is not the case because the orientation of the sites, as compared to the applied magnetic field, is random. The orientation dependence has been investigated for the experimentally measured systems mentioned above and also for a chosen number of interesting systems. Three different orientations, [001], [110] and [111], in the appropriate site symmetries, have been calculated while an at-random calculation has also been performed. The changes in the MCD effect for different orientations can be quite pronounced. A clasification for 3d transition metal systems is made based on local symmetry and zero-field splitting in the ground state.

2. Calculation details The calculations were performed using the same method as described by van der Laan and Thole [11]. Initial (F d 2d and F d 4d) and final (F p 2d, G p 1d, and G p d3) state Coulomb and exchange interactions, together with the 2p and 3d spin–orbit interactions are calculated in spherical symmetry using Cowan’s atomic multiplet approach [12]. The Coulomb and exchange integrals are renormalized to 70% of the Hartree–Fock values to account for the covalency in the systems investigated. The local site symmetry is incorporated by adding a

ligand-field term in the Hamiltonian. In O h (T d) symmetry, the 3d orbitals are split into e g (e) and t 2g (t 2) orbitals with an energy difference of 10Dq. A further lowering of the symmetry to D 4h (D 2d) splits the orbitals by the additional ligand-field parameter Ds. The ligand-field parameter Dt is maintained at zero. The ligand-field parameters for all the systems investigated are chosen to represent the local transition metal site as accurately as possible. In the tetrahedral calculations (Fe 3+, Fe 2+ and Co 2+) 10Dq = − 0:6 eV is used. In D 2d symmetry the distortion is Ds = 6 100 meV. For the octahedral symmetry calculations (Fe 3+ and Ni 2+) 10Dq = 1:5 eV is used. The same method has recently been used to calculate the X-ray absorption spectra of isolated Ni centers [13]. One of the interesting systems here is Ni(cyclam)Cl 2, in which the Ni site is high-spin in a local D 4h symmetry. The parameters of this system (10Dq = 1:6 eV and Ds = 220 meV) are used for the D 4h calculation on Ni 2+. The magnetic field is included by a term gm BH·S in the Hamiltonian. A value of 2mB H = 0:5 meV is used, which is comparable to a magnetic field of about 5 T. This is about the size of the magnetic fields used in the experiments and also about what is experimentally possible using a split-coil superconducting magnet. In our earlier calculations [8], and also in the work of van der Laan and Thole [11], a magnetic field along the z axis of the transition metal site was used. In the experiments on the metalloproteins, the metal center is oriented at random. Instead of using a spin operator that aligns the spin along the z axis, a spin operator is applied to specify a certain direction at the local site. The components of the left and right circularly polarized dipole transitions along the same direction as the spin are then calculated. A random MCD spectrum is obtained by calculating 42 points on a sphere using a subdivided icosahedron. This gives a set of points that are evenly distributed on the sphere. The calculated spectra are broadened with a convoluted Lorentzian and Gaussian to describe the intrinsic broadening mechanism and the experimental resolution. Average values of G = 0:25 eV for the L 3 edge and G = 0:5 eV for the L 2 edge and j = 0:3 eV are chosen. It is important not to choose too small values because this will create, for instance, negative structures in an MCD spectrum consisting of one final state multiplet value. Another effect of changing

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the broadening is that the relative size of the MCD effect for the main peak will change because negative side structures no longer cancel some of the main peak effect.

