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Coulomb correlation energy versus covalence in transition-metal compounds
Journal of Electron Spectroscopy and Related Phenomena 152 (2006) 107–114
Coulomb correlation energy versus covalence in transition-metal compounds I. Pollini Universit`a degli Studi di Milano, Dipartimento di Fisica, CNR-INFM, Via Celoria 16, 20133 Milano, Italy Received 19 February 2006; received in revised form 7 April 2006; accepted 8 April 2006 Available online 28 April 2006
Abstract We have performed optical and photoemission studies on Mott–Hubbard and charge transfer insulators with formal ionic configurations 3d3 (CrCl3 , CrBr3 ) and 3d8 (NiCl2 , NiBr2 , NiI2 ). The photoemission spectra have been analyzed in terms of a cluster model leading to estimates of the on-site Coulomb repulsion energy, charge transfer energy and hybridization energy parameters. The ionicity parameter fi in Cr and Ni compounds has been calculated by the means of the Phillips–Van Vechten theory: its value is about 0.80 in Cr halides, and it varies from 0.70 in NiI2 to 0.80 in NiCl2 in Ni halides. We have also considered the ionicity scale fiDT of the dielectric theory. The two scales allow a good understanding of the chemical bond character and electron correlation in these materials. © 2006 Elsevier B.V. All rights reserved. Keywords: Photoemission; Electron correlation; Covalence; Mott–Hubbard; Charge transfer; Phillips–Van Vechten
1. Introduction Electron correlation plays an important role in the electronic properties of narrow-band materials. In the studies of electron correlation in solids the Hubbard model (HM) has been widely used because of its great simplicity. That is, the spatial extent of the Coulomb interaction is limited to a single atomic site and is represented by the on-site Coulomb repulsion energy U. The HM was originally applied to the study of transition-metal oxides (TMO), where the O 2p orbitals were not thought directly involved in the transport properties because of the closed shell configuration 2s2 2p6 and only TM 3d orbitals were considered [1]. It was later recognized that in oxides and halides of late TM elements, such as Ni and Cu, oxygen and halide p orbitals are also involved in the charge transport for the presence of holes in the ligand (L) orbitals. Nevertheless, in early TMO, such as Ti, V and Cr oxides, the O 2p band lies well below TM 3d levels and only d-electrons are responsible for the transport properties. This electronic structure is of the Mott–Hubbard (MH) type as opposed to the charge transfer (CT) type occurring in late TMO, according to the theoretical model of Sawatzky and
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co-workers [2–4]. In this model the relative magnitudes of the oxygen (halide) p-to-metal 3d CT energy ∆ and on-site d–d Coulomb energy U are used to classify transition-metal compounds (TMC), which may fall in the MH regime (∆ > U) or CT regime (U > ∆) [2–6]. The electronic structure is described in terms of the parameters ∆, the energy required to transfer an electron from a L orbital to the TM 3d shell, the Coulomb energy U between two 3d electrons on the same site and the hybridization energy T between the p–d orbitals. However, more recently, it was found that in early TMO, owing to the strong p–d hybridization, is U ∼ ∆ rather than ∆ > U [3,7–9]. This has modified the original notion of the MH picture, as it is shown in the U–∆ plot of Fig. 1 [10]. We can see, for example, that Fe2 O3 is predicted to be a CT compound, as CuO or NiO, while MnO or Cr2 O3 , close to the borderline, are considered intermediate compounds. We also see that CrCl3 and CrBr3 are inside the MH region, near Mott compounds such as TiO, Ti2 O3 and MnF2 . It turned out that TMC in general are √ characterized by a strong effective hybridization Teff = nh T (nh being the formal number of holes in TM orbitals), which can no longer be neglected. That is, the resulting covalence between the TM 3d electrons and the L valence band (VB) states promotes a delocalization of d electrons, which reduces the importance of correlation effects. Notwithstanding, the HM remains a valid effective model, if one considers the strongly
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2. Experimental
Fig. 1. Diagram of U vs. ∆ for transition-metal compounds of the first transitionmetal row.
p–d hybridized orbitals (rather than the pure d orbitals) located near the Fermi level as effective orbitals and use a renormalized Coulomb energy Ueff instead of the bare energy U. Photoemission (PE) of valence and core electrons in strongly correlated systems usually exhibits many-body effects, such as the presence of satellites at several eV energies below the main line. Satellites were, for instance, observed in Cu and Ni oxides and halides. In order to interpret the observed satellites in the core-level spectra of TMC, van der Laan et al. [4,5] have identified the CT process from L to TM orbitals as another important electronic mechanism. In their model the main emission and the satellite lines are attributed to |dn+1 L1 (well screened) and |dn (poorly screened) valence shell final states, where L denotes a hole in the ligand shell and n is the number of 3d electrons in the ionic ground state. This interpretation of satellites was subsequently applied to metals and insulators by Gunnarsson and Schonhammer [11] and Zaanen et al. [12]. Finally, by neglecting the widths w and W of the TM 3d and L bands, one obtains the so-called cluster model (CM), which is equivalent to the CT model. Although TMC have been much studied and their overall properties are on the whole understood, still there are interesting points which require new attention. For instance, the present discussion of the electronic properties of Cr and Ni halides is made in connection with the ionicity of the chemical bond as defined by the parameters fi and fiDT . The fi parameter was introduced by Phillips and Van Vechten (PV) long time ago [13,14] and the fiDT parameter of the dielectric theory was then discussed in later articles [15,16]. In particular, we have here calculated the values of these parameters for core-level spectra of Cr halides and VB spectra of Ni halides. One of the aims of this work is to present safe experimental estimates of the CM parameters, which are essential for a meaningful discussion of the electronic properties of TMC within the framework of Hubbard and Anderson impurity Hamiltonians [17].
Stoichiometric crystals of CrCl3 , CrBr3 and NiCl2 , NiBr2 have been grown from the vapor phase by the dynamical transport method between 800 and 850 ◦ C for Cr halides and 600 and 700 ◦ C for Ni halides. Growth of NiI2 single crystals was carried out in two different ways, that is with a Bridgman method and by chemical transport from elements in a sealed ampoule with a thermal gradient of about 750 ◦ C. The low temperature crystal layer structure of CrCl3 (T < 238 K) and CrBr3 (T < 450 K) is like the layer structure BiI3 (space group C3i ). The structure of NiCl2 and NiBr2 layer crystals is that of the CdCl2 crystals and that of NiI2 crystals is of CdI2 type. PE spectra have been performed in ultrahigh vacuum (10−10 mmHg) with a XPS spectrometer ESCALAB MKII (Vacuum Generators), equipped with a monochromatized Al K␣1,2 (1486.6 eV) radiation and a 150 mm electron analyzer. The overall resolution of the spectrometer was about 0.7 eV. Ultraviolet photoelectron spectroscopy (UPS) spectra have been obtained with an hemispherical energy analyzer and a He discharge lamp (HeI, hν = 21.2 eV). Crystals were cleaved in situ in order to get fresh surfaces and to eliminate surface impurities. The impurity content of sample, checked by XPS measurements, has shown no trace of impurity, except for negligeable carbon and oxygen signals. The electrical charging of samples during the PE experiment was monitored by heating them to about 100–120 ◦ C. The UV radiation from the ACO synchrotron (optical line) of the University of Paris was used as a continuum light source for normal incidence reflectance measurements in Cr and Ni crystalline samples at 30 K. 3. Ionicity of chemical bond Since the ionicity coefficient fi plays a crucial role for the chemical properties of TMC, let us briefly recall its definition and physical meaning. In the framework of the PV dielectric theory the fraction of ionic character (fi ) of a chemical bond defines the average separation Eg (Phillips gap) of the valence and conduction bands as the pythagorean sum of an ionic part C and a covalent part Eh 1/2
Eg (Phillips) = (Eh2 + C2 )
.
