Photoemission spectroscopy of diluted Mn in and on solids

Journal of Electron Spectroscopy and Related Phenomena 136 (2004) 21–30

Photoemission spectroscopy of diluted Mn in and on solids T. Mizokawa a,b,∗ , A. Fujimori a,c , J. Okabayashi d , O. Rader e a

Department of Complexity Science and Engineering, University of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo 113-0033, Japan b PRESTO, Japan Science and Technology Agency, 4-1-8 Honcho Kawaguchi, Saitama, Japan c Department of Physics, University of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo 113-0033, Japan d Department of Applied Chemistry, University of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo 113-8656, Japan e BESSY, Albert-Einstein-Str. 15, D-12489 Berlin, Germany

Abstract We have studied the electronic structure of the Mn-based diluted magnetic semiconductors and the ordered Mn surface alloys using photoemission spectroscopy and configuration interaction (CI) calculation. As for the Mn-based diluted magnetic semiconductors, the electronic-structure parameters obtained from the CI analysis show systematic variation with expected chemical trends. The CI picture gives a systematic description of the d–d absorption spectra, the exchange constants between the 3d spins and host band states, and the donor and acceptor ionization energies of the diluted magnetic semiconductors. The photoemission spectra of the ordered surface alloys CuMn/Cu(1 0 0) and NiMn/Ni(1 0 0) show correlation satellites similar to the impurity Mn atom in solids. It is shown that the CI analysis can describe the correlation satellites driven by the reduced dimensionality in the ordered surface alloy systems. © 2004 Elsevier B.V. All rights reserved. PACS: 79.60.-i; 71.10.-w; 71.20.-b; 73.20.-r Keywords: Photoemission spectroscopy; Configuration interaction calculation; Diluted magnetic semiconductors; Ordered surface alloy

1. Introduction The configuration interaction (CI) approach using clustertype models is a powerful tool to describe the electronic structure of diluted transition metals in solids where the d–d Coulomb interaction and the d-host hybridization are competing. In the last decades, photoemission spectroscopy and subsequent CI analysis have successfully been applied to various diluted transition-metal systems such as Mn-based diluted magnetic semiconductors and ultrathin films of ordered Mn surface alloys. These diluted Mn systems show correlation satellites in the photoemission spectra originating from the Coulomb interaction between the atomic-like d electrons. The correlation satellites can be explained by the CI calculation on the cluster-type model where the d–d Coulomb interaction and the d-host hybridization are parameterized. The parameter values can be determined by the CI analysis of the photoemission spectra and the ground-state properties can be predicted by using ∗ Corresponding author. Tel.: +81-4-7136-3922; fax: +81-4-7136-3923. E-mail address: [email protected] (T. Mizokawa).

0368-2048/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.elspec.2004.02.129

the electronic-structure parameters obtained from the CI analysis. 3d electrons in the II–VI and III–V diluted magnetic semiconductors such as Cd1−x Mnx Te and Ga1−x Mnx As tend to be localized and provide interesting magneto-optical properties [1–3]. The strong Coulomb interaction between the 3d electrons is responsible for the multiplet structures observed in optical absorption spectra arising from intra-atomic d–d transitions. The multiplet structures in the d–d transition have traditionally been analyzed by ligand-field theory [4,5] where the intra-atomic 3d–3d Coulomb interaction is fully taken into account. Donor and acceptor ionization energies obtained from transport and charge-transfer optical absorption experiments also show variations suggestive of multiplet effects [1,6]. On the other hand, the hybridization between the transition-metal 3d and the host valence band gives rise to interaction between the localized 3d spins and the carriers in the host valence band, which manifests itself in the magneto-optical effect observed in the II–VI diluted magnetic semiconductors [2]. When the magnetic moments of the transition-metal impurities are aligned in a magnetic field, the valence band is split through the exchange interaction with the transition-metal 3d electrons. The band

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T. Mizokawa et al. / Journal of Electron Spectroscopy and Related Phenomena 136 (2004) 21–30

splitting has been observed in free exciton spectroscopy and the p–d exchange coupling between the 3d electrons and the Bloch electrons at the host valence band maximum has been evaluated experimentally [2]. If the diluted magnetic semiconductors have enough hole carriers, the 3d spins may be ferromagnetically aligned because of the strong p–d exchange interaction. Actually, p-type Ga1−x Mnx As with enough hole concentration shows ferromagnetism at low temperature [3]. The transition-metal impurities substituted for the cations in the II–VI and III–V semiconductors are tetrahedrally coordinated by the anions and can be described by the MX4 cluster model (M is a transition-metal ion and X is an anion), where the 3d–3d Coulomb interaction and the 3d-anion hybridization are taken into account and their strengths are treated as adjustable parameters. Photoemission studies on II–VI diluted magnetic semiconductors [7] such as Cd1−x Mnx Te have shown that the hybridization is quite substantial as predicted by local density approximation (LDA) calculations whereas there are also the correlation satellite features which cannot be explained by one-electron theory. CI calculations using the cluster model can explain the photoemission spectra [8] by adjusting the model parameters. An ultrathin film of ordered surface alloy c(2 × 2) CuMn/Cu(1 0 0) can also be viewed as a diluted Mn system. Since Cu and Mn atoms form a checkerboard structure, the Mn atom has only Cu nearest neighbors just like a Mn impurity in Cu. This manifests itself in the core-level and valence-band photoemission spectra as the correlation satellites [9]. CI calculation has successfully been applied to CuMn/Cu(1 0 0) and has shown that the ordered Mn atom behaves like a Mn impurity in Cu but with an even more intense satellite. This suggests that the 3d electrons of Mn N+1 electron states

