Electronic structures of magnetic semiconductors FeCr2Se4 and Fe0.5Cu0.5Cr2Se4

Electronic structures of Cr-based chalcogenide magnetic semiconductors FeCr2Se4 and Fe0.5Cu0.5Cr2Se4 are investigated by using the full-potential augmented plane wave (FLAPW) band method in both the generalized gradient approximation (GGA) and the GGA+U (GGA incorporating the on-site Coulomb interaction). The GGA band calculation for the Jahn–Teller distorted FeCr2Se4 with monoclinic structure yields an antiferromagnetic (AF) metallic electronic structure. The GGA+U band calculation yields an insulating electronic structure for AF FeCr2Se4 in agreement with experiments. The orbital ordering in FeCr2Se4 driven by the Jahn–Teller and on-site Coulomb interactions is demonstrated based on the GGA+U electronic structures. For ferrimagnetic Fe0.5Cu0.5Cr2Se4 with a cubic spinel structure, the GGA and the GGA+U yield nearly insulating and insulating electronic structures, respectively. We have also studied the experimental electronic structure of FeCr2Se4 by employing soft x-ray absorption spectroscopy, soft x-ray magnetic circular dichroism and valence-band photoemission spectroscopy. Both calculational and experimental electronic structure studies indicate that the valence states of Fe and Cr ions in FeCr2Se4 are nearly divalent (Fe2+) and trivalent (Cr3+), respectively.


Introduction
The observation of large negative magneto-resistance (MR) and metal-insulator (MI) transition in the spinel sulfide Fe 1−x Cu x Cr 2 S 4 has invoked renewed interest in Cr-based chalcogenide magnetic semiconductors FeCr 2 X 4 (X = S, Se) [1,2]. FeCr 2 S 4 is a ferrimagnetic semiconductor with T C ∼ 172 K, while isoelectronic FeCr 2 Se 4 is an antiferromagnetic (AF) insulator with T N ≈ 218 K [3]- [9]. Upon cooling, the resistivity ρ(T ) of FeCr 2 S 4 shows a crossover transition from insulator to metal near the magnetic transition temperature T C , and then shows an insulating feature again below T ∼ 140 K [2,10]. Thus, in the finite temperature range below T C , the metallic feature ( dρ dT > 0) is observed. On the other hand, the resistivity behavior of FeCr 2 Se 4 is insulating ( dρ dT < 0) all over the temperature range. At low temperatures below 75 K, FeCr 2 Se 4 appears to become ferrimagnetic with a small magnetic moment of 0.007 µ B [7]. Note that FeCr 2 Se 4 crystallizes in the Cr 3 S 4 -type monoclinic structure (I 2/m) in contrast to the cubic spinel structure of FeCr 2 S 4 .
Cu-doped FeCr 2 S 4 , Fe 1−x Cu x Cr 2 S 4 , has a higher ferrimagnetic transition temperature and a larger magnetic moment with increasing x [11]. Regardless of x, Fe 1−x Cu x Cr 2 S 4 retains the ferrimagnetic phase and the cubic spinel structure. Similarly as in FeCr 2 S 4 , the resistivity in Fe 0.5 Cu 0.5 Cr 2 S 4 also manifests semiconducting behavior for T > T C (≈340 K) and T T C , while, in the finite temperature range below T C , the metallic feature is observed. The temperature range of the metallic feature is wider for x = 0.5 than for x = 0. In contrast, Cu-doped FeCr 2 Se 4 , Fe 1−x Cu x Cr 2 Se 4 , has a different crystal structure and magnetic phase, depending on x. Fe 1−x Cu x Cr 2 Se 4 crystallizes in a monoclinic structure for 0.0 x 0.1 as FeCr 2 Se 4 , whereas, for 0.4 x 1.0, it crystallizes in a cubic spinel structure. In between 0.1 < x < 0.4, the two phases coexist with a tendency to form the spinel structure with increasing annealing time [6]. Hence, Fe 0.5 Cu 0.5 Cr 2 Se 4 (x = 0.5) has a cubic spinel structure with the ferrimagnetic phase. Transport properties are not available for Fe 0.5 Cu 0.5 Cr 2 Se 4 , but it is expected that Fe 0.5 Cu 0.5 Cr 2 Se 4 is more conductive than FeCr 2 Se 4 , as Fe 0.5 Cu 0.5 Cr 2 S 4 is than FeCr 2 S 4 .
The theoretical electronic structure of FeCr 2 Se 4 has not been reported yet. In order to understand the differences in transport and magnetic properties between FeCr 2 S 4 and FeCr 2 Se 4 , we have investigated the electronic structures of the Cr-based magnetic semiconductors FeCr 2 Se 4 and Fe 0.5 Cu 0.5 Cr 2 Se 4 . We have used both the generalized gradient approximation (GGA) [12] and the GGA + U scheme [13] (GGA + U : GGA incorporating the on-site Coulomb interaction U ) on the basis of the full-potential augmented plane wave (FLAPW) band 3 method [14]. In our earlier work [15], we have found that the band calculation for FeCr 2 S 4 in the local spin density approximation (LSDA) yields the half-metallic electronic structure [15]. Note that Fe 2+ ions at the tetrahedral sites of FeCr 2 S 4 are Jahn-Teller active. Hence, the metallic nature of FeCr 2 S 4 , obtained in the LSDA, implies that the Jahn-Teller effect is not large enough to induce the insulating ground state for FeCr 2 S 4 . In order to have the insulating ground state with orbital ordering, the effect of the Coulomb correlation between d-electrons of Fe and Cr should also be incorporated. In fact, the insulating nature of FeCr 2 S 4 and Fe 0.5 Cu 0.5 Cr 2 S 4 is described well by the LSDA + U method [15].
We have also investigated the experimental electronic structure by carrying out soft x-ray absorption spectroscopy (XAS), x-ray magnetic circular dichroism (XMCD) and valence-band photoemission spectroscopy (PES) measurements for a polycrystalline sample of FeCr 2 Se 4 . For comparison, we have carried out the same XAS, XMCD and PES experiments for Fe 0.9 Cu 0.1 Cr 2 S 4 , the electronic structure of which is considered to be close to FeCr 2 S 4 . 4 Polycrystalline samples were prepared by the standard solid-state reaction method [10]. XAS and XMCD are good experimental tools for studying the valence states of transition metal ions in solids [16]- [18] and the element-specific local magnetic moments [19,20], respectively. XAS and XMCD experiments were performed at the 2A beamline and the PES experiment at the 8A1 beamline of the Pohang Accelerator Laboratory (PAL). XAS and XMCD data were obtained at a liquid nitrogen temperature T ≈ 80 K, and the total instrumental resolution was ≈ 120 meV for XMCD at a photon energy, hν ∼ 600 eV. XMCD spectra were obtained with the applied magnetic field of ∼0.7 Tesla and the degree of circular polarization >90%. The details of the experimental conditions will be described elsewhere [21].