(1)
The homopolar energy gap Eh scales with the nearest neighbour distance dMX like Eh = a(dMX )−2.5
(a ∼ = 40.5)
(2)
and the ionic energy C can be defined through the Phillips electronegativity by ZB ZA e−Ks R , − (3) C(AB) = b rA rB ∼ 1.5. The atomic radii rA and rB with R = (rA + rB )/2 and b = are defined as half of the bond length of the group IV element belonging to the same row of the periodic table as atoms A and B, and ZA and ZB are the valence numbers of elements A and B. Ks is the Thomas–Fermi screening parameter Ks = (4Kf /πao ),
I. Pollini / Journal of Electron Spectroscopy and Related Phenomena 152 (2006) 107–114
where ao is the Bohr radius and Kf is the wave number on the surface of the Fermi sphere in the free electron approximation. The fraction of ionic character of a chemical bond is defined by fi =
C2 C2 = Eg2 Eh2 + C2
(4)
Note that the crystal structure does not appear explicitly anywhere and therefore the model can be extended to include crystals belonging to the NaCl structure or is applicable to compounds other than AN B8−N . In NiX2 (X = Cl, Br and I), for example, the number of electrons involved in the chemical bonds is 16, 8 per bond (neglecting 3d electrons) and the Eg values have been calculated from Eqs. (1)–(4) with the value of the prefactor b = 1.55 ± 0.07 adjusted to fit the experimental data and nearest neighbour distance dMX . In Table 1, we have listed the relevant electronic and chemical parameters for NiX2 , together with the calculated ionicity fi (0.72–0.76) and fiDT (0.79–0.80) parameters, and the d-electron counts nd and nd+1 estimated from 2p-XPS core-level spectra. For the ionicity parameter fiDT of CrX3 (X = Cr, Br) compounds we have followed a different procedure. By considering the energy of plasmons, observed at 22.6 and 20 eV for CrCl3 and CrBr3 in Fig. 2, we have calculated the average energy gap Eg with the Horie’ s relation [18], giving a correction of the free electron formula for the plasmon energy in insulators: (hν)2 ∼ = (hν)2FE + Eg 2 .
(5)
We have found a value of (hν)FE equal to 19.7 and 18.06 eV and of gap Eg = 10.9 and 8.59 eV, in CrCl3 and CrCBr3 , respectively. The average gap Eg is then used for calculating the
fractional ionic character: Eh 2 DT fi = 1 − Eg
109
(6)
where the homopolar energy gap Eh is obtained from Eq. (2), ˚ in CrCl3 and 2.55 A ˚ with a metal–halogen distance dMX = 2.33 A in CrBr3 The obtained ionicity parameters fiDT = 0.80 and 0.79 indicate that CrX3 have about 20% covalent character. 4. Experimental results and discussion Let us first discuss the results of photoemission and optical investigations on the Ni compounds. We shall then proceed to the more complex example of Cr compounds. Figs. 3 and 4 show the reflectance and VB-XPS spectra of NiX2 [19]. A main group of peaks (p–d excitons), between 2 and 4 eV, is followed by CT bands (p–d) between 3 and 7 eV, and interband (p–s) structures over 7–9 eV. The optical gap EgR is estimated by considering that the gaps must occur between the energy of the p–d excitons and that of CT transitions. The optical EgR values so obtained are in fine agreement with the photoconductivity gaps EgPh measured by Ronda et al. [20] and are shown in Table 1. The structure in the NiCl2 spectrum between 6 and 8 eV is mainly due to Cl 3p states, the main emission A is assigned to the 3d8 L−1 final states and the weak satellite structure B, between 8 and 12 eV, to the 3d7 hole state. The peak C is attributed to the Cl 3s valence states. The XPS spectrum of NiBr2 is similar and the same interpretation holds. The spectral features from 4 to 8 eV are mainly due to the Br 4p states and the peak A is assigned to the 3d8 L−1 configuration. The satellite B between 8 and 12 eV, is again due to a 3d7 hole state and the peak C to Br 4s
Fig. 2. Low temperature reflectance of CrCl3 and CrBr3 crystals. Charge transfer excitons and transitions (p → d) are followed by interband excitons and transitions (p → s). Energy loss peaks P at 22.6 and 20 eV are due to plasma oscillations.
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Fig. 4. Valence band XPS spectra of NiCl2 and NiBr2 . The predicted first BIS peak and the on-site Coulomb correlation energy U are indicated. Photoemission intensity in arbitrary units.
Fig. 3. Reflectance spectra of Ni halides in the energy range of charge transfer transitions (p → d) and fundamental absorption threshold (p → s) [19].
valence states. The predicted position of the 3d9 states in Fig. 4 is estimated by adding the gap energies EgR to the main emission peak. For example, in the case of NiBr2, with a conduction gap EgPh = 3.5 eV (optical gap is EgR = 3.8 eV), we can predict that the first inverse photoemission peak 3d9 will be located just above the Fermi level. This discussion can then be extended to the VB-UPS spectrum of NiI2 shown in Fig. 5. The peak B observed between 2 and 4.5 eV is mainly due to I 5p states and the peak A to 3d8 L−1 states. The 3d7 hole state observed at 5.5 eV in NiCl2 and at 4.5 eV in NiBr2 is shifted to 6 eV in NiI2 and is observed as a weak shoulder of the peak C. Although this satellite is not clearly observed and its intensity is expected to be low, we consider it a good candidate for this assignment. If this is the case, we can estimate the magnitude of the U parameter to be about 6 eV, as the optical gap value is about 2 eV. This estimate of U in NiI2 may be also more uncertain because of the matrix element effects on the DOS intensity distribution. Nickel halides can be favorably compared to the prototype material NiO [2,21,22]. The analysis of the VB-XPS measurements allows evaluating the ionic coefficients fi (or fiDT ) and to compare them to the ground state d-electron counts nd and nd+1 obtained from Ni 2p core-level spectra [12]. From the combined use of reflectance and VB-XPS spectra of NiO we
have estimated the ∆ and U parameters listed in Table 1 and have compared them to the parameters obtained from the core level (∆c-XPS ) and valence band (∆VB-XPS ) spectra of NiX2 . By taking into account the ground and final state hybridization shifts, we have then estimated a value of 6.0 eV for ∆VB-XPS for NiCl2 , and a value between 5.2 and 5.5 eV for NiBr2 . The position of the first BIS peak due to 3d9 states is still obtained by adding the gap value (EgPh = 3.5 eV) to the main PE peak A. This means that the gap energy in NiX2 corresponds to a 3d8 + 3d8 → 3d8 L−1 + 3d9 transitions, as implied by Merlin [23] and stated by Fujimori and Minami [6] and Zaanen et al. [3]. In conclusion, it
Fig. 5. Valence band UPS spectrum of NiI. The Coulomb correlation energy U and the conduction gap are indicated.
