Hybridization, crystal field and magnetism in rare earths and core level spectroscopy

Journal of Alloys and Compounds, 193 (1993) 170-174 JALCOM 2045

170

Hybridization, crystal field and magnetism in rare earths and core level spectroscopy Takeo Jo Department of Physics, Faculty of Science, Osaka University, Toyonaka 560 (Japan)

Shin Imada Department of Material Physics, Faculty of Engineering Science, Osaka University, Toyonaka 560 (Japan)

Abstract The usefulness and capability of core level spectroscopies for probing the 4f states of rare earth systems are discussed theoretically on the basis of atomic multiplet calculations including various "solid state effects". By choosing some Ce compounds, the hybridization strength between the Ce 4f orbital and ligand orbitals are shown to be well reflected in 3d and 4d core X-ray photoemission spectra. The light polarization dependence of 3d and 4d core X-ray absorption, such as linear dichroism and magnetic circular dichroism, is shown to be a powerful characteristic which can be used to detect the distribution and symmetry of 4f electron occupation.

I. Introduction A knowledge of the electronic structure of 4f electrons in rare earth systems is indispensable for an understanding of the various phenomena seen in these systems. Due to a strong centrifugal force, the wavefunction of 4f electrons is well localized even in solids and an approach from the atomic limit is known to be a good starting point for a discussion of local quantities such as valence numbers or atomic magnetic moments. The purpose of this paper is to demonstrate theoretically the usefulness and capability of soft X-ray core level spectroscopy for probing 4f electronic states of rare earths on the basis of a local description. Among various rare earth compounds, the hybridization between the 4f orbital of the Ce atom and the surrounding ions is known to cause phenomena rich in variety especially in Ce compounds [1]. The hybridization strength, the 4f affinity level and the effective interaction between the 4f electrons of each Ce compound not only determine the number of 4f electrons (i.e. 4f valence) but are also reflected in various core level spectra [2]. The Ce 3d core X-ray photoemission spectroscopy (3d XPS) is a typical example. Analysis of this from the viewpoint of the 4f configuration interaction based on the Anderson model, which parameterizes the above-mentioned quantities, has been successfully carried out to extract these parameter values [3]. In the Ce 3d XPS, a 3d core electron is excited as a photoelectron with energy e by absorbing a photon with energy ~ and the photoelectron intensity is measured as a function of the binding energy E B (o~ --e).

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Information about the initial state of 3d XPS is reflected in its spectrum through the final state interaction between the photo-produced 3d core hole and 4f electrons [4]. Until 1989, the essence of the analysis of 3d XPS based on the Anderson model was to prepare the solution of the eigenvalue problem for a 2 x 2 or 3 x 3 hamiltonian matrix, which describes the initial or final state and is spanned by the 4f °, 4f ~ or 4f 2 configuration, and to calculate the spectrum by using the "golden rule" with the solution [3]. The analysis neglects the multiplet splitting due to the 4 f - 4 f or 4 f - 3 d electrostatic interaction and the success of the analysis is not necessarily evident. In the case of the Ce 4d XPS, where the role of the 3d core in 3d XPS is replaced by the 4d core, the spectrum furthermore exhibits, due to a strong 4 d - 4 f exchange interaction, a complicated multiplet structure that depends upon the compounds, and its analysis has been an open question for a 10ng time [5]. We first give an interpretation of the apparent success of Ce 3d XPS and of 4d XPS for some Ce compounds, which was carried out for the first time by the authors on the basis of an extended Anderson model including multiplet splitting [6]. In addition to core XPS, edge structures of spectra in 3d or 4d core X-ray absorption spectroscopy (3d or 4d XAS) have been observed iff rare earths [7-9]; these correspond to the photoexcitation of a core electron into the 4f orbital by the electric dipole transition. As a result of the selection rule of the transition and the above-mentioned electrostatic interactions, the spectra, especially 4d XAS, often exhibit multiplet structures more prominent than those in 3d XPS and 4d XPS. We

© 1993 - Elsevier Sequoia. All rights reserved

T. Jo, S. Imada / Core level spectra of rare earths

can therefore expect that, by controlling the polarization of the incident photon, the structure of XAS can be used as a "fingerprint" to extract more detailed information about the electronic state such as the symmetry of the occupied states [ 10]. In the second part of this paper, we discuss various types of dichroism including magnetic circular dichroism (MCD) in the Ce 3d and 4d XAS for the hexagonal ferromagnet CeRh3 B 2 by introducing the uniaxial crystal field and molecular field in the extended Anderson model [ 11 - 14]. In the last part of this paper, we extend our discussion on M C D in core XAS to rare earth systems other than Ce. Since the 4f orbital of rare earth atoms is supposed to keep its atomic nature quite well even in solids, with some exceptions, we take an atomic approach; we discuss MCD in the 3d and 4d XAS for ions from Ce 3+ to Tm 3+ under an infinitesimal magnetic field [15]. The trend of MCD from Ce to Tm is shown to be interpreted intuitively. The present atomic calculation will be a starting point for investigating various kinds of "solid state effects" in rare earth magnets. In Section 2, we discuss the effect of hybridization on the 3d and 4d XPS in some Ce compounds. In Section 3, various kinds of incident light-polarization dependence of 3d and 4d XAS in the hexagonal ferromagnet CeRh3B2 are discussed. Section 4 is devoted to systematics of MCD in 3d and 4d XAS from Ce 3+ to Tm 3+. Section 5 gives the conclusions. 2. Core XPS in Ce compounds

