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Theory of magnetic circular dichroism in Ce L2,3-edges of mixed valence compound CeFe2
Journal of Physics and Chemistry of Solids 63 (2002) 1485±1488
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Theory of magnetic circular dichroism in Ce L2,3-edges of mixed valence compound CeFe2 H. Ogasawara a,*, K. Asakura b, K. Fukui a, I. Harada b, A. Kotani a b
a ISSP, University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8581, Japan Department of Physics, Faculty of Science, Okayama University, 3-1-1 Tsushima-naka, Okayama 700-8530, Japan
Abstract Theoretical analysis of the magnetic circular dichroism at Ce L2,3 edges in X-ray absorption spectra (XAS) of mixed valence compound CeFe2 is presented. Impurity Anderson model is used to describe the valence mixing between Ce 4f orbital and Fe 3d band with LCAO approach to describe the band nature of the Fe 3d and Ce 5d states. Our results reproduce well the two-peak structure observed both in XAS and MCD experiments, especially their energy positions and spectral widths. Anomalously small magnetic moment is consistent with our model. q 2002 Elsevier Science Ltd. All rights reserved. Keywords: A. Intermetallic compounds; A. Magnetic materials; C. XAFS (EXAFS and XANES); D. Electronic structure; D. Magnetic properties
1. Introduction Mixed valence property in Ce compounds is one of the most striking and interesting phenomena caused by strongly correlated electrons in condensed matter physics. Although a lot of works on this theme have been accumulated up to now by means of various experimental techniques, details are still to be investigated especially for electronic and magnetic states of Ce 4f and 5d electrons. X-ray absorption spectroscopy (XAS) at the Ce L2,3 edges (2p1/2,3/2 ! 5d) is suitable tool to investigate such states. High-energy spectroscopy has contributed to obtain the knowledge on such materials for long years. Recently magnetic circular dichroism (MCD) of X-ray region became available and was found to be a unique and powerful method to reveal detailed information on the magnetic properties of individual shells. MCD is de®ned as a difference between the absorption spectra for two circularly polarized lights. The difference is due to the breaking of time-reversal symmetry caused by the magnetic polarization of an absorbing atom. CeFe2 is an intermetallic compound of a cubic Laves structure with a ferromagnetism. The mixed valence nature * Corresponding author. Tel.: 181-471-36-3262; fax: 181-47136-3264. E-mail address: [email protected] (H. Ogasawara).
of it is re¯ected in its various physical properties. CeFe2 shows several anomalies compared to other isostructural rare-earth compounds RFe2, such as low Curie temperature (Tc , 230 K), small magnetic moment (m , 2.3m B) and Ê ) [1]. It is also known a short lattice constant (a , 7.3 A that resistivity and speci®c heat show anomalous behavior. The XAS at the Ce L2,3 edges of CeFe2 exhibits a characteristic two-peak structure observed usually for mixed-valent Ce compounds. The MCD at the Ce L2,3 edges also shows two-peak structure, but the energy position and the spectral width are different from those of XAS [2]. The MCD offers an opportunity to investigate the magnetic properties of the Ce 5d band directly, which is dif®cult by other experimental means, but no quantitative theoretical analysis has been so far made for the MCD in CeFe2. The purpose of this paper is to investigate the electronic and magnetic properties of CeFe2 through a model calculation of the XAS and its MCD at the Ce L2,3 edges. We try to reproduce the difference in the two-peak structures of XAS and MCD with model Hamiltonian parameters that give the physical properties of this compound. This paper is organized as follows: the model and method of calculation are presented in Section 2. The calculated results are shown in Section 3. Concluding remarks are given in Section 4.