have atomic-like character and that the magnetic moment as well as the exchange interaction can be enhanced in the ordered surface alloy compared to Mn metal. In this article, we present a set of photoemission spectra of the Mn-based diluted magnetic semiconductors and the ordered Mn surface alloys as well as results of CI analysis for the photoemission spectra. The electronic-structure parameters obtained from the CI analysis show systematic variation with expected chemical trends. The organization of this article is as follows. A brief description of the CI picture is given in Section 2. In Section 3, we present the photoemission spectra of the II–VI and III–V diluted magnetic semiconductors and discuss how to interpret the spectra based on the CI picture. The d–d absorption spectra are also analyzed using the CI calculations in Section 4. In Sections 5 and 6, based on the CI picture, we discuss the exchange constants between the 3d spins and the host band states and the donor and acceptor ionization energies of the 3d transition-metal impurities. In Section 7, we present the photoemission spectra of the ordered surface alloy CuMn/Cu(1 0 0). It is shown that the CI analysis can describe the correlation satellites driven by the reduced dimensionality. Finally, concluding remarks are given in Section 8.

2. Configuration interaction approach In the CI framework, the wave functions of the ground state and charge-conserving excited states, which we call N-electron states, are given by linear combinations of the dn , dn+1 L,. . . , d 10 L10−n configurations. Here, L denotes a hole in a ligand p orbital for the cluster model or a hole in the valence band for the Anderson impurity model. The ligand-to-3d charge-transfer energy is defined by

N-electron states

N-1 electron states

dn+2L dn-1 ∆+U

µ

EG

dn+1L

conduction band ∆eff ∆

dn+1 acceptor level donor level

U-∆

dn ED EA

d-d transitions inverse photoemission

ground state

dnL

donor level

photoemission

valence band dnL U-∆ dn-1

EG: Band gap EA: Acceptor ionization energy ED: Donor ionization energy

N-1 electron states

Fig. 1. Schematic energy-level diagrams for a dn transition-metal impurity in a II–VI semiconductor, including hybridization between the 3d and host valence band. [10] For clarity, higher-order charge-transfer states (e.g. dn+2 L2 in the N-electron states) are not shown.

T. Mizokawa et al. / Journal of Electron Spectroscopy and Related Phenomena 136 (2004) 21–30

3. Photoemission and inverse-photoemission spectra The valence-band photoemission spectra of transitionmetal impurities substituted for the cations can be explained by CI calculations on a tetrahedral MY4 cluster model (M = transition metal, Y =O, S, Se, Te, or As) [8,12]. The one-electron transfer integrals between the 3d orbitals and the ligand orbitals are expressed in terms of Slater-Koster parameters (pdσ) and (pdπ) [13]: Tt2 ≡<
t2 |H|Lt2 >= √ 4/3(pdσ)2 + 8/9(pdπ)2 and Te ≡< e|H|Le >= 2 6/3(pdπ), where Lt2 and Le are ligand orbitals with T2 and E symmetry of the Td point group, respectively [10]. Here, it should be noted that, in order to reproduce the valence-band photoemission spectra and the d–d optical absorption spectra using the same and U, the transfer integrals for the d–d optical absorption spectra had to be taken larger than those for the photoemission spectra