We adopt the extended Anderson model given by

H=HI + 11,_ with +fd~en~v+fd~(V(e)a+fva~+h.c.) --Ufd 2

nf"(1--nd~)l+ Uff ~

(1)

and

112 = Hfr(F2f, F4f, F6f) + nfd(F2df, F4df, G ldf, G3df, GSdf) + Hr(G) + Hd(~d)

(2)

H~ describes the so-called Anderson model [3]: the first, second, third, fourth and fifth terms represent, respectively, the 4f affinity level el; the energy of conduction or valence band with energy e; the matrix element of hybridization V(E); the core hole attractive potential; and the effective 4 f - 4 f repulsion Urr. v and ¢ denote the combined index of the spin and orbital states of f and d symmetries, respectively. //2 denotes the hamiltonian of a rare earth ion: the first and second terms represent the 4f-4f, 4 f - 4 d multiplet interactions with the:Slater

171

integrals, Fs and Gs, respectively; and the third and fourth terms denote the spin-orbit interaction in the 4f and 4d states with coupling constants ~f and ~d, respectively. For the parameter values of H~ adopted in this work we defer to ref. 15. We replace the conduction or valence band by a single level (for details of its justification see, for example, ref. 14) and take the level as the original energy. By diagonalizing the hamiltonian H thus obtained, we obtain for the initial (final) state the eigenvalue Ei (Efs) and eigenfunction li) (If)s); f denotes the index of final states apart from a photoelectron. In the 3d or 4d XPS, the core 3d or 4d electron is, by absorbing a photon with energy co, excited as a photoelectron with energy e. The spectrum as a function of the binding energy E B = co - e, Fxps(EB) is then, with use of these, expressed as Fxps(E,) = ~l(f]To,: li)] 2 6(EB + Ei -- E,-) f where Td,: is the operator describing photoexcitation by the dipole transition. In the calculation, the delta function 6(x) is replaced by the lorenzian with appropriate width (for details see ref. 6). Deferring to refs. 6 and 16-18 for details, we discuss 3d and 4d XPS in the spectral region corresponding to the final states with d94f t and d94f2v. The 3d XPS is, as a result of a strong 3d-core spin-orbit interaction, composed of two branches corresponding to 3d5/2 and 3d3/2 with an energy separation of about 20 eV. Each branch has a two-peak structure which arises from the bonding and antibonding states of d94fI and d94f2v [19]. In the case of 3d XPS, the width of multiplet splitting due to 3 d - 4 f interaction is comparable to or less than the effective hybridization strength. As a resuit, its multiplet structure is found to be "quenched" to a considerable extent especially in CeO2 [20], which explains the apparent success of the previous interpretation neglecting the multiplet splitting [16]. The "quenching" of the multiplet structure in 3d XPS is more remarkable in La compounds [17]. In the case of 4d XPS, the width of the multiplet splitting due to 4d 4f interaction is larger than both the hybridization and the 4d-core spin-orbit interaction. The "quenching" of the multiplet structure is not seen in the present case. Each multiplet structure modified by the hybridization surely plays a role as the "fingerprint" that identifies each compound. It confirms the trend of the 4f affinity level among the trivalent compounds and the large hybridization in CeO2. A similar analysis is extended to Ce 4d XAS [18].

3. Light-polarization dependence of Ce 3d and 4d XAS in CeRh3B 2

In the hexagonal ferromagnet CeRh3B2 with Curie temperature 112 K the Ce atoms form linear chains

T. Jo, S. Imada / Core level spectra of rare earths

172

along the c axis and the interatomic C e - C e distance in this direction is much smaller than that in the c plane [21]. The importance of a crystal-field splitting or an anisotropic hybridization in determining the 4f ground state was discussed by Kasuya et al. [22]. A recent band-structure calculation by Eriksson et al. [23] reports a relative weight for the 4f orbital with azimuthal quantum number m r = 0 of about 3 0 ° - 4 0 0 and the magnetization along the e axis (hard axis) in the ferromagnetic state arises mainly from the 4f spin moment of Ce. In order to discuss linear dichroism arising from uniaxial anisotropy and MCD, we assume, in addition to the hamiltonian given in the preceding section, a simplified crystal-field of D6h symmetry H 3 and the molecular field acting on the 4f spin, H4 given by H 3 = - A c ~, nfy (~ e A2u)

.~o .05

4dXAS l~~~j~

fl I ~gll 2- [

,00 -h -~ 6 ~ 4 6//~' I ~6'1 w(eV) Fig. 1. The calculated linear dichroism in the paramagnetic state for Ce and 4d XAS with the use of the uniaxial crystal-field Ac = 0.2 eV (see text). the direction of the orbital moment of the Ce atom, which reflects the uniaxial crystalline field or the anisotropic hybridization.