0022-3697/02/$ - see front matter q 2002 Elsevier Science Ltd. All rights reserved. PII: S 0022-369 7(02)00147-6
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H. Ogasawara et al. / Journal of Physics and Chemistry of Solids 63 (2002) 1485±1488
2. Model We use an impurity Anderson model which consists of spatially extended Ce 5d and Fe 3d states and Ce 4f and 2p states located on a single atomic site. The Hamiltonian is divided into two parts, a one-electron part and a correlation part, as H H1 1 H2 :
1
The one-electron part is given in a site representation as follows: X 1 X 1 X i;i 0 1 H1 13d am;i am;i 1 tm;m 0 am;i am 0 ;i 0 1 15d an;j an;j m;i
X
1
j;j 0 ;n;n 0
n;j
i;i 0 ;m;m 0
X
0
tn j;j;n 0 a1 n;j an 0 ;j 0 1
i;j;m;n
1 tm i;j ;n am;i an;j 1 h:c: ; 2
where t represents hopping integral, 1 3d (1 5d) the energy of Fe 3d (Ce 5d) orbital, m (n ) a set of quantum numbers (n, l, m, ms) of Fe 3d (Ce 5d) orbital, i and j are atomic sites and, a 1 (a) is the creation (annihilation) operator. The hopping integral tm i;j ;n is written explicitly as follows [3,4] Z fpm r 2 ri V rwn r 2 rj d3 r 3 tm i;j ;n
X
ll 0 jW lm; l 0 m 0 ; jd m;m 0 ;
4
jumu
where f (w ) represents one-electron wavefunction, V(r) potential function, ll 0 j radial part, W lm; l 0 m 0 ; j angular part, respectively. The index j is written as s , p , d for j 0, 1, 2 after Slater and Koster [3]. The correlation part is given as X 1 X 1 1 H 2 14f al;0 al;0 1 U4f 4f al;0 al;0 a1 l 0 ;0 al 0 ;0 112p c2p c2p l
2 U2p 4f 1
X i;0;m;l
X l
nearest neighbors for Fe±Ce and Ce±Ce pairs, and up to the third nearest neighbors for Fe±Fe pairs, considering the order of magnitude of hopping integral [5]. The hopping integrals (ddj ) of d electrons between Fe± Fe, Fe±Ce, Ce±Ce pairs are obtained after Pettifor's formula [6] together with the table by Andersen and Jepsen [7]. The relation (dds ):(ddp ):(ddd ) 6: 2 4:1 is used after Pettifor [6]. The parameter values used in the present calculation are slightly modi®ed from the original values for the purpose of better reproduction of the experiments. The used values of (dds ) are 20.042 Ry (Fe±Fe), 20.035 Ry (Fe± Ce) and 20.140 Ry (Ce±Ce), respectively. The eigenstates of H1 consist of linear combinations of the Fe 3d and Ce 5d orbitals. These states are used as the basis set to solve the total Hamiltonian H. We consider up to three con®gurations in the calculation of correlation part. The basis sets are (2p 5)4f 0, (2p 5)4f 1L and (2p 5)4f 2L 2, where L stands for a hole in the occupied eigenstates of H1. It is assumed that Ce 4f state mixes only with the 3d state of nearest neighbor Fe atoms. We do not consider multiplet effects here; spin±orbit interaction and higher multipole of the Coulomb interaction are omitted. The Ce 4f±5d exchange interaction, which plays an indispensable role in other rare-earth compounds with partially ®lled 4f shell [8,9] is also neglected, for the 4f component is expected to form an almost singlet state. In the calculation of MCD we take the z-direction to be the c-axis of the crystal. It is assumed that all the magnetic moments are aligned along c-axis (easy axis) by applying the external ®eld in the 2z direction. The Fe 3d band is split to up-spin band (majority band) and down-spin band (minority band). We do not split the Ce 5d band explicitly, but it splits through the mixing with the Fe 3d band. The spectral function is given as X ^ I v ukf uT ^ uglu2 d Ef 2 Eg 2 "v; 6 f
l;l 0
1 c1 2p c2p al;0 al;0
tm i;0 ;l
a1 m;i al;0 1 h:c: ;
(5)