I. Pollini / Journal of Electron Spectroscopy and Related Phenomena 152 (2006) 107–114
turns out that the character of the band gap in Ni compounds is mainly related to the parameter ∆ describing the lower energy cost to transfer an electron from ligands to metal ions. Thus, it is the energy separation between the L p band and the TM 3dn+1 levels that governs the electronic gap in NiX2 and NiO materials, which are considered CT compounds. It is well known that PE measures the energy of the final states, which in principle lack one electron with respect to the initial state, so that the system under investigation will screen the created photohole, a many-body process which originates the formation of satellites. The approximated 9.5 and 8.0 eV value of the Ueff in NiCl2 and NiBr2 scales well with the value observed in NiO (about 13 eV). Nevertheless, this is an oversimplification because the energy levels in NiO and NiX2 are hybridized and hybridization tends to affect the energy splittings. By making a proper correction for the hybridization effect Hufner et al. [21,22] have found for the effective parameter Ueff values within 6.0 eV ≤ Ueff ≤ 9.0 eV. Therefore the separation between the 3d7 and 3d9 configurations reflects the size of the Coulomb repulsion parameter Ueff , which represents the correlation energy U plus the hybridization shift. Because the exact magnitude of the energy shift is not known the correlation energy can only be estimated approximately. For NiX2 we deem that 6–8 eV is a fair estimate for Ueff parameter. According to Sawatsky and Allen [2], the CT gap in NiO is 4.3 eV and the Ni d–d Coulomb repulsion Ueff between 7 and 8 eV, leading to a large correlation gap in the Ni 3d band. This value is fairly higher than U = 5.0 eV, recently calculated by Bengone et al. [24]. By considering the relative magnitude of the U and ∆ parameters and the fact that ∆ is related to the ligand electronegativity, the Ni compounds have been classified as CT insulators, with a conductivity gap of p–d type [2–6]. The discussion of satellites in NiCl2 and NiBr2 has been made within the approximation of the configuration interaction (CI) cluster model scheme. For Ni halides the BIS final state position has been extrapolated by considering the reflectance spectra, while for NiO we have considered the measured BIS and UPS spectra [2,21]. In general these spectra show a main peak around 3–4 eV below EF , due to a mixed 3dn L−1 configuration, followed by L p-lines at higher binding energies. Satellite structures, observed around 8–10 eV, are distant from the Ni 3d main line by ES ∼ = 5.1 eV in NiCl2 and 4.2 eV in NiBr2 , respectively (ES = 7.1 eV in NiO). The distance between the main peak and the satellites is 1/2
ES = [(∆ − U)2 + 4(Teff )2 ]
,
(7)
where the Hamiltonian is restricted to the dn and dn+1 L−1 configurations. In the limit of |∆ − U|2Teff , the ES value can be approximated by 2Teff [7,8]. For example, in the late TMO, where the effective hybridization Teff ∼ = 2–4 eV, the satellite structures have been observed at 6–9 eV. In our case we have obtained a value of Teff equal to 2.1 eV in NiBr2 and 2.5 eV in NiCl2 (close to the 3.5 eV value in NiO). As a matter of fact the main Ni 3d band is screened by the electron transferred into the 3d8 L−1 final state configuration, while the unscreened satellite is due to the 3d7 configuration. The trends of the p–d integrals
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Table 1 Electronic and chemical parameters of Ni compounds (eV) MX2
EgR
EgPh
fi
fiDT
∆
U
nd8
nd9
NiCl2 NiBr2 NiI2 NiO
4.6 3.6 2.7 4.0a –4.3
4.7 3.5 1.8 4, 4.3
0.76 0.75 0.72
0.80 0.79
3.6 2.6 1.5 4.6
5.0 5.0 4.5 5.0
0.72 0.63 0.51 0.73
0.27 0.35 0.45 0.21
Optical gaps EgR and photoconductivity gaps EgPh [20] are listed together with ionicity coefficients fi and fiDT . CM parameters (∆, U) and ground state counts nd8 and nd9 have been calculated from 2p spectra [12]. Additional constants for all compounds are Q = 7.0 eV and T = 2 eV (1.75 eV in NiO). a The 4.0–4.3 eV gap of NiO has been directly determined from UPS and BIS spectra [2,21].
and hybridization parameters Teff are primarily governed by the intra-atomic distances, which are determined by the ionic radii of the metal and ligand ions dMX . As the distance diminishes, the overlap between the 3d orbitals and ligand p bands is larger and augments the value of Teff . The nearest neighbour distance dMX , ˚ in NiCl2 and 3.72 A ˚ in NiBr2 , allows obtainwhich is 3.51 A ing the values of the hybridization parameter Teff = 2.5 eV in NiCl2 and 2.1 eV in NiBr2 , respectively. These figures scale well with the values of Teff = 3.5 eV [2,3] and 3.8 eV [9] known for NiO. The valence band ∆ and core level ∆VB-XPS , and the Ueff and Teff parameters obtained in this work have been reported in Tables 1 and 2. Although a good agreement was in general found for the chemical bond parameters, we have noted a large difference between the CT energies measured from core level and VB spectroscopy and for the gap energies. In fact, by considering the CT parameter obtained by the c-XPS spectra, one finds gap values 2–3 eV smaller than the experimental gaps. In summary, our results show that the ionicity coefficients in NiCl2 and NiBr2 are in good correspondence with ground state counts numbers nd8 and nd9 , yet our figures indicate a smaller covalence than expected from the d-electron count parameters. Let us now proceed to the study of Cr halides. We first discuss the electronic properties of CrCl3 and CrBr3 compounds obtained by photoemission in the VB region [10,25]. The VB spectra (not reported here) present a main Cr 3d emission band below 10 eV and weak satellite features separated from the main line by ES = 7.9 and 7.7 eV. The main Cr 3d emission, located around 3 eV, has been assigned to Cr 3d2 (poorly screened) final states. From the XPS and (predicted) BIS peaks we have obtained the position of the Hubbard bands (Cr 3d2 and Cr 3d4 ) and have estimated the on-site Coulomb repulsion parameter U, which is about is 3.0 eV for CrX3 . The nearest example to CrX3 is that of Cr2 O3 , an intermediate compound, which has the Table 2 CM parameters ∆VB-XPS , Ueff and Teff analyzed in this work MX2
Ueff
∆VB-XPS
∆c-XPS
Teff
nd8
nd9
NiCl2 NiBr2 NiO
8 8 10
6.0 5.0–5.5 7.0
3.6 2.6 4.6
2.5 2.1 3.8
0.71 0.61 0.73
0.23 0.32 0.21
The valence band and core-levels parameters ∆ are shown together with the ground state counts (nd8 , nd9 ) determined by the Groningen school [4,5,12]. Energies are in eV.
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U and ∆ parameters equal to 5.5 eV and the satellite distance ES = 11.5 eV [8]. Although the Cr halides are MH insulators, the presence of a slight p–d hybridization in the final states may reduce their ionic character somewhat, with a consequent electron redistribution in the electronic structure. In this sense, the electronic configuration for the main emission might have been written as d3 L−1 , as in late TMC, but the gap character of CrX3 changes from a (d3 L−1 –d4 ) type (CT regime) to a (d2 –d4 ) type (MH regime) owing to the strong ionicity (large ∆) of these compounds. This in line with the change of the gap character in some early TMC is good (e.g. TiO and Ti2 O3 ) and corresponds to the inversion of 3dn L−1 and 3dn−1 states in the (N − 1)-UPS scheme of levels [3]. Therefore, since it is mainly the splitting of 3d bands which makes CrX3 insulating and determines the electrical nature, Cr halides are rightly described as typical MH insulators. Now we discuss the Cr 2p main emission and satellites shown in Fig. 6. These spectra, observed between 575 and 605 eV, are split by spin–orbit interaction, which is sufficiently large (about 10 eV), compared to the crystal field multiplet splittings (about 4 eV), to completely separate the 2p1/2 and 2p3/2 components. Our satellite distance from the main peak observed at ES ∼ = 10.3 eV in CrCl3 and 11.1 eV in CrBr3 , is lower than that reported by Okusawa [26]. Although the Cr 2p spectra of TMO (Cr2 O3 ) or halides [26], such as MnCl2 or FeBr2 may be described in principle by the CT model, this picture is not too good for CrCl3 and CrBr3 , because the core-level PE is very likely not due to CT processes. The example of Cr halides is more difficult, because there is no simple relation between the
Fig. 6. Photoemission of core-level Cr 2p electrons in CrCl3 and CrBr3 compounds.
Fig. 7. Summary of photoemission spectra of Cr 3p and 3s electrons in CrCl3 and CrBr3 compounds. The Cr2 O3 spectrum is adapted from Uozomi et al. [8].
