Local electronic structure of Cr in the II-VI diluted ferromagnetic semiconductor Zn$_{1-x}$Cr$_x$Te

The electronic structure of the Cr ions in the diluted ferromagnetic semiconductor Zn$_{1-x}$Cr$_x$Te ($x=0.03$ and 0.15) thin films has been investigated using x-ray magnetic circular dichroism (XMCD) and photoemission spectroscopy (PES). Magnetic-field ($H$) and temperature ($T$) dependences of the Cr $2p$ XMCD spectra well correspond to the magnetization measured by a SQUID magnetometer. The line shape of the Cr $2p$ XMCD spectra is independent of $H$, $T$, and $x$, indicating that the ferromagnetism is originated from the same electronic states of the Cr ion. Cluster-model analysis indicates that although there are two or more kinds of Cr ions in the Zn$_{1-x}$Cr$_x$Te samples, the ferromagnetic XMCD signal is originated from Cr ions substituted for the Zn site. The Cr 3d partial density of states extracted using Cr $2p \to 3d$ resonant PES shows a broad feature near the top of the valence band, suggesting strong $s$,$p$-$d$ hybridization. No density of states is detected at the Fermi level, consistent with their insulating behavior. Based on these findings, we conclude that double exchange mechanism cannot explain the ferromagnetism in Zn$_{1-x}$Cr$_{x}$Te.