∆ = 6.5 eV Zn1-xMnxO ∆ = 3.0 eV Intensity

≡ E(dn+1 L) − E(dn ) and the 3d–3d Coulomb interaction energy by U ≡ E(dn−1 ) + E(dn+1 ) − 2E(dn ), where     E(dn Lm ) is the center of gravity of the dn Lm multiplet. These definitions make clear the chemical trends of the parameters [10,11]. It is also possible to define the charge-transfer energy eff and the Coulomb interaction energy Ueff with respect to the lowest term of each multiplet. In the present model, the multiplet splittings are given in terms of Racah parameters B and C, which are usually fixed to the free-ion values [5]. The energy of the ground state E0 (N) as well as those of the excited dn multiplet terms are obtained by diagonalizing the Hamiltonian in the N-electron subspace as shown in the middle panel of Fig. 1. In the right panel of Fig. 1, we show the energy levels of the (N − 1)-electron states, namely, the final states of photoemission which are given by linear combinations of dn−1 , dn L, dn+1 L2 , . . . . The lowest energy level of the (N − 1)-electron system is the first ionization level of the N-electron system. This is the first donor level (A0 → A+ ) for a neutral impurity state (A0 ) and corresponds to the transition A− → A0 for a negatively-charged impurity state (A− ), respectively. The ionization energy is given by E0 (N − 1) − E0 (N) + c , where c is the energy of the conduction band minimum. The energy levels for the (N + 1)-electron states are shown in the left panel of Fig. 1. The lowest energy level of the (N +1)-electron system is the affinity level of the N-electron system or the first acceptor level A0 → A− for the neutral ground state (A0 ). This level corresponds to the second acceptor level (A− → A2− ) if the ground state is negatively charged (A− ). The ionization energy is given by E0 (N +1)−E0 (N)−v , where v is the energy of the valence band maximum. If we replot the electron removal energies E(N −1)−E0 (N) downward and combine it with the electron addition energies E(N + 1) − E0 (N) as in the left panel of Fig. 1, we can effectively map the many-electron energies onto the one-electron energy-level scheme.

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Zn1-xMnxS ∆ = 2.0 eV Zn1-xMnxSe ∆ = 1.5 eV Zn1-xMnxTe ∆ = 1.5 eV

Ga1-xMnxAs

10 5 0 Binding Energy relative to VBM (eV) Fig. 2. Mn 3d-derived photoemission spectra of Zn1−x Mnx Y (Y = O, S, Se, Te) and Ga1−x Mnx As. The solid curves show the CI calculations using the MnY4 cluster model [10]. Experimental results are taken from [7,16,17].

[14], indicating that the transfer integrals for the N-electron system are larger than those for the (N − 1)-electron system. Gunnarsson and Jepsen [15] have shown that the transfer integrals depend on the local electronic configuration significantly. Following their results, we have assumed that the transfer integrals between dn−1 and dn L are smaller by ∼ 20% and those between dn+1 and dn+2 L larger by ∼ 20% than those between dn and dn+1 L, and so on. Values for dn -dn+1 L are presented in this article. In Fig. 2, we compare the Mn 3d-derived photoemission spectra of Zn1−x Mnx Y (Y = O, S, Se, and Te) [7,17] and Ga1−x Mnx As [16] with those calculated using the CI cluster model [10]. The Mn 3d component of the photoemission spectra can be extracted using the Mn 3p → 3d resonant photoemission method. The difference spectrum between the off-resonance and on-resonance spectra provides the Mn 3d component of the photoemission spectrum. The three-peak structure in the Mn 3d spectra of Zn1−x Mnx Y (Y=O, S, Se, and Te) are well reproduced by the CI calculations. The obtained parameter sets are listed in Table 1. In going from O to S to Se to Te, the charge-transfer energy decreases as the electronegativity of the ligand decreases. The transfer integral (pdσ) also decreases as the distance between the transition-metal cation and the ligand anions Table 1 Parameters used to calculate the valence-band photoemission spectra for Mn2+ impurities in ZnO, ZnS, ZnSe, ZnTe, and GaAs (in eV)

Zn1−x Mnx O (A0 :Mn2+ ) Zn1−x Mnx S (A0 :Mn2+ ) Zn1−x Mnx Se (A0 :Mn2+ ) Zn1−x Mnx Te (A0 :Mn2+ ) Ga1−x Mnx As (A− :Mn2+ )



U

(pdσ)

6.5 3.0 2.5 2.0 1.5

5.0 4.0 4.0 4.0 3.5

−1.4 −1.3 −1.2 −1.1 −1.1

T. Mizokawa et al. / Journal of Electron Spectroscopy and Related Phenomena 136 (2004) 21–30

increases [13]. In going from Zn1−x Mnx S to Zn1−x Mnx Te, the intensity within ∼ 2.5 eV of the valence-band maximum relative to the main peak at ∼ 3.4 eV decreases and that of the satellite structure at 5–9 eV increases, which is well reproduced by the present parameter sets. This is because the energy-level ordering of the ionic (d5 or d4 ) and charge-transfer (d6 L or d5 L) configurations is inverted between the N-electron and the (N − 1)-electron states and, consequently, the changes in and (pdσ) as functions of the ligand atoms affect the photoemission spectra constructively [10]. In addition to the Mn-based compounds, the photoemission spectrum of Cd1−x Fex Se was successfully analyzed by the cluster-model analysis [18]. The Mn 3d spectrum of Ga1−x Mnx As has a three-peak structure similar to that observed in Zn1−x Mnx Y. This result implies that the Mn ions in Ga1−x Mnx As are essentially Mn2+ and are negatively ionized, which is consistent with the large magnetization of ferromagnetic Ga1−x Mnx As [3]. Actually, as shown in Fig. 2, the Mn 3d spectrum is well reproduced by the CI calculation of the cluster model assuming the Mn2+ (A− ) ground state. The obtained parameter set is shown in Table 1 and is compared with those for Zn1−x Mnx Y. One can see that the charge-transfer energy of Ga1−x Mnx As is close to that of Zn1−x Mnx Te. This result is reasonable because As and Te have almost the same electronegativity. Cd1−x Mnx Te was also studied using inverse-photoemission spectroscopy [19]. In Fig. 3, we plot the inverse photoemission spectrum (the electron addition spectrum) in combination with the photoemission spectrum (the electron removal spectrum) and compare the experimental results with the CI cluster-model calculation. The Mn 3d-derived structure ∼ 4.8 eV above the valence-band maximum is reproduced in the CI calculation because the intra-atomic 3d–3d Coulomb interaction is taken into account in a proper way.