where 1 4f and 1 2p are energies of the Ce 4f and Ce 2p orbitals located on a single atomic site 0, U4f 4f Coulomb interaction between 4f electrons, 2U2p 4f Coulomb interaction between 2p hole and 4f electron and l a set of quantum numbers n; l; m; ms of Ce 4f orbital, respectively. The last term in H2 represents the mixing between the Ce 4f orbital and Fe 3d orbital. We disregard the Coulomb interaction between 4f and 5d states, as well as between 2p and 5d states, for simplicity. In the following, we adopt a cluster approach of Ce17Fe28, where Ce and Fe atoms up to the second nearest neighbor from the central Ce atom (at j 0) are taken into account. We take into account the hopping integral up to the second
where ugl Eg represents the ground state (energy), u f l Ef ®nal states (energies), T ^ transition matrix. The superscript ^ represents the helicity of incident photon, with which Ce 2p electron is excited to the Ce 5d components of the unoccupied states of H1. We neglect the contribution from the quadrupolar transition here. We assume that the photon wave vector is in the 1z direction. With this geometry, we de®ne MCD as [10] DI I 1 v 2 I 2 v:
7
3. Results First, we consider the limiting case of the Ce 4f 0 con®guration (Ce 41), where the H2 term can be omitted. After that the correlation effect is considered. In Fig. 1(a) we give the calculated partial DOS of Ce 5d and Fe 3d states for up and down spins. Here the partial DOS
H. Ogasawara et al. / Journal of Physics and Chemistry of Solids 63 (2002) 1485±1488
DOS (eV-1 (CeFe2)-1)
1
of the Ce17Fe28 cluster is convoluted by a semi-elliptical function with a width of 0.1 eV. In this calculation, the center of gravity of the Ce 5d band is set at 0 eV, and that of the Fe 3d band at 23.57 eV with an exchange splitting of ^0.25 eV, which reproduces the experimental magnitude of the MCD. The Fermi energy is set at EF 23.1 eV. The average occupation numbers (spin moments) of Fe 3d band and Ce 5d band are, respectively, 6.4 (1.3m B) and 1.7 (20.18m B). It is to be noted that the spin splitting of the unoccupied Ce 5d states is con®ned to the energy region near the Fermi energy due to the hybridization with the overlapping Fe 3d band. Without 4f hybridization (so that for the Ce 4f 0 con®guration), the Ce L2,3 edge XAS is calculated with the transition from Ce 2p core to the Ce 5d component in the unoccupied states of the one-electron DOS. The calculated XAS is shown in Fig. 1(b) with the solid line. The spectrum is convoluted with a Lorentzian with a width of 3.0 eV (half width at half maximum (HWHM)) in order to take into account the lifetime effect of the core hole, as well as experimental resolution. The MCD spectrum for this XAS is also shown in Fig. 1(b) with the dotted line. The strong spin polarization in the Ce 5d band results in the strong MCD spectrum near the Fermi energy. Here the width of the MCD is signi®cantly narrower than the width of the XAS, which corresponds to the total width of the unoccupied Ce 5d band. The calculated result for CeFe2 with the correlation effect is presented in Fig. 2 with the experimental results by Giorgetti et al. [2]. In the calculation of XAS, we use the backgrounds shown with the dashed curve. The parameters
(a)
spin up
0.5
0
-0.5
spin down
Ce 5d Fe 3d
-1
EF
(b)
Intensity (arb.units)
L3-XAS
MCD x50 0 -4
-2
0
2
4
6
1487
8
Relative Energy (eV) Fig. 1. (a) Calculated partial density of states per CeFe2 formula units for Fe 3d band (dotted) and Ce 5d band (solid). (b) Calculated XAS and MCD for a limit of Ce 41.
Intensity (arb. units)
Ce L3
MCD x150
-10
0
10
20
Relative Energy (eV) Fig. 2. Calculated XAS and MCD (solid) for CeFe2, compared with the experimental XAS (cross) and MCD (dot) by Giorgetti et al. [2].