3. Zero-field splitting The 3d transition metal sites in metalloproteins and inorganic model compounds are rarely at high symmetry; almost all of these systems have a local distortion. This is also the case for the Fe 3+ ion in rubredoxin. The ground state in LS coupling in T d symmetry is 6A 1, so there is no direct energy gain in having a distortion as there is, for example, in Jahn– Teller systems. Including the 3d spin–orbit coupling, the ground state is degenerate and the symmetries are E 2 and G [14]. Upon a lowering of the local symmetry to D 2d, the ground state is split into three twofold degenerate levels. As it is the spin moment that splits up, the three levels can be labeled with ms = 6 1=2, 3=2 and 5=2. The origin of this so called zero-field splitting (ZFS) of the 6A 1 ground state in distorted T d symmetry has been studied [15,16]. The origin is spin–orbit coupling to low-symmetry-split 3d–3d excited states. For the Fe 3+ system this is the second-order spin–orbit coupling of the 6A 1 to the 4T 1 level which is split into an xy and a z component. In the calculations, the following pattern is observed: ms = 6 1=2 is lowest, with the ms = 6 3=2 at 2D, and the ms = 6 5=2 at a 6D higher energy. The value of D found in the calculations is less then 0.01 meV; experimentally a value of D of about 0.1 meV is obtained. The contribution to the ZFS from the ligand charge-transfer bands are neglected in our calculations [15,16], just as are covalency effects on the splitting of the 4T 1 state. Both explain the discrepancy between the experimental values and the values obtained in our calculation. In the Fe 3+ system, the ZFSs are small. A 5 T magnetic field will mix these levels with the result that large MCD effects are observed because of the emergence of a Zeeman splitting. A different situation is encountered for the Ni-substituted form of rubredoxin [13]. The symmetry is D 2d and the ZFS parameter D is positive and quite large (D = 7:7 meV). Here the ZFS is much larger than the applied magnetic field, and due to the ms = 0 ground state no noticeable MCD effect is expected for a 5 T magnetic field.

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Zero-field splittings are also observed in linear dichroism experiments at Dy/Si(111) [17] and Er/ Si(111) [18] interfaces. No magnetic field is applied and the linear dichroism effect is a result of preferentially occupying the 6 15/2 levels of the 4I 15/2 ground state.

4. Results and discussion In principle, the systems can be classified into three different classes depending on the difference in the MCD effect between the different orientations. The underlying parameters are the symmetry of the local site, and the size of the zero-field splitting of the LS coupled ground state.

Fig. 1. Isotropic X-ray absorption spectrum (top) and at-random magnetic circular dichroism spectrum (bottom) for Fe 3+ in T d symmetry. The 10Dq value used was − 0.6 eV. The vertical lines indicate the strength and positions of individual transitions before linewidth broadening.

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Fig. 2. Magnetic circular dichroism spectra for the three directions of alignment of the magnetic moment for Fe 3+ in T d symmetry. The 10Dq value used was − 0.6 eV. The ground state (ms = − 5=2), first excited state ( − 3/2) and second excited state ( − 1/2) spectra are shown for each orientation. The vertical lines indicate the strength and positions of individual transitions before linewidth broadening.

4.1. Spherically symmetric systems The first class of systems is characterized as having a spherical electronic structure. In Fig. 1 is shown the isotropic X-ray absorption spectrum (XAS) for Fe 3+ in T d symmetry. At the L 3 edge position, we have the main peak structure B with two shoulders A and C and a side structure labeled D. At the L 2 edge we have a two-peaked structure (E and F). The three principal directions in the T d structure are shown in Fig. 2. All

the structures in the MCD spectra are directly related to absorption features in the isotropic XAS. The maximum MCD effect, defined as (I l − I r)/(I l,max + I r,max) in the MCD spectrum, is always at peak B and is slightly different for the three directions. It is highest for the [001] direction where it reaches 63.2%, whereas it is 57.0 and 55.6% for the two other directions. The shoulders (A and C) and the side structures (D) change slightly in position and intensity at the L 3 edge. At the L 2 edge, the changes are stronger

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Fig. 3. Isotropic X-ray absorption spectrum (top) and the at-random magnetic circular dichroism spectrum (bottom) for Fe 3+ in O h symmetry. The 10Dq value used was 1.5 eV. The vertical lines indicate the strength and positions of individual transitions before linewidth broadening.

and we have a dip between peaks E and F in the [001] direction. The first and second excited states have, in the first approximation, ms = − 3=2 and ms = − 1=2 character. The total integrated intensities in the individual L 3 and L 2 edges in the spectra are 60 and 20%, as compared to the ms = − 5=2 spectrum. The effects in the individual structures are slightly off. For the main peak B there is a reduction to 57.6% (18.2%) in the [001] direction and 61.2% (20.9%) in the other two directions. The side and shoulder structures at the L 3 edge change much more for the first and second excited state MCD spectra. Also, the structures at the L 2 edge change more. In the [001] direction, peak E almost disappears, and what is left is at a much lower energy. In the [111] direction there is a dip between peaks E and F in the spectra for the excited states.