satellite energy distance and the energy of the optical CT transitions. Therefore an additional mechanism is called for in order to explain the satellites structures, as, for instance, intra-shell electron correlation effects between 3d and 2p electrons [27–29]. This is, for instance, the case of Mn2+ and Fe2+ ions in strongly correlated materials, where the satellite distance from the main emission was found to be more than 20 eV [30,31]. Finally, we have shown in Fig. 7 the Cr 3p and Cr 3s spectra of Cr halides, together with the Cr 3s spectrum of Cr2 O3 by Uozomi et al. [8]. The spectra look rather similar, with satellites which in principle may be discussed with a CM. We see, for example, that the Cr 3s spectrum of Cr2 O3 , in addition to the main peak split by 3d–3s exchange interaction (E ∼ = 4.1 eV), presents two satellites at ES ∼ 12.5 eV and 15 eV and a third = one at ES ∼ = 20 eV (see Fig. 3 in ref. [7]). The Cr 3s spectrum measured by Zimmerman et al. [32] in CrCl3 films shows an exchange splitting E ∼ = 4.2 eV and a very weak satellite, while the Cr2 O3 spectrum reported by Uozomi et al. [8], in addition to the exchange split main peak (E ∼ = 4.1 eV), presents two weak satellites at ES ∼ = 12.5 and 15 eV and a third one at ES ∼ = 20 eV, the first two assigned to a CT process and the third one to a CI effect. Even if the CrX3 spectra look similar to that of Cr2 O3 , we think that the interpretation of the main band and satellites is not the same, as the hybridization strength in Cr2 O3 is much stronger than in CrX3 and the XPS spectra present different characteristics. In fact, it turns out that the satellite properties in CrX3 insulators are more similar to those measured in MnF2 and FeF2 ionic compounds [29–31]. We see, for example, that the Cr 3s main emission has a three or four peak structure instead of two, which cannot be explained by a simple exchange–splitting mechanism, so that we need to consider an additional excitation mechanism, either a CT process or an intra-shell electron correlation, as a possible origin for the observed satellites. Here, we can discard the former mechanism for Cr 3s core levels, since the exchange splitting is closely related to the local magnetic moment of CrX3 insulators, as expected from its dependence
I. Pollini / Journal of Electron Spectroscopy and Related Phenomena 152 (2006) 107–114
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Table 3 CM parameters (eV) for the 2p core level and VB photoemission in TMC Compound
dn
∆
U
T
Teff
Q2p
Reference
MnF2 MnO FeF2 Cr2 O3 CrCl3 CrBr3
d5
10.0 6.5, 10.5a 9.2 5.5 6.5 5.5
3.4 7.0 4.0 5.5 3.3 3.1
1.3 1.9, 2.0a 1.5 3.5 1.6 1.6
2.90 4.2, 4.5a 3.0 7.6 3.6 3.6
4.9 7.5a 5.7 6.5 4.7 4.3
[30] [30] [30] [7]
a
d5 d6 d3 d3 d3
Ref. [33].
on the total Cr 3d spin number S [32]. In the Cr 3p spectrum of CrCl3 the larger satellite structure is separated from the main line by ES ∼ = 8.8 eV, but the analysis is more complicated due to the existence of pronounced multiplet splittings and spin–orbit effects. In Cr 3s spectrum of CrBr3 the main emission is still split by exchange interaction (E ∼ = 4.25 eV) and is followed by a satellite at ES ∼ = 10 eV and a broad band at about 22 eV. The properties of satellites observed in Cr 3s and Cr 3p core levels of CrX3 halides look very similar to the ones observed in MnO and MnF2 compounds. The comparison between the atomic gas phase and the solid spectra in the latter compounds has demonstrated that in these outer core hole states the dominant origin of solid state spectra is found in unscreened intra-atomic multiplet splittings with correlated induced satellites [27–31]. In conclusion, we consider that the main emission in outer core-level Cr 3s spectra is due to unscreened intra-atomic multiplet splittings accompanied by correlation induced satellites. Some of these examples have been summarized in Table 3. As a final consideration, we may add that, at least in the case of relatively ionic compounds, the Cr 3s multiplet structure is interpreted in an intra-atomic way, and that the CT screening does not play a major role in the main and satellite photoemission. However, it must be noted that if the ligand electronegativity decreases, as, for example, in MnCl2 , FeCl2 or Cr2 O3 , CT satellites may become more important and hence the main emission in 3s spectra may lose its purity of spin state [27]. In this case the exchange splitting of the main line no more reflects the 3d magnetic moment in 3dn states. The localized screening may also have an important effect in TM 2p emission, because the hole is more localized in radial extent and the core approximation is more valid. Further, the overlap between the inner 2p orbitals from which emission occurs and the valence shell is much lower and reduces the exchange and correlation effects in the final state. Thus, an inner hole acts to more strongly polarize its surroundings, and the exchange and correlation effects, which produce and stabilize the formed multiplet, are much weaker than for an outer hole. This, however, does not occur in CrCl3 and CrBr3 ionic compounds, where the Cr 2p satellites at high binding energy are not determined by CT processes. 5. Conclusions The electronic structure of Cr compounds looks similar to that of Ti2 O3 , MnF2 or FeF2 materials, located under the boundary separating MH and CT regimes in the phase-diagram. Photoemission spectroscopy has shown that hybridization may play an
important role in the classification scheme of TMC. In particular, for early TMC, the presence of a large p–d hybridization in the final states may reduce their ionic character with a consequent electron redistribution affecting the electronic structure and band gap character. A new estimate of the CM parameters in CrCl3 and CrBr3 has shown that these materials do not have such a large hybridization as early TMO. This is supported by the fact that the p–d CT energy ∆ is larger than the Cr 3d intra-atomic correlation energy U. Our results confirm that Cr halides are MH compounds [3,25], where the insulating nature is mainly due to the Cr 3d on site correlation energy U. We have also found that the final state screening (charge transfer) in Cr 3s core levels does not play a major role in the main emission nor affect the satellite structures in a relevant way. This can explain why the Cr 3s exchange splitting in Cr halides is proportional to the local magnetic moment. As for the Ni halides, classified as CT compounds, we have obtained by VB photoemission reliable estimates of the CM parameters. Effective CM parameters have shown that the correlation energy U is larger than both the charge transfer energy ∆ and the dispersion 3d bandwidth w. In particular, we have shown the connection between the ionic character of the chemical bond in Ni halides and the covalence parameters calculated from the Ni 2p core-level spectra by Sawatzky and co-workers and the internal consistency of the CM parameters. It turns out that the quantity which is strongly altered in going from Cr to Ni compounds in the first TM row is the CT energy, which is consistent with the behavior of the optical gap. References [1] J. Hubbard, Proc. R. Soc. Lond. A 277 (1964) 237; J. Hubbard, Proc. R. Soc. Lond. A 281 (1964) 401. [2] G.A. Sawatzky, J.W. Allen, Phys. Rev. Lett. 24 (1984) 2339. [3] J. Zaanen, G.A. Sawatzky, J.W. Allen, Phys. Rev. Lett. 55 (1985) 418. [4] G. van der Laan, C. Westra, C. Haas, G.A. Sawatzky, Phys. Rev. B 23 (1981) 4369; G. van der Laan, Solid State Commun. 42 (1982) 165. [5] G. van der Laan, J. Zaanen, G.A. Sawatzky, R. Karnatak, J.M. Esteva, Phys. Rev. B 33 (1986) 4253. [6] A. Fujimori, F. Minami, Phys. Rev. B 30 (1984) 957. [7] A.E. Bocquet, T. Mikozawa, K. Morikawa, A. Fujimori, S.R. Barman, K. Maiti, D.D. Sarma, Y. Tokura, M. Onoda, Phys. Rev. B 53 (1996) 1161. [8] T. Uozomi, K. Okada, A. Kotani, R. Zimmerman, P. Steiner, S. Hufner, Y. Tezuka, S. Shin, J. Electr. Spectrosc. Relat. Phenom. 83 (1997) 9. [9] R. Zimmermann, P. Steiner, R. Claessen, F. Reinert, S. Hufner, P. Blaha, P. Dufek, J. Phys: Condens. Matter 11 (1999) 1657. [10] I. Pollini, A. Mosser, J.C. Parlebas, Phys. Rep. 355 (1) (2001) 1–72.
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[11] O. Gunnarsson, K. Schonhammer, Phys. Rev. B 28 (1983) 4315; O. Gunnarsson, K. Schonhammer, Phys. Rev. B 31 (1985) 4815. [12] J. Zaanen, C. Westra, G.A. Sawatzky, Phys Rev. B 33 (1986) 8060. [13] J.C. Phillips, Phys. Rev. Lett. 20 (1968) 550. [14] J.C. Phillips, J.A. Van Vechten, Phys. Rev. Lett. 22 (1969) 705. [15] S.P. Kowalczyk, L. Ley, F.R. McFeely, D.A. Shirley, J. Chem. Phys. 61 (1974) 2850. [16] J. Thomas, I. Pollini, Phys. Rev. B 32 (1985) 2522. [17] P.W. Anderson, Phys. Rev. 124 (1961) 41. [18] C. Horie, Prog. Theor. Phys. 21 (1959) 113. [19] J. Thomas, G. Jezequel, I. Pollini, J. Phys. Condens. Matter 2 (1990) 5439. [20] C.R. Ronda, G.J. Arends, C. Haas, Phys. Rev. B 35 (1987) 4038. [21] S. Hufner, T. Riesterer, Phys. Rev. B 33 (1986) 7267. [22] S. Hufner, F. Hulliger, J. Osterwalder, T. Riesterer, Solid State Commun. 50 (1984) 83.