Zn1-xMnxO ∆ = 6.5 eV satellite

Intensity

24

Zn1-xMnxS ∆ = 2.5 eV

satellite

MnO ∆ = 6.0 eV

20

satellite

10

0

Relative Binding Energy (eV)

Fig. 4. Mn 2p core-level photoemission spectra of Zn1−x Mnx O, Zn1−x Mnx S, and MnO. The CI calculations using the MnY4 cluster model are shown by the solid curves.

In Fig. 4, the Mn 2p core level photoemission spectra of Zn1−x Mnx O and Zn1−x Mnx S are compared with the result of the CI calculation. The satellite structures in the Mn 2p spectra are also well reproduced using the parameter set similar to that obtained from the valence-band photoemission spectra.

4. d–d Optical absorption spectra Rich multiplet structures due to d–d transitions have been observed in the optical spectra of the II–VI semiconductors doped with the 3d transition-metal impurities because they have relatively large band gaps. In Fig. 5, the d–d optical absorption spectra [21] are compared with CI cluster-model calculations [10] for various transition-metal impurities in the ZnS host. The obtained parameters are listed in Table 2. The value of thus obtained monotonically decreases in going from lighter to heavier transition-metal atoms as expected from chemical trends whereas eff exhibits non-monotonic behavior due to the multiplet effects [11]. The calculated d–d transition energies are generally in good Table 2 Parameters used to calculate the d–d optical absorption spectra for 3d transition-metal impurities in ZnS and ZnSe (in eV) ZnS

V2+

Fig. 3. Mn 3d-derived photoemission [7] and inverse-photoemission spectra [19] for Cd1−x Mnx Te compared with those obtained by the CI cluster model.

Cr2+ Mn2+ Fe2+ Co2+ Ni2+

ZnSe

B

C

U

( eff )

(pdσ)

( eff )

(pdσ)

0.095 0.103 0.119 0.131 0.138 0.135

0.354 0.425 0.412 0.484 0.541 0.600

3.0 3.5 4.0 4.5 5.0 5.5

4.5(3.6) 4.0(1.9) 3.0(5.2) 2.0(3.3) 1.5(2.9) 1.0(2.3)

−1.3 −1.2 −1.3 −1.24 −1.1 −1.2

4.0(3.1) 3.5(1.4) 2.5(4.7) 1.5(2.8) 1.0(2.4) 0.5(1.8)

−1.2 −1.1 −1.2 −1.05 −1.0 −1.1

T. Mizokawa et al. / Journal of Electron Spectroscopy and Related Phenomena 136 (2004) 21–30

25

Fig. 5. Energy levels for various transition-metal impurities (from V2+ to Ni2+ ) in ZnS calculated using the CI cluster model [10] compared with experimental d–d optical absorption spectra.

agreement with the experimental results. Here, we compare the calculated multiplet structures with the energies of absorption maxima in the spectra which approximately correspond to the purely electronic (Frank-Condon) transition energies. For Zn1−x Mnx S, the ground state of the Mn2+ impurity is 6 A1 in the tetrahedral coordination geometry. The energy levels for the lowest excited terms 4 T1 , 4 T2 , 4 T , and 4 E, which originate from the 4 G term of the free 1 d5 ion, are in good agreement with experiment. Agreement is less satisfactory for higher terms 4 E, 4 T1 and 4 T2 , which are derived from the 4 D and 4 P terms, because the energy levels of the 4 D and 4 P of the free d5 ion already cannot be reproduced well within the Racah parameter scheme. Agreement for the 4 T1 level of Co2+ and the 3 T1 level of Cr2+ is also poor because the energy level of 4 P for the free d7 ion and that of 3 P for the free d4 ion cannot be reproduced within the Racah parameter scheme.