1488
H. Ogasawara et al. / Journal of Physics and Chemistry of Solids 63 (2002) 1485±1488
used are 14f 2 EF 20:6 eV; U2p 4f 10.0 eV and U4f 4f 9.0 eV. The hopping integral (dfs ) 0.3 eV for the Ce 4f± Fe 3d mixing is decided to reproduce the Ce 3d XPS. We take the ratio between the hopping integrals to be (dfs ):(dfp ):(dfd ) . 10: 2 4:0 after Kasuya et al. [11]. The characteristic two-peak structure is obtained both for the XAS and MCD and reproduces the experiment well. The calculated ground state 4f number is n f , 0:62: From the calculation it is con®rmed that the high-energy peak corresponds to the 4f 0 ! 2p 54f 05d 1 component, while the ®rst peak corresponds to the mixture of the 4f 1L and 4f 2L 2 components. The width of MCD is signi®cantly narrower than the corresponding XAS peaks and the peak positions are shifted to the lower energy. It is obvious from the result of Fig. 1 that the MCD peak of each con®guration should appear in the lower energy position of XAS and have narrower width. The width of the ®rst peak of MCD is a bit wider than the second one, because the ®rst peak corresponds to the strongly mixed 4f 1L and 4f 2L 2 states, while the second one is the 4f 0 state which directly re¯ects the result of Fig. 1. 4. Concluding remarks In this paper, we show that the calculation based on the impurity Anderson model combined with LCAO cluster calculation reproduces the experiments of the XAS and its MCD of CeFe2 at the Ce L2,3 edges. In this model, the Ce 5d band is spin-polarized through the mixing with the spinpolarized Fe 3d band. The induced polarization is largest near the Fermi level, where the Fe 3d band and Ce 5d band mixes strongly. Because of this, the peak position of MCD is located at the bottom of the unoccupied 5d band. This explains why the width and peak position of MCD is narrower and shifted to lower energy compared to XAS. In the case of CeFe2, the two peaks in XAS are assigned to 4f 0 and 4f 1 1 4f 2 peaks, each of which has a corresponding MCD peak at its lower energy side. Therefore the naive view of the molecular ®eld from Fe 3d band acting on all over the Ce 5d band is not appropriate for the interpretation of MCD.
The value of the exchange splitting for the Fe 3d band is smaller than other RFe2 compounds to reproduce the experimental MCD. Through the mixing with the spin-split Fe 3d band, the Ce 5d band is polarized anti-parallel to the Fe 3d moment. This is consistent to the low Curie temperature and small magnetic moments of CeFe2. This reduction of the Fe 3d magnetism may be due to the mixing with Ce 4f level, where the 4f level is polarized parallel to the Fe 3d moment. If the exchange interaction between Ce 5d and 4f states is introduced, their spins tend to align parallel. A frustrated situation is supposed to occur in this system, which decreases the magnetic nature. This frustration is also consistent with the instability of the ferromagnetism of CeFe2 with the chemical substitution. We believe the present model calculation gives a good starting point for further investigation and the potential possibility of MCD for magnetic mixed-valence systems.