INTRODUCTION
Ferromagnetic diluted magnetic semiconductors (DMS's) have opened a way for the manipulation of the spin degree of freedom of electrons through interaction between the local moments of doped magnetic ions and the spins of charge carriers in the host semiconductors.
Therefore, ferromagnetic DMS's have been considered to be key materials for semiconductor spin electronics or spintronics [1,2], which is intended to manipulate both the charge and spin degrees of freedom of electrons in semiconductors. If ferromagnetism occurs as a result of interaction between the local magnetic moments of doped ions and the spins of charge carriers, the magnetism is called carrier-induced ferromagnetism, and the III-V DMS's Ga 1−x Mn x As and In 1−x Mn x As are prototypical systems of carrier-induced ferromagnetism [3]. Using the III-V DMS's, new functional devices such as circular polarized light detectors [4], spin-related light-emitting diodes [5], and field-effect transistors controlling ferromagnetism [6] have been fabricated. However, these devices only act at low temperatures since the Curie temperatures (T C 's) of the DMS's are below room temperature. Therefore, ferromagnetic DMS's having T C above room temperature are strongly desired for practical applications of spintronic devices. Ever since the theoretical prediction of ferromagnetism having T C exceeding room temperature in wide-gap semiconductor-based DMS's [7], there have been many reports on room-temperature ferromagnetism of wide-gap DMS's such as Ga 1−x Mn x N and Zn 1−x Co x O [8]. In order to see whether the ferromagnetic properties are intrinsic or extrinsic, anomalous Hall effects [9], magnetic circular dichroism (MCD) in visibleto-ultraviolet region [10], and carrier-doping dependence of the ferromagnetism [11,12] have been studied since these properties of DMS are derived from interaction between the host semiconductor and the doped magnetic ions.
The II-VI semiconductor ZnTe crystallizes in the zinc-blend structure as shown in Fig. 1(a), has a band gap of ∼ 2.4 eV, and shows p-type electrical conductivity. Cr-doped ZnTe crystal, in which the Cr concentration is below 1%, has been investigated before the discovery of ferromagnetism in heavily Cr-doped ZnTe thin films. Infrared absorption [13] and electron spin resonance [14] studies of bulk Zn 1−x Cr x Te have suggested that the Cr ions are divalent and are subjected to tetragonal Jahn-Teller distortion. MCD measurements in visible-to-ultraviolet region on bulk Zn 1−x Cr x Te crystals have revealed a positive p-d exchange constant Nβ, that is, the exchange interaction between the hole spin and the local magnetic moment is ferromagnetic [15]. Recently, Saito et al. [16] have succeeded to prepare ZnTe thin films doped with high concentration of Cr atoms (x ∼ 20%) by the molecular beam epitaxy (MBE) technique. The Zn 1−x Cr x Te thin films showed ferromagnetism at room temperature and their MCD signals observed at the absorption edge of ZnTe showed magnetic-field (H) and temperature (T ) dependences which follow these of magnetization (M), indicating that there is strong interaction between the spins of host s,p-band electrons and the magnetic moments of the doped Cr ions [16,17]. Therefore, Zn 1−x Cr x Te has attracted much attention as an intrinsic DMS with strong s,p-d interaction.
The ferromagnetic properties of Zn 1−x Cr x Te thin films have been investigated so far [18]. Effects of doping on the ferromagnetism of Zn 1−x Cr x Te have been studied [19,20,21].
Iodine (I), which is expected to be an electron dopant, enhances the ferromagnetism while nitrogen (N), which is expected to be a hole dopant, suppresses it [19,20]. These effects have been explained based on the double-exchange mechanism [19,22]. However, carrier-induced ferromagnetism in Zn 1−x Cr x Te is doubted because the Zn 1−x Cr x Te films are highly insulating. Furthermore, the tendency that N doping increases hole carrier concentration and suppresses the ferromagnetism is opposite to the observation for Ga 1−x Mn x As [23], in which the ferromagnetic property is enhanced by the increase of hole concentration. Recently, spatially inhomogeneous distributions of the Cr ions have been pointed out to influence the magnetic properties [24,25,26]. Spatially resolved energy-dispersive x-ray spectroscopy study has recently revealed that co-doping with I induces inhomogeneous formation of Cr-rich (Zn,Cr)Te nano-regions, whereas co-doping with N results in homogeneous Cr-ion distributions [21].
X-ray magnetic circular dichroism (XMCD) and resonant photoemission spectroscopy (RPES) are powerful tools to investigate the electronic structure of DMS [27,28,29,30,31,32,33,34,35,36]. XMCD is defined as the difference between the core-level x-ray absorption spectroscopy (XAS) spectra taken with right-handled (µ + ) and left-handled (µ − ) circularly polarized x rays. Because XMCD is sensitive only to magnetically active species, it is very efficient to extract information about the electronic and magnetic properties of doped magnetic ions. In RPES, when the incident photon energy is adjusted to the 2p → 3d core excitation energy, the photoemission intensity of the 3d partial density of states (PDOS) is resonantly enhanced [37,38].
Our previous Cr 2p XMCD measurements on Zn 1−x Cr x Te (x = 0.045) thin film [39] have revealed that the orbital moment of the Cr 3d electrons is largely quenched compared with the value of the Cr 2+ ion in the tetrahedral crystal field. The XMCD intensity increased with increasing H up to 7 T, indicating the existence of paramagnetism and/or superparamagnetism in Zn 1−x Cr x Te, and that the magnetically active Cr ions had a single chemical environment although a small amount of magnetically inactive Cr ions existed. Atomic multiplet theory analysis has suggested that the Cr ions are divalent and are subjected to tetragonal Jahn-Teller distortion, whose distortion axes are equally distributed in the X, Y and Z directions. The valence-band PES spectra showed suppressed spectral weight near the Fermi level (E F ) [39]. Based on these observations, we have proposed that the spec-tral suppression is originated from the Jahn-Teller distortion and/or Coulomb interaction between Cr 3d electrons.
However, some points remain to be confirmed concerning the above suggestions. Since the XMCD spectra were recorded only in the applied magnetic field parallel to the c axis, the direction of Jahn-Teller distortion was not confirmed experimentally. In addition, the at high fields the paramagnetic (or superparamagnetic) and antiferromagnetic XMCD signals become detectable [39]. In order to see the consistency between the macroscopic and microscopic magnetic measurements, comparison of the XMCD intensity with the magnetization M is made in Fig. 2 shell, a strong temperature dependence of the XAS spectra is expected due to the degeneracy of the orbital degree of freedom in the ground state. For the Cr 2+ ion having the d 4 electronic configuration in the T d crystal field, the t 2 states are partially occupied and the orbital degree of freedom survives. However, the Cr L 2,3 XAS spectra of Zn 1−x Cr x Te did not change with temperature as shown in Fig. 3. This result implies that the orbital degeneracy is lifted due to a Jahn-Teller distortion which splits the t 2 levels [40]. Alternatively, the 3d shell may be completely filled, i.e., the Cr ion is in the Cr + state and has the d 5 electronic configuration.