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In Fig. 1 is also shown the MCD spectrum based on the random calculation. The MCD effect is 57.8% for the random case. Only the ms = − 5=2 MCD spectrum is shown, because the ms = − 3=2 and ms = − 1=2 MCD spectra scale in intensity to exactly 60 and 20% of this spectrum. In the random spectra, the sum of left and right is exactly two-thirds of the isotropic spectrum. This means that the z orientation spectrum is one-third of the isotropic spectrum, which is not true for the different individual directions. The strength of the MCD effect is influenced by hybridization. The width of the peaks is determined by Coulomb and exchange integrals together with the ligand-field contribution. More covalent ligands have a larger reduction of the Slater integrals, and peak C will move closer towards peak B. This means that in the sum of the left and right circularly polarized absorption spectra peak B increases, while in the MCD spectrum peak B will decrease, which means that the maximum MCD effect decreases. In Fig. 3 is shown the isotropic X-ray absorption spectrum for Fe 3+ in O h symmetry. The structures are quite similar to the T d symmetry spectra, except for peak A, which is now a side structure instead of a shoulder. Fig. 4 shows the spectra for the three principal directions. For the ms = − 5=2 states, the structures A and C are less intense for the [001] direction while peak F becomes a double-peaked structure in the [111] direction, and has a strong intensity in the [001] direction. The MCD intensity in peak B is lowest for the [001] direction with 42.7%, and reaches 49.2% for the [110] direction and 51.3% for the [111] direction. The first and second excited states have again a total integrated intensity over the L 3 and L 2 edge of 60 and 20% as compared to the ground-state spectrum. The intensity of peak B is almost equal to 60% for the first excited state and changes for the second excited state from 21.6% for the [001] direction to 17.7% for the [111] direction. The L 2 edge in the excited state spectra has changed to a three-peaked structure for the [001] direction. The random MCD spectrum shown in Fig. 3 has a 47.6% effect in the main peak B, which is in between the maximum effects for the [001] and [111] directions. Compared with the MCD effect in the T d

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Fig. 4. Magnetic circular dichroism spectra for the three directions of alignment of the magnetic moment for Fe 3+ in O h symmetry. The 10Dq value used was 1.5 eV. The ground state (ms = − 5=2), first excited state ( − 3/2) and second excited state ( − 1/2) spectra are shown for each orientation. The vertical lines indicate the strength and positions of individual transitions before linewidth broadening.

symmetry, the effect is smaller in O h symmetry, which is probably due to the separate structure A. The ground state for Fe 3+ in T d and O h symmetry in LS coupling is 6A 1(g) and is a half-filled 3d shell with no orbital moment. The total MCD intensity in the combined L 3 and L 2 edge is equal to zero, which is what would be expected based on, and in accordance with, the orbital moment sum rule [6].

In Fig. 5 is shown the isotropic X-ray absorption spectrum and the at-random MCD spectrum for Co 2+ in T d symmetry. Although the isotropic X-ray absorption spectrum still has a large number of final state multiplets, it has a simple structure with a main peak (B and E) and shoulder (D and F) at the L 3 and L 2 edges. The at-random MCD at the L 3 edge shows more structure with a small negative structure A in

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Fig. 5. Isotropic X-ray absorption spectrum (top) and the at-random magnetic circular dichroism spectrum (bottom) for Co 2+ in T d symmetry. The 10Dq value used was −0.6 eV. The vertical lines indicate the strength and positions of individual transitions before linewidth broadening.