5. Exchange constants In the II–VI and III–V semiconductors, the conduction band is mainly formed by the s orbitals of the cation and the valence band by the p orbitals of the anion. The exchange interaction between the s electrons in the conduction band and the d electrons of the transition-metal impurities is derived from the direct exchange. On the other hand, the exchange interaction between the p electrons in the valence band and the d electrons is mainly derived from the p–d hybridization [2,22,23]. Especially at the Γ point, the top of the valence

band is purely constructed from the anion p orbitals which can only hybridize with the d orbitals of t2 symmetry. When the magnetic moments of the transition-metal impurities are aligned in a magnetic field, the valence and conduction bands are split through the exchange interaction with the 3d electrons. By measuring the band splitting, the exchange constant Nβ between the 3d electrons and the Bloch electrons at the valence band maximum has been obtained [2]. Let us consider an Anderson impurity model in which the 3d–3d Coulomb interaction is taken into account in terms of Kanamori parameters, u, u , j, and j  [24]. The Anderson impurity Hamiltonian is given by: [25] H = Hp + Hd + Hpd ,  p Hp = k p + k,σ pk,σ ,

(1) (2)

k,σ

Hd = d

 m,σ 

+u

+ dm,σ dm,σ + u



m=m

×



m>m ,σ

×



m=m

×



m=m

 m

+ + dm,↑ dm,↑ dm,↓ dm,↓

+ + dm,↑ dm,↑ dm  ,↓ dm ,↓

+ (u − j  )

+ +  dm,σ dm,σ dm  ,σ dm ,σ + j

+ + dm,↑ dm ,↑ dm,↓ dm ,↓ + j + + dm,↑ dm ,↑ dm  ,↓ dm,↓ ,

(3)

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T. Mizokawa et al. / Journal of Electron Spectroscopy and Related Phenomena 136 (2004) 21–30 Zn1-xCoxS

Zn1-xCrxS

t2 t2 e e δeff

δeff

-δeff + u + 2j

Nβ = -16/S[1/3(pdσ) - 2√3/9(pdπ)]2[1/δeff + 1/(-δeff + u + 2j)]

Zn1-xFexS t2

δeff + 4j

e δeff

-δeff + u + 3j

Nβ = -16/S[1/3(pdσ) - 2√3/9(pdπ)]2[1/δeff + 1/(-δeff + u + 3j)] δeff + 6j

Zn1-xMnxS

-δeff + u' - j

t2 e δeff

-δeff + u + 4j

Nβ = -16/S[1/3(pdσ) - 2√3/9(pdπ)]2[1/δeff + 1/(-δeff + u + 4j)]

Fig. 6. Configurations which contribute to the p–d exchange interaction in the second order of the hybridization term for Zn1−x Cox S, Zn1−x Fex S, Zn1−x Mnx S, and Zn1−x Crx S. The configurations for the ground state (dn ), affinity states (dn+1 ) and ionization states (dn−1 ) are shown on the left, middle and right, respectively, below which the energy difference between the ground state and each affinity or ionization state is shown.

Hpd =

 k,m,σ

+ Vk,m dm,σ pk,σ + H.c. pd

(4)

Eq. (2) represents the Hamiltonian for the anion p electrons of the host semiconductor, where k labels the wave vector in the first Brillouin zone. Eq. (3) describes the Hamiltonian for the 3d electrons of the transition-metal impurity, in which σ and m are indices for the spin and orbital, respectively. We have to assume the relationships u = u − 2j and j  = j in order to retain the rotational invariance in real space of the Coulomb term. The relationship between Racah and Kanamori parameters are given by u = A+4B + 3C and j = 5/2B + C. Hybridization between the 3d orbitals and the host band states is expressed by Eq. (4). The multiplet-averaged 3d–3d Coulomb interaction U is given by u − 20/9j. The charge-transfer energy can be related to U through = d − p + nU, where p is the center of the host valence band. Because of the p–d hybridization term, a hole created at the valence band maximum can hybridize with the 3d orbitals. In the CI picture, the lowest dn L0 configuration, where L0 denotes a hole at the valence band maximum, hybridizes with the dn−1 and dn+1 L20 configurations. The energy difference between the lowest terms of dn L0 and dn+1 L20 is given by δeff ≡ eff − WV /2, where WV is the width of the host valence band contributing to the hybridization term and is fixed at 2 eV. This can be justified because a tight-binding model calculation has shown that the upper 2 eV of the valence band mainly contributes to the hybridization term although the total width of the valence band for ZnS and ZnSe is 4–5 eV [10]. The lowest term of dn−1 is by Ueff − δeff higher than that of dn L0 . The

Bloch state at the valence band maximum located at the Γ point hybridizes only with the 3d orbitals with t2 symmetry. pd Its transfer integral V0,t2 is given by 1/3(pdσ) − 2/9(pdπ). Using the electronic-structure parameters , U, (pdσ), and (pdπ) obtained from the CI calculation for the d–d optical absorption and photoemission spectra, we can calculate Nβ’s for the 3d transition-metal impurities in the second order of perturbation with respect to the hybridization term [22,23]. Configurations which contribute to the p–d exchange interaction are summarized in Fig. 6 for the Mn2+ , Fe2+ , Co2+ , and Cr2+ impurities. For the Mn2+ , Fe2+ , and Co2+ impurities, where the t2 orbitals are half filled, only those ligand holes whose spins are antiparallel to that of the transition-metal impurity can be transferred into the unoccupied t2 orbitals in the intermediate state. The configurations of the allowed intermediate states are shown in Fig. 6. As a result, the p–d exchange is antiferromagnetic in the Mn2+ , Fe2+ , and Co2+ impurities. The exchange constant Nβ is given by: 16 Nβ = − S