References [1] J.J.M. Franse, R.J. Radwanski, in: K.H.J. Buschow (Ed.), Handbook of Magnetic Materials, vol. 7, North-Holland, Amsterdam, 1993, p. 307. [2] C. Giorgetti, S. Pizzini, E. Dartyge, A. Fontaine, F. Baudelet, C. Brouder, Ph. Bauer, G. Krill, S. Miraglia, D. Fruchart, J.P. Kappler, Phys. Rev. B 48 (1993) 12732. [3] J.C. Slater, G.F. Koster, Phys. Rev. 94 (1954) 1498. [4] R.R. Sharma, Phys. Rev. B 19 (1979) 2813. [5] H. Yamada, J. Inoue, K. Terao, S. Kanda, M. Shimizu, J. Phys. F: Metal Phys. 14 (1984) 1943. [6] D.G. Pettifor, J. Phys. F: Metal Phys. 7 (1977) 613. [7] O.K. Andersen, O. Jepsen, Physica 91B (1977) 317. [8] X. Wang, T.C. Leung, B.N. Harmon, P. Carra, Phys. Rev. B 47 (1993) 9087. [9] K. Fukui, H. Ogasawara, A. Kotani, I. Harada, H. Maruyama, N. Kawamura, K. Kobayashi, J. Chaboy, A. Marcelli, Phys. Rev. B 64 (2001) 104405. [10] F. Baudelet, Ch. Giorgetti, S. Pizzini, Ch. Brouder, E. Dartyge, A. Fountaine, J.P. Kappler, G. Krill, J. Electron Spectrosc. Relat. Phenom. 62 (1993) 153. [11] T. Kasuya, O. Sakai, K. Takegahara, M. Takeshige, J. Magn. Magn. Mater. 52 (1985) 1.
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Theory of magnetic circular dichroism in Ce L2,3-edges of mixed valence compound CeFe2 H. Ogasawara a,*, K. Asakura b, K. Fukui a, I. Harada b, A. Kotani a b
a ISSP, University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8581, Japan Department of Physics, Faculty of Science, Okayama University, 3-1-1 Tsushima-naka, Okayama 700-8530, Japan
Abstract Theoretical analysis of the magnetic circular dichroism at Ce L2,3 edges in X-ray absorption spectra (XAS) of mixed valence compound CeFe2 is presented. Impurity Anderson model is used to describe the valence mixing between Ce 4f orbital and Fe 3d band with LCAO approach to describe the band nature of the Fe 3d and Ce 5d states. Our results reproduce well the two-peak structure observed both in XAS and MCD experiments, especially their energy positions and spectral widths. Anomalously small magnetic moment is consistent with our model. q 2002 Elsevier Science Ltd. All rights reserved. Keywords: A. Intermetallic compounds; A. Magnetic materials; C. XAFS (EXAFS and XANES); D. Electronic structure; D. Magnetic properties
1. Introduction Mixed valence property in Ce compounds is one of the most striking and interesting phenomena caused by strongly correlated electrons in condensed matter physics. Although a lot of works on this theme have been accumulated up to now by means of various experimental techniques, details are still to be investigated especially for electronic and magnetic states of Ce 4f and 5d electrons. X-ray absorption spectroscopy (XAS) at the Ce L2,3 edges (2p1/2,3/2 ! 5d) is suitable tool to investigate such states. High-energy spectroscopy has contributed to obtain the knowledge on such materials for long years. Recently magnetic circular dichroism (MCD) of X-ray region became available and was found to be a unique and powerful method to reveal detailed information on the magnetic properties of individual shells. MCD is de®ned as a difference between the absorption spectra for two circularly polarized lights. The difference is due to the breaking of time-reversal symmetry caused by the magnetic polarization of an absorbing atom. CeFe2 is an intermetallic compound of a cubic Laves structure with a ferromagnetism. The mixed valence nature * Corresponding author. Tel.: 181-471-36-3262; fax: 181-47136-3264. E-mail address: [email protected] (H. Ogasawara).
of it is re¯ected in its various physical properties. CeFe2 shows several anomalies compared to other isostructural rare-earth compounds RFe2, such as low Curie temperature (Tc , 230 K), small magnetic moment (m , 2.3m B) and Ê ) [1]. It is also known a short lattice constant (a , 7.3 A that resistivity and speci®c heat show anomalous behavior. The XAS at the Ce L2,3 edges of CeFe2 exhibits a characteristic two-peak structure observed usually for mixed-valent Ce compounds. The MCD at the Ce L2,3 edges also shows two-peak structure, but the energy position and the spectral width are different from those of XAS [2]. The MCD offers an opportunity to investigate the magnetic properties of the Ce 5d band directly, which is dif®cult by other experimental means, but no quantitative theoretical analysis has been so far made for the MCD in CeFe2. The purpose of this paper is to investigate the electronic and magnetic properties of CeFe2 through a model calculation of the XAS and its MCD at the Ce L2,3 edges. We try to reproduce the difference in the two-peak structures of XAS and MCD with model Hamiltonian parameters that give the physical properties of this compound. This paper is organized as follows: the model and method of calculation are presented in Section 2. The calculated results are shown in Section 3. Concluding remarks are given in Section 4.