front of the main peak structure B and a clear shoulder C. The L 3 edge shoulder D has negative intensity in the MCD spectrum. In Fig. 6 is shown the orientation dependence. The ground state in LS coupling is 4A 2. There is very little change between different orientations in the ground state. The effect in the main peak B is 63.4% for the [001] direction and 64.6% for the [111] direction. The spectra are almost identical, with only very small changes. The first excited state spectra show larger changes between the different orientations. For the L 3 edge this is at A and C, while the main peak changes in intensity, from 29.7% of the ground state effect for the [111] direction to 31.7% for the [110] direction to 37.4% for the [001] direction. The L 2 edge also shows changes in the peak position for the strongest peak E. The random MCD spectrum in Fig. 5 shows a

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63.7% effect in peak B, which is one of the largest MCD effects observed for the 3d transition metals in general. The excited state effect is again exactly 33.3% of the ground state MCD effect. The last system that will be discussed in this category is Ni 2+ in O h symmetry. The ground state is 3A 2g in LS coupling, which means that the applied magnetic field will split the spin part into three levels, ms = + 1, 0, − 1. Thus only the ground state (ms = − 1) shows an MCD effect. The spectra for the at-random and different orientation spectra are exactly the same [19]. There are only small changes in the left and right circular absorption spectra for the three orientations. The reason for this is most likely the limited number of final states in this system. There are no 3d–3d interactions in the final states. All the four systems discussed are quite similar in response. They all have an electronic structure that is spherical with a half-filled shell (d 5) or subshell (t 32g in O h or e 2 in T d). In LS coupling the ground states are 6A 1(g) for the Fe 3+ systems and 4A 2 and 3A 2g for Co 2+ and Ni 2+, respectively. ZFSs are absent or very small (d 5 splitting to E 2 and G) as compared to the applied magnetic field. The differences between different orientations are found to be small or even absent like the Ni 2+ system in O h symmetry. The reason for this is the spherical electronic structure, which means that only small changes are to be expected at the L edges for different orientations, which also means small changes in the MCD spectra. Other systems belonging to this group are d 3 (Cr 3+, V 2+) in O h symmetry, and d 2 in T d symmetry. The MCD effect of the excited states scales directly to the ground state MCD effect for the at-random spectrum. In a first approximation, the z axis oriented MCD spectrum ([001]) is comparable to the atrandom MCD spectrum. 4.2. Distorted spherical symmetry systems In the second category, two systems will be discussed, namely Fe 3+ in D 2d symmetry and Ni 2+ in D 4h symmetry. Both systems are distorted firstcategory systems with a lowered symmetry. Fig. 7 shows the isotropic X-ray absorption spectrum of Fe 3+ in D 2d symmetry. The ligand-field parameter Ds is chosen to be 100 meV. In the isotropic XAS spectrum the changes are small. The overall

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Fig. 6. Magnetic circular dichroism spectra for the three directions of alignment of the magnetic moment for Co 2+ in T d symmetry. The 10Dq value used was −0.6 eV. The ground state (ms = − 3=2) and first excited state (−1/2) spectra are shown for each orientation. The vertical lines indicate the strength and positions of individual transitions before linewidth broadening.

intensity in peak B has dropped a little and the shoulder labeled C has a small increase in intensity. The t 2 and e orbitals are split by 3Ds and 4Ds, respectively, and, although Ds = 100 meV, this is hardly visible in the XAS spectrum. The width of the multiplet structure at the L 3 edge is about 4 eV, which is still about one order larger than the applied splittings. The changes in the MCD effect for the different orientations as shown in Fig. 8, however, are quite visible. The main peak B has much more intensity in the [001] (66%) direction compared with the [110] (53%) direction. In addition, the peak has shifted by almost 400 meV. The shoulder A also changes sign, from negative for [001] to positive for [110]. The same change of sign is also observed at peak E at the L 2 edge. The change in peak position of structure G at the L 2 edge is about 250 meV, with an intensity change of almost 30%. The [111] orientation MCD spectrum is in between the other two directions. The first and second excited state MCD spectra show the same intensity pattern for the [001] and [110] directions. The main peak (B) in the excited state [001] MCD spectra has a higher intensity. For the [110] and [111] directions, there is a relative intensity change at the shoulder C and at the L 2 edge at F. The at-random MCD spectrum as shown in Fig. 7