(3)

7

4. Systematics of M C D in 3d and 44t XAS from Ce 3+ to Tm 3+

and Ha = 2AM Y', s~(v)nfv

.~S

(4)

¥

respectively: H 3 causes a preferential occupation of the A2u symmetry state, i.e. mr-- 0 state. In Ha, sz(v) represents the z component of spin of the vth state [ 14]. In the 3d or 4d XAS, a core 3d or 4d electron is photoexcited into the 4f state by absorbing a photon with energy 09. The spectrum, as a function of 09, FXAS(C0) is expressed as

Fxns(f°) ----Z ](f]Tdrli)l 2 6(Ei + co - Ef) f

where Tar is the operator describing the 3d or 4d ~4f dipole transition and f stands for the index of the final state of XAS. A part of the calculated spectrum is here shown by a histogram or the lorenzian convolution (for details see refs. 13 and 14). We assume that li> (If)) is a superposition of 4t`0 and 4flv (d94f1 and d94f2v) configurations and adopt parameters of our model so that the number of 4f electrons is 0.90 [24] (for details see ref. 14). By taking into account the above-mentioned band-structure calculation, we adopt the crystal-field Ac = 0.2eV where 40% of 4f electrons occupy the mr = 0 orbit. Figure 1 shows the calculated polarization dependence of 4d XAS in the paramagnetic state. The 4d XAS is composed of a giant-absorption region and a prethreshold region, which are dipole-allowed and "nominally dipole-forbidden" (spin-orbit induced) regions respectively. The results for 3d XAS [14] and 4d XAS shown in Fig. 1 agree qualitatively with the recent observations by Nakai et al. [25] and Fujimori et al. [26] respectively. We also discussed the MCD in 3d and 4d XAS by applying a molecular field AM (see eqn. (4)) [11, 12, 14]. Results show that the MCD feature is very sensitive to

We calculate the MCD spectrum in 3d and 4d XAS (the spectrum for positive helicity minus that for negative helicity) for the ground state from Ce 3+ (the 4f electron number n = 1) to Tm 3+ (n = 12) ions in an infinitesimal magnetic field, which are shown in Figs. 2(a) and 2(b), respectively [15]. The 3d XAS spectrum is composed of Ms(3ds/2) and Ma(3d3/2) peaks. If we define the absorption intensity for the positive helicity light by I+ and that for the negative helicity one by I_, the calculated MCD in 3d XAS can be summarized as follows: (1) In the case of n < 7, I+ and I_ are nearly the same in the M5 region, while in the M4 region I+ is larger than I_. (2) In the case of n = 7 (Gd3+), I+ is larger than I_ in the M5 region, while I+ is smaller than I_ in the M4 region. (3) In the case of n > 7, I+ is larger than I_ in both the M5 and M4 regions. The calculated MCD in 4d XAS is summarized as follows: (1) In the cases of both n < 7 and n > 7, I+ is larger (smaller) than I_ in the higher (lower) energy region; the intensity in the prethreshold region with fine multiplet structures is weaker for positive helicity. (2) In the case o f n = 7, I+ is larger (smaller) than I_ in the lower (higher) energy region. The above-mentioned features of MCD in both 3d XAS and 4d XAS can be interpreted intuitively by the three key factors: (1) In the initial state, the electrons (holes) are mainly distributed among the 4f orbitals, specified by the azimuthal quantum number mr and the spin; for those with negative mf and up spin for n < 7 (those

173

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with positive mf and up spin for n > 7), and for n = 7, all the down-spin states are occupied. (2) The d , f electric dipole transition into the 4f orbital with positively (negatively) larger mf is more favourable for positive (negative) helicity light. Furthermore, the core s p i n - o r b i t interaction makes the transition between up-spin (down-spin) states by positive helicity light more dominant, for ds/2 ( d 3 / 2 ) and for the transition by the negative helicity light the role of the spin states is interchanged. (3) The exchange interactions between a 4f electron and a 3d or 4d core hole (with the same spin) push up the final state energy, and the leading term of the interaction is proportional to the above-mentioned d , f transition probability. The features of M C D in 3d XAS are, if we note the large 3 d - c o r e s p i n - o r b i t interaction, seen to be understood by the above-mentioned factors (1) and (2), and

those in 4d XAS are, if we note larger 4 d - 4 f exchange interaction, seen to be understood by the factors ( 1 ) (3).

5. Conclusions We have theoretically demonstrated the usefulness of core level spectroscopies in probing the 4f state of rare earth systems. The hybridization strength between the Ce 4f orbital with surrounding ligands in some Ce compounds is shown to be well reflected in 3d and 4d core XPS. Core 3d and 4d XAS in rare earth systems with the use of various types of polarized light are shown to give detailed information about symmetry of the 4f electron distributions in magnets or in substances with uniaxial symmetry.

174

T. Jo, S. Imada ] Core level spectra of rare earths

Acknowledgments T h e a u t h o r s t h a n k J. K a n a m o r i , A. K o t a n i , A. Fujim o r i , K. Y a m a g u c h i a n d S. N a k a i for discussions.

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