XMCD sum rules
By applying the XMCD sum rules [41,42], one can estimate the spin (M spin ) and orbital magnetic moments (M orb ) of the Cr ion separately by where p, q, and r are the integrated intensities of the XAS and XMCD spectra as shown in Fig. 4(a), N d is the number of 3d electrons, and M T is the expectation value of the magnetic dipole operator, which is negligibly small with respect to M spin because of relatively weak spin-orbital coupling in 3d electrons [41]. The ratio M orb /M spin was estimated to be ∼ 0.11 ± 0.12, indicating that the orbital moment is significantly suppressed, consistent with the previous XMCD measurements [39]. Thus, the candidate electronic structures for the magnetically active Cr ions are the Cr 2+ ion in D 2d symmetry or Cr + (d 5 ) configuration, as shown in Fig. 4(b). Below, we shall discuss the electronic structure of the Cr ions under these constraints.

Incident photon angle dependence
When the Cr 2+ ion is under the uniaxial distortion of tetragonal symmetry D 2d , the electronic state should have an anisotropy. Calculations using atomic multiplet theory for  XAS and XMCD spectra with various θ.

CONFIGURATION-INTERACTION CLUSTER-MODEL CALCULATION
The substitutional magnetic ion in a II-VI DMS is tetrahedrally coordinated by anions as shown in Fig. 1(b), and therefore the electronic structure of the magnetic ion is influenced Based on these considerations, we have performed CI cluster-model calculations on Cr 2+ in a D 2d crystal field assuming the isotropic distribution of the Jahn-Teller axes and on Cr 2+ with negative ∆. In the letter case, the ground state electronic configuration becomes 3d 5 L (L denotes a hole in the host valence band), which is referred to "Cr + " hereafter. Figure 6 shows comparison of the experimental spectra with calculated ones, where the calculated spectra are shifted to adapt the Cr 2p 3/2 peak at 576 eV to the experimental one. The where u ′ and j are Kanamori parameters, δ eff = ∆ eff + W V /2, ∆ eff is the effective chargetransfer energy, and W V is the width of the host valence band. In the distorted CrTe 4 cluster, the first term of equation (3) becomes dominant [47]. The p-d exchange constant estimated from the parameters is Nβ = 1.3 ± 0.9 eV (> 0: ferromagnetic), consistent with the result of the MCD measurements [45]. The results indicate that the ferromagnetism in giving support to the previous XMCD and PES results [39].

RESONANT PHOTOEMISSION SPECTROSCOPY
Although the previous measurements on Zn 1  band than that of the x = 0.03 sample as shown in Fig. 7(b). However, there is no density of states (DOS) at E F for both the x = 0.03 and 0.15 samples, corresponding to their insulating behaviors. Based on these findings, it is likely that the spectral suppression near E F is originated from both the Jahn-Teller distortion and Coulomb interaction between Cr 3d electrons as proposed in the previous measurements [39]. Since the ferromagnetism realized by the double-exchange mechanism requires a finite DOS at E F [22,48], the observations indicate that the double-exchange mechanism appears difficult in Zn 1−x Cr x Te. The present results suggest that the ferromagnetic interaction between the spins of the s,p band electrons and local moments of the d orbitals is strong but the ferromagnetic interaction between the d orbitals is shortranged because the top of the valence band has d character [49]. In order to obtain further understanding of the ferromagnetic interaction, systematic XMCD measurements of "carrier-doped" (I and/or N doped) Zn 1−x Cr x Te are highly desired. From the report on the doping effects [21], both the hole-carrier concentration and the inhomogeneous Cr distribution affect the ferromagnetic properties of Zn 1−x Cr x Te thin film.
In the present work, we have measured Zn 1−x Cr x Te thin films having different Cr concentration. In this case, it is likely that the effects of the Cr inhomogeneity on the ferromagnetism are more dominant than these of the carrier concentration. Considering the fact that the ferromagnetic XMCD signal of Zn 1−x Cr x Te is independent of Cr concentration and that