1 1 + −δeff + Ueff δeff



2

2 1 (pdσ) − (pdπ) 3 9

(5) for the Mn2+ , Fe2+ , and Co2+ impurities [22,23]. Ueff is u + 4j, u + 3j, and u + 2j and the magnitude of the local spin S is 5/2, 2 and 3/2 for the Mn2+ , Fe2+ and Co2+ impurities, respectively. The Nβ values for Cd1−x Mnx Y (Y = S, Se, and Te) evaluated using the above parameters are −1.1,

T. Mizokawa et al. / Journal of Electron Spectroscopy and Related Phenomena 136 (2004) 21–30

Fig. 7. Exchange constant for M 2+ impurities in ZnSe compared with the experimental results [26,27].

−1.0 −0.9,1 in qualitative agreement with the experimental results, −1.8, −1.11, and −0.88 for Y = S, Se, and Te, respectively [2]. The Nβ values for the Mn2+ , Fe2+ , and Co2+ impurities in ZnSe (see Fig. 7) are calculated to be −1.0, −1.5, and −2.0 eV, respectively. These values are also in agreement with the experimental values of −1.31, −1.74, and −2.2 eV for the Mn2+ , Fe2+ , and Co2+ impurities in ZnSe, respectively [26]. The exchange constant Nβ for Cr2+ in ZnSe is positive, namely, the Cr2+ spin couples ferromagnetically with the spin of the hole in the host valence band [27].For the Cr2+ impurity, a ligand hole whose spin is parallel as well as antiparallel to the Cr2+ spincan be transferred to the unoccupied t2 orbitals. As a result, ferromagnetic and antiferromagnetic terms coexist in the p–d exchange interaction. The configurations which contribute to the p–d exchange in the Cr2+ impurity are shown in Fig. 6. Since the Cr2+ impurity is expected to have a Jahn-Teller distortion, the evaluation of Nβ is complicated. The exchange constant is sensitive to the populations of the unoccupied xy, yz, and zx orbitals in the t2 subshell. Here, we have assumed that the populations of the CrY4 tetrahedra compressed along the x-, yand z-directions are equal, namely, the populations of the Cr sites with the unoccupied xy, yz, and zx orbitals are equal [27,28]. It has also been assumed that the magnitude of the Jahn-Teller splitting is negligibly small compared with δeff to evaluate the exchange constant. Nβ’s for the Cr2+ impurities in ZnS and ZnSe thus calculated are −0.2 eV and +1.2 eV, respectively. The positive Nβ value for the Cr2+ impurity in ZnSe is in agreement with the experimental value +0.85 eV [27]. Nβ for the Cr2+ impurity in ZnS, however, becomes negative because δeff of Cr2+ in ZnS is large compared with that of Cr2+ in ZnSe, which disagrees with the experimental result [29]. Since the exchange constant is given by the difference between the ferromagnetic and antiferromagnetic contributions and the ferromagnetic term is proportional to 1 The Nβ values presented here are slightly different from the values reported previously [25] because the slightly different B, C, and (pdσ) values have been used. However, the difference is small and is not essential.

27

1/δeff , the sign of Nβ is sensitive to δeff . The sign of the exchange constant is also sensitive to the populations of the xy, yz, and zx orbitals. In other words, it is possible to control the sign of the exchange constant by applying a uniaxial stress. If all the CrY4 tetrahedra are compressed along the z-direction, namely, the xy orbital is unoccupied at all the Cr sites, Nβ of Cr2+ in ZnS is predicted to be positive. V2+ and Ni2+ impurities, where the t2 orbitals are partially filled, should also be accompanied by the Jahn-Teller distortion. Under the same assumption that the populations of the tetrahedra elongated along the x-, y- and z-directions are equal, the p–d exchange constants can be evaluated. The V2+ impurity is expected to show the same behavior as the Cr2+ impurity because the t2 subshell is less than half-filled. However, Nβ for V2+ in ZnSe is evaluated to be negative and is ∼−0.3 eV. This is because δeff of V2+ is much larger than that of Cr2+ in ZnSe. For Ti2+ , where the t2 orbitals are empty, ligand holes can be transferred into the t2 orbitals irrespective of their spin direction. The configuration obtained by the transfer of the ligand hole whose spin is parallel to the Ti2+ spin is stabilized by the intra-atomic exchange interaction j. Therefore, the p–d exchange constant for Ti2+ becomes positive and is evaluated to be ∼ +1.1 eV. As for the Mn2+ impurity in GaAs, Nβ is predicted to be antiferromagnetic, −1.0 eV [20], which is as large as the Nβ of Cd1−x Mnx Te. This can be understood because the electronic-structure parameters for Mn2+ in GaAs are similar to those for Mn2+ in CdTe. The negative Nβ is consistent with the magnetic circular dichroism measurement of Ga1−x Mnx As (x = 0.074) [30] although the magnitude of Nβ is small compared with the estimation from magnetic transport measurement [31]. Interestingly, another magnetic circular dichroism measurement of very dilute samples shows that Nβ is positive [32]. This is probably because a Mn3+ -like impurity state is realized in the very dilute samples and behaves like the Cr2+ impurity in ZnSe.