has a slightly lower intensity compared to the non-distorted spectrum in Fig. 1. The MCD effect as compared to the sum of the left and right circularly polarized absorption is, however, 57.8%, comparable to the T d symmetry. The first and second excited state MCD spectra scale and are, as far as the intensity is concerned, exactly 60 and 20% of the ground state MCD spectrum. The at-random MCD spectra for Fe 3+ in T d and D 2d symmetry show that the z axis approximation in T d symmetry explaining the MCD effect for the first paramagnetic MCD result obtained [8] was valid. In Fig. 9 is shown the orientation dependence of Ni 2+ in D 4h symmetry. The isotropic XAS spectrum is different from the O h symmetry spectrum in that the main peak of the L 3 edge has split into two peaks [13,19]. The energy difference is closely related to the 4Ds splitting of the e g orbitals. The lower symmetry also introduces a small ZFS, and two levels are found 0.04 meV apart, with the ms = 0 being the lower. The applied magnetic field is, however, much larger and will introduce the necessary magnetization. The orientation dependence is quite strong. Peak A, which is related to the absorption to a z 2 3d orbital is negative for the [001] direction and is the strongest positive feature for the [110] direction. Peak B, which is related to absorption to the x 2 − y 2 3d orbital, is the

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intensity is low in the left and right circularly polarized spectra. In the [110] direction it is opposite; the z polarized absorption spectrum is along the [110] direction mainly into the x 2 − y 2 3d orbital, while the left and right can reach the z 2 orbital. The Fe 3+ system in D 2d symmetry is still spherical. It has a closed minority spin 3d shell, but the splitting of the e and t 2 orbitals together with the different orientations of the magnetic field also lead to different polarization dependences for left and right circularly and z polarized light. That must explain the effect seen upon orientation for [001] and [110]. The effects observed in this second class of systems can be quite strong. This is, of course, not limited to the two systems shown, but can also be expected for Fe 3+ in D 4h or D 3d symmetry, Co 2+ in D 2d symmetry, and distortions from O h symmetry in d 3 and T d symmetry in d 2. 4.3. Large zero-field splitting systems

Fig. 7. Isotropic X-ray absorption spectrum (top) and the at-random magnetic circular dichroism spectrum (bottom) for Fe 3+ in D 2d symmetry. Selected ligand-field parameters: 10Dq = − 0:6 eV; Ds = 100 meV. The vertical lines indicate the strength and positions of individual transitions before linewidth broadening.

strongest positive feature in [001] and is a small positive shoulder in [110]. The MCD effect in the [001] direction is quite high at 69.8%; it reaches 50% for the [110] direction and 47.3% for the [111] direction. At the L 2 edge there is no direct relationship with the 4Ds splitting in the spectrum; however peak D is positive in the [001] direction. The [111] direction MCD spectrum is identical to the at-random spectrum, which is probably a result of the limited number of final states present in this system. Both systems presented in this class have small ZFSs in common. It is clear from the Ni 2+ system in D 4h symmetry that the effects seen for these two systems are related to polarizations in the left and right circularly polarized spectra. For the [001] direction in Ni 2+, peak A is related to the z 2 3d orbital which means that it has the strongest intensity in the absorption spectrum for the z polarized direction. The