[23] R. Merlin, Phys. Rev. Lett. 54 (1985) 2727. [24] O. Bengone, M. Alouani, P. Blochl, J. Hugel, Phys. Rev. B 62 (2000) 16392. [25] I. Pollini, Phys. Rev. B 60 (1999) 16170. [26] C. Okusawa, Phys. Stat. Sol. (b) 24 (1984) 673. [27] S.J. Oh, G. Gweon, H. Park, J. G. Phys. Rev. Lett. 68 (1992) 2850. [28] P.S. Bagus, A.J. Freeman, F. Sasaki, Phys. Rev. Lett. 30 (1973) 850. ¨ [29] E.K. Viinikka, Y. Ohrn, Phys. Rev. B 11 (1975) 4168. [30] C.S. Fadley, D.A. Shirley, A.J. Freeman, P.S. Bagus, J.V. Mallow, Phys. Rev. Lett. 23 (1969) 1397. [31] S.P. Kowalczyk, L. Ley, R.A. Pollak, F.R. McFeely, D.A. Shirley, Phys. Rev. B 7 (1973) 4009. [32] R. Zimmermann, P. Steiner, R. Claessen, F. Reinert, S. Hufner, J. Electr. Spectrosc. Relat. Phenom. 96 (1998) 179. [33] K. Okada, A. Kotani, J. Phys. Soc. Jpn. 61 (1992) 4619.
Coulomb correlation energy versus covalence in transition-metal compounds I. Pollini Universit`a degli Studi di Milano, Dipartimento di Fisica, CNR-INFM, Via Celoria 16, 20133 Milano, Italy Received 19 February 2006; received in revised form 7 April 2006; accepted 8 April 2006 Available online 28 April 2006
Abstract We have performed optical and photoemission studies on Mott–Hubbard and charge transfer insulators with formal ionic configurations 3d3 (CrCl3 , CrBr3 ) and 3d8 (NiCl2 , NiBr2 , NiI2 ). The photoemission spectra have been analyzed in terms of a cluster model leading to estimates of the on-site Coulomb repulsion energy, charge transfer energy and hybridization energy parameters. The ionicity parameter fi in Cr and Ni compounds has been calculated by the means of the Phillips–Van Vechten theory: its value is about 0.80 in Cr halides, and it varies from 0.70 in NiI2 to 0.80 in NiCl2 in Ni halides. We have also considered the ionicity scale fiDT of the dielectric theory. The two scales allow a good understanding of the chemical bond character and electron correlation in these materials. © 2006 Elsevier B.V. All rights reserved. Keywords: Photoemission; Electron correlation; Covalence; Mott–Hubbard; Charge transfer; Phillips–Van Vechten
1. Introduction Electron correlation plays an important role in the electronic properties of narrow-band materials. In the studies of electron correlation in solids the Hubbard model (HM) has been widely used because of its great simplicity. That is, the spatial extent of the Coulomb interaction is limited to a single atomic site and is represented by the on-site Coulomb repulsion energy U. The HM was originally applied to the study of transition-metal oxides (TMO), where the O 2p orbitals were not thought directly involved in the transport properties because of the closed shell configuration 2s2 2p6 and only TM 3d orbitals were considered [1]. It was later recognized that in oxides and halides of late TM elements, such as Ni and Cu, oxygen and halide p orbitals are also involved in the charge transport for the presence of holes in the ligand (L) orbitals. Nevertheless, in early TMO, such as Ti, V and Cr oxides, the O 2p band lies well below TM 3d levels and only d-electrons are responsible for the transport properties. This electronic structure is of the Mott–Hubbard (MH) type as opposed to the charge transfer (CT) type occurring in late TMO, according to the theoretical model of Sawatzky and
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co-workers [2–4]. In this model the relative magnitudes of the oxygen (halide) p-to-metal 3d CT energy ∆ and on-site d–d Coulomb energy U are used to classify transition-metal compounds (TMC), which may fall in the MH regime (∆ > U) or CT regime (U > ∆) [2–6]. The electronic structure is described in terms of the parameters ∆, the energy required to transfer an electron from a L orbital to the TM 3d shell, the Coulomb energy U between two 3d electrons on the same site and the hybridization energy T between the p–d orbitals. However, more recently, it was found that in early TMO, owing to the strong p–d hybridization, is U ∼ ∆ rather than ∆ > U [3,7–9]. This has modified the original notion of the MH picture, as it is shown in the U–∆ plot of Fig. 1 [10]. We can see, for example, that Fe2 O3 is predicted to be a CT compound, as CuO or NiO, while MnO or Cr2 O3 , close to the borderline, are considered intermediate compounds. We also see that CrCl3 and CrBr3 are inside the MH region, near Mott compounds such as TiO, Ti2 O3 and MnF2 . It turned out that TMC in general are √ characterized by a strong effective hybridization Teff = nh T (nh being the formal number of holes in TM orbitals), which can no longer be neglected. That is, the resulting covalence between the TM 3d electrons and the L valence band (VB) states promotes a delocalization of d electrons, which reduces the importance of correlation effects. Notwithstanding, the HM remains a valid effective model, if one considers the strongly
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2. Experimental
Fig. 1. Diagram of U vs. ∆ for transition-metal compounds of the first transitionmetal row.
p–d hybridized orbitals (rather than the pure d orbitals) located near the Fermi level as effective orbitals and use a renormalized Coulomb energy Ueff instead of the bare energy U. Photoemission (PE) of valence and core electrons in strongly correlated systems usually exhibits many-body effects, such as the presence of satellites at several eV energies below the main line. Satellites were, for instance, observed in Cu and Ni oxides and halides. In order to interpret the observed satellites in the core-level spectra of TMC, van der Laan et al. [4,5] have identified the CT process from L to TM orbitals as another important electronic mechanism. In their model the main emission and the satellite lines are attributed to |dn+1 L1 (well screened) and |dn (poorly screened) valence shell final states, where L denotes a hole in the ligand shell and n is the number of 3d electrons in the ionic ground state. This interpretation of satellites was subsequently applied to metals and insulators by Gunnarsson and Schonhammer [11] and Zaanen et al. [12]. Finally, by neglecting the widths w and W of the TM 3d and L bands, one obtains the so-called cluster model (CM), which is equivalent to the CT model. Although TMC have been much studied and their overall properties are on the whole understood, still there are interesting points which require new attention. For instance, the present discussion of the electronic properties of Cr and Ni halides is made in connection with the ionicity of the chemical bond as defined by the parameters fi and fiDT . The fi parameter was introduced by Phillips and Van Vechten (PV) long time ago [13,14] and the fiDT parameter of the dielectric theory was then discussed in later articles [15,16]. In particular, we have here calculated the values of these parameters for core-level spectra of Cr halides and VB spectra of Ni halides. One of the aims of this work is to present safe experimental estimates of the CM parameters, which are essential for a meaningful discussion of the electronic properties of TMC within the framework of Hubbard and Anderson impurity Hamiltonians [17].