6. Donor and acceptor ionization energies In the II–VI diluted magnetic semiconductors, the transition-metal ions tend to form the neutral impurity state (A0 ). In that case, the donor and acceptor levels may be located within the band gap as schematically shown in Fig. 1. When eff < Ueff , the donor level has mainly dn L character and the acceptor level has mainly dn+1 character. As can be seen from Table 2, many transition-metal impurities in the II–VI semiconductors satisfy this condition. Then the “effective Mott-Hubbard energy” UDA (see Fig. 1), i.e., the difference between the donor and acceptor levels, is determined by eff rather than Ueff and therefore dn L-like donor and dn+1 -like acceptor levels can be formed within the band gap in spite of the large U [33]. We can study the dn L-like discrete states split-off from the valence-band continuum using the Anderson impurity model instead of the cluster model [34,35]. In order to solve the model

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Hamiltonian numerically, the intra-atomic multiplet coupling is approximated by retaining only the diagonal matrix elements in Kanamori parameters [11]. As for the transfer integrals, we introduce Vt2 () ≡< t2 |H|Lt2 () > and Ve () ≡< e|H|Le () >, where  is the energy of the valence electron. The energy dependence of |Vt2 ()|2 and |Ve ()|2 is assumed to be a semi-ellipsoid with an appropriate band width WV , which is taken to be ∼ 2 eV for the sulfides and selenides. Although the width of the valence band is 4–5 eV for ZnS or ZnSe studied here, the top 2–3 eV of the valence-band is found to mainly contribute to |Vt2 ()|2 and |Ve ()|2 . Actually, a tight-binding calculation shows that a band with relatively small dispersion ∼ 2–3 eV, which is mainly constructed from the anion p and cation s orbitals, strongly hybridizes with the impurity 3d orbitals. In actual impurity-model calculations, the valence-band  ∞ continuum is replaced by 10–20 discrete states, and −∞ d|Vt2 ()|2 ∞ and −∞ d|Ve ()|2 are assumed to be equal to Tt22 and Te2 , respectively. Under this condition, the WV → 0 limit corresponds to the cluster model. For Cr2+ , a d4 L-like split-off state is formed well below the d4 L continuum in the (N − 1)-electron state through the strong hybridization with the d3 state, which originally lies Ueff − eff ∼ 1.1 eV above the center of the d4 L continuum. The split-off state corresponds to the donor level in the band gap. Since UDA ∼ eff and eff is smaller than the band gap of ZnS, the lowest energy level of the (N + 1)-electron state or the acceptor level is located below the conduction-band minimum. On the other hand, in the (N − 1)-electron state of Mn2+ in ZnS, a discrete state hardly splits off from the d5 L continuum because the d4 state is too far (Ueff − eff ∼ 3.2 eV) above the center of the d5 L continuum, which is stabilized by the exchange energy of the half-filled d5 shell, to induce a split-off state. An acceptor level is also not formed for Mn2+ within the band gap of ZnS since eff is much larger than the band gap. In Fig. 8, we show the donor and acceptor ionization levels calculated using the parameter sets in Table 2 and compare the predicted values with experimental results [1,6]. The calculated values are generally in good agreement with

Fig. 8. Donor and acceptor ionization levels for various 3d transition-metal impurities in ZnSe calculated using the Anderson impurity model. The calculations are compared with experimental values [1].

Fig. 9. Ionization levels for negatively-charged 3d transition-metal impurities in GaAs calculated using the Anderson impurity model. The calculations are compared with experimental values [1].

the experimental results. For most of the transition metal impurities, since eff is smaller than the band gaps of ZnS and ZnSe, the acceptor levels are located below the conduction band minimum. The calculated results explain the general lowering of the donor and acceptor levels with increasing atomic number of the transition-metal impurities as due to the monotonic decrease of . Furthermore, the non-monotonic behavior of eff , which is due to the multiplet effects, gives the local maxima and minima at Cr, Mn, and Fe in Fig. 8. For the III–V diluted magnetic semiconductors, the transition-metal impurities tend to be negatively charged (A− ). In that case, the first ionization and affinity levels correspond to transitions from A− to A0 , and from A− to A2− , respectively. In Fig. 9, the first ionization and the first affinity levels are compared with experimental results [1]. For the Mn impurity, the parameter set in Table 1 is used as an input. The parameters for the other transition-metal impurities have been deduced by assuming that the chemical trends of for GaAs is the same as that for ZnS. The calculated values are generally in good agreement with the experimental results as shown in Fig. 9. The energy level of the A− → A2− transition has the local maximum at Mn and that of the A− → A0 transition has the local minimum at Mn. This is because the d5 configuration of Mn2+ is stabilized by the intra-atomic exchange j. The binding energy of the d5 L-like split-off state corresponds to the energy level of the A− → A0 transition relative to the valence band maximum or the first acceptor level for the A0 impurity. Since this binding energy is very small for Ga1−x Mnx As,2 it is expected that the A0 -like bound state is easily destroyed with substantial hole concentration. This is probably the reason why the negatively-charged Mn2+ impurities exist in heavily doped Ga1−x Mnx As [31] while the neutral impurity is realized only in very dilute Ga1−x Mnx As [36].