The interaction between the magnetic field and the ZFS pattern constitutes the main interaction determining the size of the MCD effect and the orientation dependence in the third class of systems. The only system belonging to this class, which has been experimentally investigated [9], is the reduced Fe 2+ form of rubredoxin. It has a D 2d symmetry. In Fig. 10 is shown the orientation dependence. The ZFS pattern constitutes of three levels, with ms = 6 2 the lowest, and with ms = 6 1 at 3D and ms = 0 at 4D. The value of D is 1.3 meV, which makes the size of the ZFS comparable to the applied magnetic field. This makes the overall orientation dependence quite complicated. In the [001] direction we can still easily understand what is happening: the ground state has mainly ms = − 2 character, and the first excited state has mainly ms = + 2 character. They are split from the ms = 6 2 lowest state by the applied magnetic field. The second and third excited states belong to the ms = 6 1 level, while the fourth excited state shows no effect in the MCD spectrum, which is what is expected for a level with ms = 0 character. For the [110] and [111] directions the size of the MCD effects is quite different for the five levels shown. The magnetic field is not large enough to create a Zeeman splitting, and it splits or is a distortion of the ZFS

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Fig. 8. Magnetic circular dichroism spectra for the three directions of alignment of the magnetic moment for Fe 3+ in D 2d symmetry. Selected ligand-field parameters: 10Dq = − 0:6 eV; Ds = 100 meV. The ground state (ms = − 5=2), first excited state (−3/2) and second excited state (−1/2) spectra are shown for each orientation. The vertical lines indicate the strength and positions of individual transitions before linewidth broadening.

pattern. This is evident from the size of the MCD effect for the [110] and [111] directions, but also from the splittings of the ms = 6 2 level. For the [110] direction, the splitting of the ms = 6 2 level is only 0.02 meV, which means that the first excited state will be significantly populated at 1.5 K. Luckily it also has the same sign as the ground state. The isotropic XAS and at-random MCD spectra are shown in Fig. 11. The size of the MCD effect in the at-random spectrum is 20.6%, while it is 39.4% in

the [001] direction. The two spectra are, scaling the [001] to about 50%, different in intensity at peak A and also at peaks E and F at the L 2 edge. The isotropic XAS spectrum is not very sensitive to the size of the ligand-field parameter Ds. It is unclear how much the changes in the MCD spectra for different orientations are due to polarizations. Peaks A and E in the [110] direction have changed sign as compared to the [001] direction. It is clear that in systems where the ZFS parameter

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Fig. 9. Magnetic circular dichroism spectra for the three directions of alignment of the magnetic moment for Ni 2+ in D 4h symmetry. Selected ligand-field parameters: 10Dq = 1:6 eV; Ds = 220 meV. The vertical lines indicate the strength and positions of individual transitions before linewidth broadening.

D is of the order of the applied magnetic field, the orientation dependence becomes quite complicated and large effects can be expected. The Ni 2+ system in D 2d symmetry [13] discussed earlier also belongs to this category. Here the ZFS parameter D is quite large and unfortunately positive, so that no noticeable MCD effect can be expected. Other systems belonging to this class are Fe 2+ and Co 2+ in distorted O h symmetry, Mn 3+ and Cr 2+ (both d 4) in the Jahn–Teller distorted D 4h symmetry, d 2 systems in distorted O h symmetry and d 3 in distorted T d symmetry.

positive sign. For the other two directions, the effect is again negative and for a random calculation the L 2 edge MCD effect is again 50% with a negative sign. This factor of two in the size of the MCD effect is exactly what was found to be missing in the experimental work on Cu [10]. The only 3d system not mentioned up till now is d 1. This system could also be partly on its own, as is Cu 2+. The ground state with one 3d electron is S = 1=2. There are, of course, final state Coulomb and exchange integrals.

4.4. Cu 2+ L 2 edge 5. Conclusions A final example is a system difficult to characterize in any of the three classes, it is Cu 2+ in O h and D 4h symmetry. The ground state is d 9 and has one unpaired electron (S = 1=2), which is with a quenched orbital moment twofold degenerate, so there is no ZFS pattern. In the final states, all Coulomb and exchange integrals are zero because of the filled 3d shell. A simple spectrum is expected with two final states split by the 2p core hole spin–orbit coupling. The branching ratio and MCD effect have been worked out in D 4h symmetry for the [001] direction [20]. The orientation dependence of the MCD effect is, however, quite remarkable at the L 2 edge. In O h symmetry with degenerate e g orbitals, the effect at the L 2 edge is 50%, with a negative sign. Most Cu 2+ systems are Jahn–Teller systems; therefore they are distorted and have a lowered D 4h symmetry. The MCD effect at the L 2 edge for the [001] direction is 100% and has a