Stoichiometric crystals of CrCl3 , CrBr3 and NiCl2 , NiBr2 have been grown from the vapor phase by the dynamical transport method between 800 and 850 ◦ C for Cr halides and 600 and 700 ◦ C for Ni halides. Growth of NiI2 single crystals was carried out in two different ways, that is with a Bridgman method and by chemical transport from elements in a sealed ampoule with a thermal gradient of about 750 ◦ C. The low temperature crystal layer structure of CrCl3 (T < 238 K) and CrBr3 (T < 450 K) is like the layer structure BiI3 (space group C3i ). The structure of NiCl2 and NiBr2 layer crystals is that of the CdCl2 crystals and that of NiI2 crystals is of CdI2 type. PE spectra have been performed in ultrahigh vacuum (10−10 mmHg) with a XPS spectrometer ESCALAB MKII (Vacuum Generators), equipped with a monochromatized Al K␣1,2 (1486.6 eV) radiation and a 150 mm electron analyzer. The overall resolution of the spectrometer was about 0.7 eV. Ultraviolet photoelectron spectroscopy (UPS) spectra have been obtained with an hemispherical energy analyzer and a He discharge lamp (HeI, hν = 21.2 eV). Crystals were cleaved in situ in order to get fresh surfaces and to eliminate surface impurities. The impurity content of sample, checked by XPS measurements, has shown no trace of impurity, except for negligeable carbon and oxygen signals. The electrical charging of samples during the PE experiment was monitored by heating them to about 100–120 ◦ C. The UV radiation from the ACO synchrotron (optical line) of the University of Paris was used as a continuum light source for normal incidence reflectance measurements in Cr and Ni crystalline samples at 30 K. 3. Ionicity of chemical bond Since the ionicity coefficient fi plays a crucial role for the chemical properties of TMC, let us briefly recall its definition and physical meaning. In the framework of the PV dielectric theory the fraction of ionic character (fi ) of a chemical bond defines the average separation Eg (Phillips gap) of the valence and conduction bands as the pythagorean sum of an ionic part C and a covalent part Eh 1/2
Eg (Phillips) = (Eh2 + C2 )
.
(1)
The homopolar energy gap Eh scales with the nearest neighbour distance dMX like Eh = a(dMX )−2.5
(a ∼ = 40.5)
(2)
and the ionic energy C can be defined through the Phillips electronegativity by ZB ZA e−Ks R , − (3) C(AB) = b rA rB ∼ 1.5. The atomic radii rA and rB with R = (rA + rB )/2 and b = are defined as half of the bond length of the group IV element belonging to the same row of the periodic table as atoms A and B, and ZA and ZB are the valence numbers of elements A and B. Ks is the Thomas–Fermi screening parameter Ks = (4Kf /πao ),
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where ao is the Bohr radius and Kf is the wave number on the surface of the Fermi sphere in the free electron approximation. The fraction of ionic character of a chemical bond is defined by fi =
C2 C2 = Eg2 Eh2 + C2
(4)
Note that the crystal structure does not appear explicitly anywhere and therefore the model can be extended to include crystals belonging to the NaCl structure or is applicable to compounds other than AN B8−N . In NiX2 (X = Cl, Br and I), for example, the number of electrons involved in the chemical bonds is 16, 8 per bond (neglecting 3d electrons) and the Eg values have been calculated from Eqs. (1)–(4) with the value of the prefactor b = 1.55 ± 0.07 adjusted to fit the experimental data and nearest neighbour distance dMX . In Table 1, we have listed the relevant electronic and chemical parameters for NiX2 , together with the calculated ionicity fi (0.72–0.76) and fiDT (0.79–0.80) parameters, and the d-electron counts nd and nd+1 estimated from 2p-XPS core-level spectra. For the ionicity parameter fiDT of CrX3 (X = Cr, Br) compounds we have followed a different procedure. By considering the energy of plasmons, observed at 22.6 and 20 eV for CrCl3 and CrBr3 in Fig. 2, we have calculated the average energy gap Eg with the Horie’ s relation [18], giving a correction of the free electron formula for the plasmon energy in insulators: (hν)2 ∼ = (hν)2FE + Eg 2 .
(5)
We have found a value of (hν)FE equal to 19.7 and 18.06 eV and of gap Eg = 10.9 and 8.59 eV, in CrCl3 and CrCBr3 , respectively. The average gap Eg is then used for calculating the
fractional ionic character: Eh 2 DT fi = 1 − Eg
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(6)
where the homopolar energy gap Eh is obtained from Eq. (2), ˚ in CrCl3 and 2.55 A ˚ with a metal–halogen distance dMX = 2.33 A in CrBr3 The obtained ionicity parameters fiDT = 0.80 and 0.79 indicate that CrX3 have about 20% covalent character. 4. Experimental results and discussion Let us first discuss the results of photoemission and optical investigations on the Ni compounds. We shall then proceed to the more complex example of Cr compounds. Figs. 3 and 4 show the reflectance and VB-XPS spectra of NiX2 [19]. A main group of peaks (p–d excitons), between 2 and 4 eV, is followed by CT bands (p–d) between 3 and 7 eV, and interband (p–s) structures over 7–9 eV. The optical gap EgR is estimated by considering that the gaps must occur between the energy of the p–d excitons and that of CT transitions. The optical EgR values so obtained are in fine agreement with the photoconductivity gaps EgPh measured by Ronda et al. [20] and are shown in Table 1. The structure in the NiCl2 spectrum between 6 and 8 eV is mainly due to Cl 3p states, the main emission A is assigned to the 3d8 L−1 final states and the weak satellite structure B, between 8 and 12 eV, to the 3d7 hole state. The peak C is attributed to the Cl 3s valence states. The XPS spectrum of NiBr2 is similar and the same interpretation holds. The spectral features from 4 to 8 eV are mainly due to the Br 4p states and the peak A is assigned to the 3d8 L−1 configuration. The satellite B between 8 and 12 eV, is again due to a 3d7 hole state and the peak C to Br 4s
Fig. 2. Low temperature reflectance of CrCl3 and CrBr3 crystals. Charge transfer excitons and transitions (p → d) are followed by interband excitons and transitions (p → s). Energy loss peaks P at 22.6 and 20 eV are due to plasma oscillations.
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Fig. 4. Valence band XPS spectra of NiCl2 and NiBr2 . The predicted first BIS peak and the on-site Coulomb correlation energy U are indicated. Photoemission intensity in arbitrary units.
Fig. 3. Reflectance spectra of Ni halides in the energy range of charge transfer transitions (p → d) and fundamental absorption threshold (p → s) [19].
valence states. The predicted position of the 3d9 states in Fig. 4 is estimated by adding the gap energies EgR to the main emission peak. For example, in the case of NiBr2, with a conduction gap EgPh = 3.5 eV (optical gap is EgR = 3.8 eV), we can predict that the first inverse photoemission peak 3d9 will be located just above the Fermi level. This discussion can then be extended to the VB-UPS spectrum of NiI2 shown in Fig. 5. The peak B observed between 2 and 4.5 eV is mainly due to I 5p states and the peak A to 3d8 L−1 states. The 3d7 hole state observed at 5.5 eV in NiCl2 and at 4.5 eV in NiBr2 is shifted to 6 eV in NiI2 and is observed as a weak shoulder of the peak C. Although this satellite is not clearly observed and its intensity is expected to be low, we consider it a good candidate for this assignment. If this is the case, we can estimate the magnitude of the U parameter to be about 6 eV, as the optical gap value is about 2 eV. This estimate of U in NiI2 may be also more uncertain because of the matrix element effects on the DOS intensity distribution. Nickel halides can be favorably compared to the prototype material NiO [2,21,22]. The analysis of the VB-XPS measurements allows evaluating the ionic coefficients fi (or fiDT ) and to compare them to the ground state d-electron counts nd and nd+1 obtained from Ni 2p core-level spectra [12]. From the combined use of reflectance and VB-XPS spectra of NiO we
have estimated the ∆ and U parameters listed in Table 1 and have compared them to the parameters obtained from the core level (∆c-XPS ) and valence band (∆VB-XPS ) spectra of NiX2 . By taking into account the ground and final state hybridization shifts, we have then estimated a value of 6.0 eV for ∆VB-XPS for NiCl2 , and a value between 5.2 and 5.5 eV for NiBr2 . The position of the first BIS peak due to 3d9 states is still obtained by adding the gap value (EgPh = 3.5 eV) to the main PE peak A. This means that the gap energy in NiX2 corresponds to a 3d8 + 3d8 → 3d8 L−1 + 3d9 transitions, as implied by Merlin [23] and stated by Fujimori and Minami [6] and Zaanen et al. [3]. In conclusion, it
Fig. 5. Valence band UPS spectrum of NiI. The Coulomb correlation energy U and the conduction gap are indicated.