2 The splitting is very small and comparable to the accuracy of the present calculation. Therefore, it is difficult to conclude whether a spilt-off state is formed or not in Ga1−x Mnx As. Experimentally, it is 110 meV [36].

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7. Ordered surface alloy of CuMn/Cu(1 0 0) The valence-band photoemission and inverse-photoemission spectra of the c(2 × 2) CuMn ordered surface alloy are shown in Fig. 10(a) [9]. The correlation satellites are observed at binding energies of 8 and 9.6 eV. The Mn 2p core-level photoemission spectrum shown in Fig. 11 also shows the intense satellite structure. The LDA calculation cannot explain the satellite structures (Fig. 10(c)), indicating that the observed satellites are caused by multi-electron effects. The results of the CI calculation using a MnCu8 cluster model are plotted by solid curves in Fig. 10(d) and 11 for the valence-band and Mn 2p core-level photoemission spectra, respectively. In addition to the satellite structures, the Mn 3d peak observed in the inverse-photoemission spectrum is also well reproduced by the CI calculation. In the MnCu8 cluster model with D4v symmetry, one-electron transfer integrals (Tb1 , Ta1 , Tb2 , and Te ) between the Mn 3d orbitals and the ligand orbitals constructed from the Cu 3d orbitals (Lb1 , La1 , Le , and Lb2 ) are expressed in terms of (ddσ), (ddπ), and (ddδ) [13]. (Here, Tb1 ≡< b1 |H|Lb1 >, Ta1 ≡< a1 |H|La1 >, Tb2 ≡< b2 |H|Lb2 >, and Te ≡< e|H|Le >) Assuming (ddσ):(ddπ):(ddδ) = −0.53:0.23:−0.02, Tb1 :Ta1 :Tb2 :Te = 21.5:21.0:30.7:25.0. The obtained parameters are = 0.0 eV, U = 4.0  eV, and T = 0.85 eV for the valence-band 2 + T 2 + T 2 + T 2 ). The obtained paspectrum (T ≡ Tb1 e a1 b2 rameters are = 1.5 eV, U=3.0 eV, and T = 1.0 eV for the Mn 2p core level. Fig. 11 also shows the Mn 2p spectrum of c(2 × 2) NiMn/Ni(1 1 0) in which the intense satellite structure is observed. The CI calculation using a MnNi7 cluster model gives = 1.0 eV, U = 3.0 eV, and T = 1.2 eV [37].

c(2x2) Mn/Cu(100) h ν=49 eV

PES

Intensity (Arb. Units)

(a)

IPES

h ν=58 eV

Ei=14.5 eV Mn3d

Cu Satellite

Mn3d Cu3d

Mn Satellite

(b) Clean Cu(100)

Cu4s,p

IPES

PES Cu3d

Cu4s,p

(c) FLAPW Mn 3d LDOS majority minority

(d) CI Theory U=4 eV, ∆=0 eV T=0.85 eV

-15

-10

Energy

-5

0

Fig. 11. Mn 2p core-level photoemission spectrum and the CI calculation for CuMn/Cu(1 0 0) and NiMn/Ni(1 1 0) [9,37].

8. Concluding Remark We have shown that various experimental results on 3d transition-metal impurities in II–VI and III–V semiconductors can be consistently explained within the CI picture: the d–d optical absorption, photoemission and inverse-photoemission spectra and donor and acceptor ionization energies can be reproduced by a single set of parameters, , U and (pdσ). It is shown that the physical properties are controlled both by the smooth variation of as a function of the impurity atomic number and by the apparently irregular variation of eff originated from the multiplet effects. The variation of the p–d exchange constant in various system is also qualitatively explained. Also the CI approach can be applied to the ordered surface alloy CuMn/Cu(1 0 0) and NiMn/Ni(1 1 0). Applications of the present method to a wider range of diluted systems as well as to the calculation of other physical properties remain to be made in future.

5

relative to E F (eV)

Fig. 10. (a) Photoemission and inverse-photoemission spectra of the CuMn ordered surface alloy on Cu(1 0 0). (b) Those of clean Cu. (c) Mn density of states obtained from LDA calculation. (d) Mn 3d spectrum obtained from the CI calculation using the MnCu8 cluster model [9].

Acknowledgements The authors would like to thank Dr. K. Ando, Prof. A.K. Bhattacharjee and Prof. M. Taniguchi for useful discussion. Financial support from a Grant-in-Aid for Scientific

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