0022-3697/02/$ - see front matter q 2002 Elsevier Science Ltd. All rights reserved. PII: S 0022-369 7(02)00147-6
1486
H. Ogasawara et al. / Journal of Physics and Chemistry of Solids 63 (2002) 1485±1488
2. Model We use an impurity Anderson model which consists of spatially extended Ce 5d and Fe 3d states and Ce 4f and 2p states located on a single atomic site. The Hamiltonian is divided into two parts, a one-electron part and a correlation part, as H H1 1 H2 :
1
The one-electron part is given in a site representation as follows: X 1 X 1 X i;i 0 1 H1 13d am;i am;i 1 tm;m 0 am;i am 0 ;i 0 1 15d an;j an;j m;i
X
1
j;j 0 ;n;n 0
n;j
i;i 0 ;m;m 0
X
0
tn j;j;n 0 a1 n;j an 0 ;j 0 1
i;j;m;n
1 tm i;j ;n am;i an;j 1 h:c: ; 2
where t represents hopping integral, 1 3d (1 5d) the energy of Fe 3d (Ce 5d) orbital, m (n ) a set of quantum numbers (n, l, m, ms) of Fe 3d (Ce 5d) orbital, i and j are atomic sites and, a 1 (a) is the creation (annihilation) operator. The hopping integral tm i;j ;n is written explicitly as follows [3,4] Z fpm r 2 ri V rwn r 2 rj d3 r 3 tm i;j ;n
X
ll 0 jW lm; l 0 m 0 ; jd m;m 0 ;
4
jumu
where f (w ) represents one-electron wavefunction, V(r) potential function, ll 0 j radial part, W lm; l 0 m 0 ; j angular part, respectively. The index j is written as s , p , d for j 0, 1, 2 after Slater and Koster [3]. The correlation part is given as X 1 X 1 1 H 2 14f al;0 al;0 1 U4f 4f al;0 al;0 a1 l 0 ;0 al 0 ;0 112p c2p c2p l
2 U2p 4f 1
X i;0;m;l
X l
nearest neighbors for Fe±Ce and Ce±Ce pairs, and up to the third nearest neighbors for Fe±Fe pairs, considering the order of magnitude of hopping integral [5]. The hopping integrals (ddj ) of d electrons between Fe± Fe, Fe±Ce, Ce±Ce pairs are obtained after Pettifor's formula [6] together with the table by Andersen and Jepsen [7]. The relation (dds ):(ddp ):(ddd ) 6: 2 4:1 is used after Pettifor [6]. The parameter values used in the present calculation are slightly modi®ed from the original values for the purpose of better reproduction of the experiments. The used values of (dds ) are 20.042 Ry (Fe±Fe), 20.035 Ry (Fe± Ce) and 20.140 Ry (Ce±Ce), respectively. The eigenstates of H1 consist of linear combinations of the Fe 3d and Ce 5d orbitals. These states are used as the basis set to solve the total Hamiltonian H. We consider up to three con®gurations in the calculation of correlation part. The basis sets are (2p 5)4f 0, (2p 5)4f 1L and (2p 5)4f 2L 2, where L stands for a hole in the occupied eigenstates of H1. It is assumed that Ce 4f state mixes only with the 3d state of nearest neighbor Fe atoms. We do not consider multiplet effects here; spin±orbit interaction and higher multipole of the Coulomb interaction are omitted. The Ce 4f±5d exchange interaction, which plays an indispensable role in other rare-earth compounds with partially ®lled 4f shell [8,9] is also neglected, for the 4f component is expected to form an almost singlet state. In the calculation of MCD we take the z-direction to be the c-axis of the crystal. It is assumed that all the magnetic moments are aligned along c-axis (easy axis) by applying the external ®eld in the 2z direction. The Fe 3d band is split to up-spin band (majority band) and down-spin band (minority band). We do not split the Ce 5d band explicitly, but it splits through the mixing with the Fe 3d band. The spectral function is given as X ^ I v ukf uT ^ uglu2 d Ef 2 Eg 2 "v; 6 f
l;l 0
1 c1 2p c2p al;0 al;0
tm i;0 ;l
a1 m;i al;0 1 h:c: ;
(5)