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turns out that the character of the band gap in Ni compounds is mainly related to the parameter ∆ describing the lower energy cost to transfer an electron from ligands to metal ions. Thus, it is the energy separation between the L p band and the TM 3dn+1 levels that governs the electronic gap in NiX2 and NiO materials, which are considered CT compounds. It is well known that PE measures the energy of the final states, which in principle lack one electron with respect to the initial state, so that the system under investigation will screen the created photohole, a many-body process which originates the formation of satellites. The approximated 9.5 and 8.0 eV value of the Ueff in NiCl2 and NiBr2 scales well with the value observed in NiO (about 13 eV). Nevertheless, this is an oversimplification because the energy levels in NiO and NiX2 are hybridized and hybridization tends to affect the energy splittings. By making a proper correction for the hybridization effect Hufner et al. [21,22] have found for the effective parameter Ueff values within 6.0 eV ≤ Ueff ≤ 9.0 eV. Therefore the separation between the 3d7 and 3d9 configurations reflects the size of the Coulomb repulsion parameter Ueff , which represents the correlation energy U plus the hybridization shift. Because the exact magnitude of the energy shift is not known the correlation energy can only be estimated approximately. For NiX2 we deem that 6–8 eV is a fair estimate for Ueff parameter. According to Sawatsky and Allen [2], the CT gap in NiO is 4.3 eV and the Ni d–d Coulomb repulsion Ueff between 7 and 8 eV, leading to a large correlation gap in the Ni 3d band. This value is fairly higher than U = 5.0 eV, recently calculated by Bengone et al. [24]. By considering the relative magnitude of the U and ∆ parameters and the fact that ∆ is related to the ligand electronegativity, the Ni compounds have been classified as CT insulators, with a conductivity gap of p–d type [2–6]. The discussion of satellites in NiCl2 and NiBr2 has been made within the approximation of the configuration interaction (CI) cluster model scheme. For Ni halides the BIS final state position has been extrapolated by considering the reflectance spectra, while for NiO we have considered the measured BIS and UPS spectra [2,21]. In general these spectra show a main peak around 3–4 eV below EF , due to a mixed 3dn L−1 configuration, followed by L p-lines at higher binding energies. Satellite structures, observed around 8–10 eV, are distant from the Ni 3d main line by ES ∼ = 5.1 eV in NiCl2 and 4.2 eV in NiBr2 , respectively (ES = 7.1 eV in NiO). The distance between the main peak and the satellites is 1/2
ES = [(∆ − U)2 + 4(Teff )2 ]
,
(7)
where the Hamiltonian is restricted to the dn and dn+1 L−1 configurations. In the limit of |∆ − U|2Teff , the ES value can be approximated by 2Teff [7,8]. For example, in the late TMO, where the effective hybridization Teff ∼ = 2–4 eV, the satellite structures have been observed at 6–9 eV. In our case we have obtained a value of Teff equal to 2.1 eV in NiBr2 and 2.5 eV in NiCl2 (close to the 3.5 eV value in NiO). As a matter of fact the main Ni 3d band is screened by the electron transferred into the 3d8 L−1 final state configuration, while the unscreened satellite is due to the 3d7 configuration. The trends of the p–d integrals
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Table 1 Electronic and chemical parameters of Ni compounds (eV) MX2
EgR
EgPh
fi
fiDT
∆
U
nd8
nd9
NiCl2 NiBr2 NiI2 NiO
4.6 3.6 2.7 4.0a –4.3
4.7 3.5 1.8 4, 4.3
0.76 0.75 0.72
0.80 0.79
3.6 2.6 1.5 4.6
5.0 5.0 4.5 5.0
0.72 0.63 0.51 0.73
0.27 0.35 0.45 0.21
Optical gaps EgR and photoconductivity gaps EgPh [20] are listed together with ionicity coefficients fi and fiDT . CM parameters (∆, U) and ground state counts nd8 and nd9 have been calculated from 2p spectra [12]. Additional constants for all compounds are Q = 7.0 eV and T = 2 eV (1.75 eV in NiO). a The 4.0–4.3 eV gap of NiO has been directly determined from UPS and BIS spectra [2,21].
and hybridization parameters Teff are primarily governed by the intra-atomic distances, which are determined by the ionic radii of the metal and ligand ions dMX . As the distance diminishes, the overlap between the 3d orbitals and ligand p bands is larger and augments the value of Teff . The nearest neighbour distance dMX , ˚ in NiCl2 and 3.72 A ˚ in NiBr2 , allows obtainwhich is 3.51 A ing the values of the hybridization parameter Teff = 2.5 eV in NiCl2 and 2.1 eV in NiBr2 , respectively. These figures scale well with the values of Teff = 3.5 eV [2,3] and 3.8 eV [9] known for NiO. The valence band ∆ and core level ∆VB-XPS , and the Ueff and Teff parameters obtained in this work have been reported in Tables 1 and 2. Although a good agreement was in general found for the chemical bond parameters, we have noted a large difference between the CT energies measured from core level and VB spectroscopy and for the gap energies. In fact, by considering the CT parameter obtained by the c-XPS spectra, one finds gap values 2–3 eV smaller than the experimental gaps. In summary, our results show that the ionicity coefficients in NiCl2 and NiBr2 are in good correspondence with ground state counts numbers nd8 and nd9 , yet our figures indicate a smaller covalence than expected from the d-electron count parameters. Let us now proceed to the study of Cr halides. We first discuss the electronic properties of CrCl3 and CrBr3 compounds obtained by photoemission in the VB region [10,25]. The VB spectra (not reported here) present a main Cr 3d emission band below 10 eV and weak satellite features separated from the main line by ES = 7.9 and 7.7 eV. The main Cr 3d emission, located around 3 eV, has been assigned to Cr 3d2 (poorly screened) final states. From the XPS and (predicted) BIS peaks we have obtained the position of the Hubbard bands (Cr 3d2 and Cr 3d4 ) and have estimated the on-site Coulomb repulsion parameter U, which is about is 3.0 eV for CrX3 . The nearest example to CrX3 is that of Cr2 O3 , an intermediate compound, which has the Table 2 CM parameters ∆VB-XPS , Ueff and Teff analyzed in this work MX2
Ueff
∆VB-XPS
∆c-XPS
Teff
nd8
nd9
NiCl2 NiBr2 NiO
8 8 10
6.0 5.0–5.5 7.0
3.6 2.6 4.6
2.5 2.1 3.8
0.71 0.61 0.73
0.23 0.32 0.21
The valence band and core-levels parameters ∆ are shown together with the ground state counts (nd8 , nd9 ) determined by the Groningen school [4,5,12]. Energies are in eV.
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U and ∆ parameters equal to 5.5 eV and the satellite distance ES = 11.5 eV [8]. Although the Cr halides are MH insulators, the presence of a slight p–d hybridization in the final states may reduce their ionic character somewhat, with a consequent electron redistribution in the electronic structure. In this sense, the electronic configuration for the main emission might have been written as d3 L−1 , as in late TMC, but the gap character of CrX3 changes from a (d3 L−1 –d4 ) type (CT regime) to a (d2 –d4 ) type (MH regime) owing to the strong ionicity (large ∆) of these compounds. This in line with the change of the gap character in some early TMC is good (e.g. TiO and Ti2 O3 ) and corresponds to the inversion of 3dn L−1 and 3dn−1 states in the (N − 1)-UPS scheme of levels [3]. Therefore, since it is mainly the splitting of 3d bands which makes CrX3 insulating and determines the electrical nature, Cr halides are rightly described as typical MH insulators. Now we discuss the Cr 2p main emission and satellites shown in Fig. 6. These spectra, observed between 575 and 605 eV, are split by spin–orbit interaction, which is sufficiently large (about 10 eV), compared to the crystal field multiplet splittings (about 4 eV), to completely separate the 2p1/2 and 2p3/2 components. Our satellite distance from the main peak observed at ES ∼ = 10.3 eV in CrCl3 and 11.1 eV in CrBr3 , is lower than that reported by Okusawa [26]. Although the Cr 2p spectra of TMO (Cr2 O3 ) or halides [26], such as MnCl2 or FeBr2 may be described in principle by the CT model, this picture is not too good for CrCl3 and CrBr3 , because the core-level PE is very likely not due to CT processes. The example of Cr halides is more difficult, because there is no simple relation between the
Fig. 6. Photoemission of core-level Cr 2p electrons in CrCl3 and CrBr3 compounds.