The systems discussed can be divided into three different classes, each class having a very clear effect regarding the MCD spectra for different orientations. The underlying parameters are the symmetry of the site, and, connected to this, the size of the ZFS parameter D. They determine to which class a system belongs. Systems in the first class have a spherical electronic structure. They have a closed (sub)shell in undistorted O h and T d symmetries. Examples are d 5 in O h and T d symmetry, with two systems shown, namely Fe 3+ in the O h and T d symmetries. Also d 7 in T d symmetry (Co 2+) and d 8 in O h symmetry (Ni 2+) belong to this group, just as d 3 in O h and d 2 in T d symmetries. The effects upon orientation to be expected for these kinds of systems are small, or even absent as is the case for Ni 2+ in O h symmetry. For these systems, the random

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Fig. 10. Magnetic circular dichroism spectra for the three directions of alignment of the magnetic moment for Fe 2+ in D 2d symmetry. Selected ligand-field parameters: 10Dq = − 0:6 eV; Ds = − 100 meV. The ground state to fourth excited state spectra are shown for each orientation. The vertical lines indicate the strength and positions of individual transitions before linewidth broadening.

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Fig. 11. Isotropic X-ray absorption spectrum (top) and the atrandom magnetic circular dichroism spectrum (bottom) for Fe 2+ in D 2d symmetry. Selected ligand-field parameters: 10Dq = − 0:6 eV; Ds = − 100 meV. The vertical lines indicate the strength and positions of individual transitions before linewidth broadening.

MCD spectrum is quite comparable to the z-axis oriented one. Systems in the second class are symmetry-distorted first-class systems. The distortion has split the e g (e) and t 2g (t 2) orbitals of the O h (T d) symmetry. The ZFS pattern, which evolves from introducing the distortion, has a small ZFS parameter D. The applied magnetic field can overcome the ZFS pattern and orient the spin fully. This creates the necessary Zeeman splitting. In the two systems shown (Ni 2+ in D 4h and Fe 3+ in D 2d symmetry), the effects are strong. For these systems it is not correct to assume that a random orientation can be described by a z-axis oriented calculation. Other systems in this class would be distorted systems like, for instance, d 5 or d 3 in D 4h or D 3d and d 2 and d 7 in D 2d symmetries.

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The third class contains systems which can be characterized as having a significant ZFS. The ZFS parameter D can be so large that the applied magnetic field merely distorts the ZFS pattern. No clear Zeeman splitting pattern emerges. Very large changes in the MCD effect for the different orientations are observed. For an at-random system careful calculations have to be done to analyze the experimental MCD effect. This includes not only the magnetic field but also the temperature, because some levels can be quite close together. A temperature of 1.5 K will populate not only the lowest level, but can also populate the first excited level. An example is Fe 2+ in D 2d symmetry. The at-random MCD spectrum has about half the intensity of the [001] direction spectrum. The size of the ZFS parameter D for Fe 2+ in D 2d symmetry is D = − 1:3 meV, and in D 4h and D 3d symmetries with reasonable ligand-field values, it is D = − 0:62 meV and + 1:5 meV. Other candidate systems belonging to this class are d 4 (Mn 3+ and Cr 2+) systems, Co 2+ in distorted O h symmetry, d 2 systems in distorted O h symmetry and d 3 in distorted T d symmetry. The large positive D system Ni 2+ in the D 2d symmetry also belongs to this class but no noticeable MCD effect can be expected. The sign of the ZFS pattern is important because it determines for large values if an MCD effect can be expected at all. This is not limited to single atom systems but has already been observed in a coupled two Fe atom (Fe 2+, Fe 3+) system [21] where, because of the sign of the ZFS parameter D, no noticeable MCD effect was observed for the Fe 2+ component. Orientation effects in MCD spectra are not limited to inorganic model compounds and metalloproteins only. They are characteristic for paramagnetic systems, so they can also be observed in paramagnetic systems like, for instance, some of the diluted magnetic semiconductors. For single crystal paramagnetic systems, the MCD effect for the different orientations can be observed and can consequently also be used to study the paramagnetic site. For a part, these effects can also be present in ferromagnetic samples. This could be because they are polycrystalline in a strong applied magnetic field, or because the single crystal has a distribution of site orientations.