where 1 4f and 1 2p are energies of the Ce 4f and Ce 2p orbitals located on a single atomic site 0, U4f 4f Coulomb interaction between 4f electrons, 2U2p 4f Coulomb interaction between 2p hole and 4f electron and l a set of quantum numbers n; l; m; ms of Ce 4f orbital, respectively. The last term in H2 represents the mixing between the Ce 4f orbital and Fe 3d orbital. We disregard the Coulomb interaction between 4f and 5d states, as well as between 2p and 5d states, for simplicity. In the following, we adopt a cluster approach of Ce17Fe28, where Ce and Fe atoms up to the second nearest neighbor from the central Ce atom (at j 0) are taken into account. We take into account the hopping integral up to the second
where ugl Eg represents the ground state (energy), u f l Ef ®nal states (energies), T ^ transition matrix. The superscript ^ represents the helicity of incident photon, with which Ce 2p electron is excited to the Ce 5d components of the unoccupied states of H1. We neglect the contribution from the quadrupolar transition here. We assume that the photon wave vector is in the 1z direction. With this geometry, we de®ne MCD as [10] DI I 1 v 2 I 2 v:
7
3. Results First, we consider the limiting case of the Ce 4f 0 con®guration (Ce 41), where the H2 term can be omitted. After that the correlation effect is considered. In Fig. 1(a) we give the calculated partial DOS of Ce 5d and Fe 3d states for up and down spins. Here the partial DOS
H. Ogasawara et al. / Journal of Physics and Chemistry of Solids 63 (2002) 1485±1488
DOS (eV-1 (CeFe2)-1)
1
of the Ce17Fe28 cluster is convoluted by a semi-elliptical function with a width of 0.1 eV. In this calculation, the center of gravity of the Ce 5d band is set at 0 eV, and that of the Fe 3d band at 23.57 eV with an exchange splitting of ^0.25 eV, which reproduces the experimental magnitude of the MCD. The Fermi energy is set at EF 23.1 eV. The average occupation numbers (spin moments) of Fe 3d band and Ce 5d band are, respectively, 6.4 (1.3m B) and 1.7 (20.18m B). It is to be noted that the spin splitting of the unoccupied Ce 5d states is con®ned to the energy region near the Fermi energy due to the hybridization with the overlapping Fe 3d band. Without 4f hybridization (so that for the Ce 4f 0 con®guration), the Ce L2,3 edge XAS is calculated with the transition from Ce 2p core to the Ce 5d component in the unoccupied states of the one-electron DOS. The calculated XAS is shown in Fig. 1(b) with the solid line. The spectrum is convoluted with a Lorentzian with a width of 3.0 eV (half width at half maximum (HWHM)) in order to take into account the lifetime effect of the core hole, as well as experimental resolution. The MCD spectrum for this XAS is also shown in Fig. 1(b) with the dotted line. The strong spin polarization in the Ce 5d band results in the strong MCD spectrum near the Fermi energy. Here the width of the MCD is signi®cantly narrower than the width of the XAS, which corresponds to the total width of the unoccupied Ce 5d band. The calculated result for CeFe2 with the correlation effect is presented in Fig. 2 with the experimental results by Giorgetti et al. [2]. In the calculation of XAS, we use the backgrounds shown with the dashed curve. The parameters
(a)
spin up
0.5
0
-0.5
spin down
Ce 5d Fe 3d
-1
EF
(b)
Intensity (arb.units)
L3-XAS
MCD x50 0 -4
-2
0
2
4
6
1487
8
Relative Energy (eV) Fig. 1. (a) Calculated partial density of states per CeFe2 formula units for Fe 3d band (dotted) and Ce 5d band (solid). (b) Calculated XAS and MCD for a limit of Ce 41.