Fig. 7. Summary of photoemission spectra of Cr 3p and 3s electrons in CrCl3 and CrBr3 compounds. The Cr2 O3 spectrum is adapted from Uozomi et al. [8].
satellite energy distance and the energy of the optical CT transitions. Therefore an additional mechanism is called for in order to explain the satellites structures, as, for instance, intra-shell electron correlation effects between 3d and 2p electrons [27–29]. This is, for instance, the case of Mn2+ and Fe2+ ions in strongly correlated materials, where the satellite distance from the main emission was found to be more than 20 eV [30,31]. Finally, we have shown in Fig. 7 the Cr 3p and Cr 3s spectra of Cr halides, together with the Cr 3s spectrum of Cr2 O3 by Uozomi et al. [8]. The spectra look rather similar, with satellites which in principle may be discussed with a CM. We see, for example, that the Cr 3s spectrum of Cr2 O3 , in addition to the main peak split by 3d–3s exchange interaction (E ∼ = 4.1 eV), presents two satellites at ES ∼ 12.5 eV and 15 eV and a third = one at ES ∼ = 20 eV (see Fig. 3 in ref. [7]). The Cr 3s spectrum measured by Zimmerman et al. [32] in CrCl3 films shows an exchange splitting E ∼ = 4.2 eV and a very weak satellite, while the Cr2 O3 spectrum reported by Uozomi et al. [8], in addition to the exchange split main peak (E ∼ = 4.1 eV), presents two weak satellites at ES ∼ = 12.5 and 15 eV and a third one at ES ∼ = 20 eV, the first two assigned to a CT process and the third one to a CI effect. Even if the CrX3 spectra look similar to that of Cr2 O3 , we think that the interpretation of the main band and satellites is not the same, as the hybridization strength in Cr2 O3 is much stronger than in CrX3 and the XPS spectra present different characteristics. In fact, it turns out that the satellite properties in CrX3 insulators are more similar to those measured in MnF2 and FeF2 ionic compounds [29–31]. We see, for example, that the Cr 3s main emission has a three or four peak structure instead of two, which cannot be explained by a simple exchange–splitting mechanism, so that we need to consider an additional excitation mechanism, either a CT process or an intra-shell electron correlation, as a possible origin for the observed satellites. Here, we can discard the former mechanism for Cr 3s core levels, since the exchange splitting is closely related to the local magnetic moment of CrX3 insulators, as expected from its dependence
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Table 3 CM parameters (eV) for the 2p core level and VB photoemission in TMC Compound
dn
∆
U
T
Teff
Q2p
Reference
MnF2 MnO FeF2 Cr2 O3 CrCl3 CrBr3
d5
10.0 6.5, 10.5a 9.2 5.5 6.5 5.5
3.4 7.0 4.0 5.5 3.3 3.1
1.3 1.9, 2.0a 1.5 3.5 1.6 1.6
2.90 4.2, 4.5a 3.0 7.6 3.6 3.6
4.9 7.5a 5.7 6.5 4.7 4.3
[30] [30] [30] [7]
a
d5 d6 d3 d3 d3
Ref. [33].
on the total Cr 3d spin number S [32]. In the Cr 3p spectrum of CrCl3 the larger satellite structure is separated from the main line by ES ∼ = 8.8 eV, but the analysis is more complicated due to the existence of pronounced multiplet splittings and spin–orbit effects. In Cr 3s spectrum of CrBr3 the main emission is still split by exchange interaction (E ∼ = 4.25 eV) and is followed by a satellite at ES ∼ = 10 eV and a broad band at about 22 eV. The properties of satellites observed in Cr 3s and Cr 3p core levels of CrX3 halides look very similar to the ones observed in MnO and MnF2 compounds. The comparison between the atomic gas phase and the solid spectra in the latter compounds has demonstrated that in these outer core hole states the dominant origin of solid state spectra is found in unscreened intra-atomic multiplet splittings with correlated induced satellites [27–31]. In conclusion, we consider that the main emission in outer core-level Cr 3s spectra is due to unscreened intra-atomic multiplet splittings accompanied by correlation induced satellites. Some of these examples have been summarized in Table 3. As a final consideration, we may add that, at least in the case of relatively ionic compounds, the Cr 3s multiplet structure is interpreted in an intra-atomic way, and that the CT screening does not play a major role in the main and satellite photoemission. However, it must be noted that if the ligand electronegativity decreases, as, for example, in MnCl2 , FeCl2 or Cr2 O3 , CT satellites may become more important and hence the main emission in 3s spectra may lose its purity of spin state [27]. In this case the exchange splitting of the main line no more reflects the 3d magnetic moment in 3dn states. The localized screening may also have an important effect in TM 2p emission, because the hole is more localized in radial extent and the core approximation is more valid. Further, the overlap between the inner 2p orbitals from which emission occurs and the valence shell is much lower and reduces the exchange and correlation effects in the final state. Thus, an inner hole acts to more strongly polarize its surroundings, and the exchange and correlation effects, which produce and stabilize the formed multiplet, are much weaker than for an outer hole. This, however, does not occur in CrCl3 and CrBr3 ionic compounds, where the Cr 2p satellites at high binding energy are not determined by CT processes. 5. Conclusions The electronic structure of Cr compounds looks similar to that of Ti2 O3 , MnF2 or FeF2 materials, located under the boundary separating MH and CT regimes in the phase-diagram. Photoemission spectroscopy has shown that hybridization may play an
important role in the classification scheme of TMC. In particular, for early TMC, the presence of a large p–d hybridization in the final states may reduce their ionic character with a consequent electron redistribution affecting the electronic structure and band gap character. A new estimate of the CM parameters in CrCl3 and CrBr3 has shown that these materials do not have such a large hybridization as early TMO. This is supported by the fact that the p–d CT energy ∆ is larger than the Cr 3d intra-atomic correlation energy U. Our results confirm that Cr halides are MH compounds [3,25], where the insulating nature is mainly due to the Cr 3d on site correlation energy U. We have also found that the final state screening (charge transfer) in Cr 3s core levels does not play a major role in the main emission nor affect the satellite structures in a relevant way. This can explain why the Cr 3s exchange splitting in Cr halides is proportional to the local magnetic moment. As for the Ni halides, classified as CT compounds, we have obtained by VB photoemission reliable estimates of the CM parameters. Effective CM parameters have shown that the correlation energy U is larger than both the charge transfer energy ∆ and the dispersion 3d bandwidth w. In particular, we have shown the connection between the ionic character of the chemical bond in Ni halides and the covalence parameters calculated from the Ni 2p core-level spectra by Sawatzky and co-workers and the internal consistency of the CM parameters. It turns out that the quantity which is strongly altered in going from Cr to Ni compounds in the first TM row is the CT energy, which is consistent with the behavior of the optical gap. References [1] J. Hubbard, Proc. R. Soc. Lond. A 277 (1964) 237; J. Hubbard, Proc. R. Soc. Lond. A 281 (1964) 401. [2] G.A. Sawatzky, J.W. Allen, Phys. Rev. Lett. 24 (1984) 2339. [3] J. Zaanen, G.A. Sawatzky, J.W. Allen, Phys. Rev. Lett. 55 (1985) 418. [4] G. van der Laan, C. Westra, C. Haas, G.A. Sawatzky, Phys. Rev. B 23 (1981) 4369; G. van der Laan, Solid State Commun. 42 (1982) 165. [5] G. van der Laan, J. Zaanen, G.A. Sawatzky, R. Karnatak, J.M. Esteva, Phys. Rev. B 33 (1986) 4253. [6] A. Fujimori, F. Minami, Phys. Rev. B 30 (1984) 957. [7] A.E. Bocquet, T. Mikozawa, K. Morikawa, A. Fujimori, S.R. Barman, K. Maiti, D.D. Sarma, Y. Tokura, M. Onoda, Phys. Rev. B 53 (1996) 1161. [8] T. Uozomi, K. Okada, A. Kotani, R. Zimmerman, P. Steiner, S. Hufner, Y. Tezuka, S. Shin, J. Electr. Spectrosc. Relat. Phenom. 83 (1997) 9. [9] R. Zimmermann, P. Steiner, R. Claessen, F. Reinert, S. Hufner, P. Blaha, P. Dufek, J. Phys: Condens. Matter 11 (1999) 1657. [10] I. Pollini, A. Mosser, J.C. Parlebas, Phys. Rep. 355 (1) (2001) 1–72.
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