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References [1] B.T. Thole, G. van der Laan, G.A. Sawatzky, Phys. Rev. Lett. 55 (1985) 2086. [2] G. van der Laan, B.T. Thole, G.A. Sawatzky, J.B. Goedkoop, J.C. Fuggle, J.-M. Esteva, R. Karnatak, J.P. Remeike, H.A. Dabkowska, Phys. Rev. B 34 (1986) 6529. [3] C.T. Chen, F. Sette, Y. Ma, S. Modesti, Phys. Rev. B 42 (1990) 7262. [4] F. Sette, C.T. Chen, Y. Ma, S. Modesti, N.V. Smith, X-ray and innershell processes, AIP Conf. Proc. 215 (1990) 787. [5] P. Rudolf, F. Sette, L.H. Tjeng, G. Meigs, C.T. Chen, J. Magn. Magn. Mater. 109 (1992) 109. [6] B.T. Thole, P. Carra, F. Sette, G. van der Laan, Phys. Rev. Lett. 68 (1992) 1943. [7] P. Carra, B.T. Thole, M. Alterelli, X. Wang, Phys. Rev. Lett. 70 (1993) 694. [8] J. van Elp, S.J. George, J. Chen, G. Peng, C.T. Chen, L. H. Tjeng, G. Meigs, H.-J. Lin, Z.H. Zhou, M.W.W. Adams, B.G. Searle, S.P. Cramer, Proc. Natl. Acad. Sci. USA 90 (1993) 9664. [9] J. van Elp, S.J. George, G. Peng, B.G. Searle, Z.H. Zhou, M.W.W. Adams, C.T. Chen, S.P. Cramer, in: S. Fineschi (Ed.), X-ray and Ultraviolet Polarimetry, SPIE Conf. Proc. 2010, San Diego, 1993, p. 181.

[10] S.J. George, J. van Elp, J. Chen, G. Peng, S. Mitra-Kirtley, O.C. Mullins, S.P. Cramer, in: B. Chance et al. (Eds.), Synchrotron Radiation in Biosciences, Clarendon Press, 1994, Chapter 4.8. [11] G. van der Laan, B.T. Thole, Phys. Rev. B 43 (1991) 13401. [12] R.D. Cowan, The Theory of Atomic Structure and Spectra, University of California Press, Berkeley, 1981. [13] J. van Elp, G. Peng, B.G. Searle, S. Mitra-Kirtley, Y.-H. Huang, M.K. Johnson, Z.H. Zhou, M.W.W. Adams, M.J. Maroney, and S.P. Cramer, J. Am. Chem. Soc. 116 (1994) 1918. [14] F.M.F. de Groot, Ph.D. Thesis, University of Nijmegen, 1991. [15] J.C. Deaton, M.S. Gebhard, E.I. Solomon, Inorg. Chem. 28 (1989) 877. [16] M.S. Gebhard, J.C. Deaton, S.A. Koch, M. Millar, E.I. Solomon, J. Am. Chem. Soc. 112 (1990) 2217. [17] M. Sacchi, O. Sakho, G. Rossi, Phys. Rev. B 43 (1991) 1276. [18] P. Castrucci, F. Yubero, F.C. Vicentin, J. Vogel, M. Sacchi, Phys. Rev. B 52 (1995) 14 035. [19] J. van Elp, B.G. Searle, J. Phys. (Paris) Colloq., in press. [20] G. van der Laan, B.T. Thole, Phys. Rev. B 42 (1990) 6670. [21] J. van Elp, G. Peng, Z.H. Zhou, S. Mukund, M.W.W. Adams, Phys. Rev. B 53 (1996) 2523.