Intensity (arb. units)
Ce L3
MCD x150
-10
0
10
20
Relative Energy (eV) Fig. 2. Calculated XAS and MCD (solid) for CeFe2, compared with the experimental XAS (cross) and MCD (dot) by Giorgetti et al. [2].
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H. Ogasawara et al. / Journal of Physics and Chemistry of Solids 63 (2002) 1485±1488
used are 14f 2 EF 20:6 eV; U2p 4f 10.0 eV and U4f 4f 9.0 eV. The hopping integral (dfs ) 0.3 eV for the Ce 4f± Fe 3d mixing is decided to reproduce the Ce 3d XPS. We take the ratio between the hopping integrals to be (dfs ):(dfp ):(dfd ) . 10: 2 4:0 after Kasuya et al. [11]. The characteristic two-peak structure is obtained both for the XAS and MCD and reproduces the experiment well. The calculated ground state 4f number is n f , 0:62: From the calculation it is con®rmed that the high-energy peak corresponds to the 4f 0 ! 2p 54f 05d 1 component, while the ®rst peak corresponds to the mixture of the 4f 1L and 4f 2L 2 components. The width of MCD is signi®cantly narrower than the corresponding XAS peaks and the peak positions are shifted to the lower energy. It is obvious from the result of Fig. 1 that the MCD peak of each con®guration should appear in the lower energy position of XAS and have narrower width. The width of the ®rst peak of MCD is a bit wider than the second one, because the ®rst peak corresponds to the strongly mixed 4f 1L and 4f 2L 2 states, while the second one is the 4f 0 state which directly re¯ects the result of Fig. 1. 4. Concluding remarks In this paper, we show that the calculation based on the impurity Anderson model combined with LCAO cluster calculation reproduces the experiments of the XAS and its MCD of CeFe2 at the Ce L2,3 edges. In this model, the Ce 5d band is spin-polarized through the mixing with the spinpolarized Fe 3d band. The induced polarization is largest near the Fermi level, where the Fe 3d band and Ce 5d band mixes strongly. Because of this, the peak position of MCD is located at the bottom of the unoccupied 5d band. This explains why the width and peak position of MCD is narrower and shifted to lower energy compared to XAS. In the case of CeFe2, the two peaks in XAS are assigned to 4f 0 and 4f 1 1 4f 2 peaks, each of which has a corresponding MCD peak at its lower energy side. Therefore the naive view of the molecular ®eld from Fe 3d band acting on all over the Ce 5d band is not appropriate for the interpretation of MCD.
The value of the exchange splitting for the Fe 3d band is smaller than other RFe2 compounds to reproduce the experimental MCD. Through the mixing with the spin-split Fe 3d band, the Ce 5d band is polarized anti-parallel to the Fe 3d moment. This is consistent to the low Curie temperature and small magnetic moments of CeFe2. This reduction of the Fe 3d magnetism may be due to the mixing with Ce 4f level, where the 4f level is polarized parallel to the Fe 3d moment. If the exchange interaction between Ce 5d and 4f states is introduced, their spins tend to align parallel. A frustrated situation is supposed to occur in this system, which decreases the magnetic nature. This frustration is also consistent with the instability of the ferromagnetism of CeFe2 with the chemical substitution. We believe the present model calculation gives a good starting point for further investigation and the potential possibility of MCD for magnetic mixed-valence systems.
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