Electronic structure of FeCr 2 Se 4
We have performed both the GGA and GGA + U band calculations for a monoclinic FeCr 2 Se 4 of a layered-type structure (see figure 1). We employed the structural data from the literature [9]. Both Fe and Cr ions are located at the centers of face-shared distorted octahedra. This feature of the octahedral environment of Fe ions in FeCr 2 Se 4 is different from that of the tetrahedral environment of Fe ions in FeCr 2 S 4 . As shown in figure 1(b), FeCr 2 Se 4 is known to have a rather complicated AF structure. Fe and Cr spins are antiferromagnetically aligned along the aand b-directions, while they are aligned ferromagnetically along the c-direction [5]. Hence, to describe the AF structure, one needs to consider a (2 × 2 × 1) supercell of eight formula units of FeCr 2 Se 4 .
In the GGA calculation, FeCr 2 Se 4 with the above AF supercell structure is found to be more stable than ferrimagnetic FeCr 2 Se 4 and the simple AF FeCr 2 Se 4 of layered type. This finding is in agreement with experiment. But, as shown in figure 2, the GGA calculation for the AF supercell FeCr 2 Se 4 yields the metallic phase with high Fe-d density of states (DOS) at the Fermi energy (E F ), in disagreement with experiment. Due to Jahn-Teller active Fe 2+ ions, the FeS 6 octahedra in the monoclinic FeCr 2 Se 4 are distorted. Hence, the resulting metallic phase in the GGA calculation reflects that the Jahn-Teller interaction is not large enough to induce the insulating phase in FeCr 2 Se 4 . Thus, to describe the insulating phase of FeCr 2 Se 4 , we have performed the GGA + U calculation for the AF supercell of FeCr 2 Se 4 . Figure 3 provides the DOS of the AF supercell of FeCr 2 Se 4 in the GGA + U scheme. We have employed the following parameters: U = 2.45 eV and J = 0.95 eV (J is the intra-atomic exchange interaction) for Fe d-electrons; U = 1.50 eV and J = 0.82 eV for Cr d-electrons. The energy gap feature is clearly seen near E F , which takes place due to the splitting of Fe-d DOS by the on-site Coulomb interaction U . Fe-d DOS in figure 3(b) indicates that the Fe-t 2g minority spin states are split into the lower and upper Hubbard bands to have a valence state close to Fe 2+ . Cr-d DOS in figure 3(c) shows that Cr-t 2g majority spin states are filled to have ≈Cr 3+ valence states. Se-p DOS in figure 3(d), however, shows that many of the Se-p states are unoccupied. This implies that the covalent bonding nature also exists in FeCr 2 Se 4 , and so the ionic valence states of Fe 2+ and Cr 3+ ions should be considered as just nominal.
In figure 4(a) is plotted the charge density on the x y-plane of the monoclinic FeCr 2 Se 4 at z = 1/2 of figure 1(a). Here, the charge density is obtained by integrating the density of the specific spin over the finite energy interval up to E F , as indicated in figure 3(b). Thus the local charge density of Fe corresponds to the minority spin part, while the local charge density of Cr to the majority spin part. The zigzag bonding nature along Se, Cr, Se, Fe, Se, Cr and Se ions is shown along the b-direction. To examine the bonding nature between Fe and neighboring Se ions, we have plotted in figure 4(b) the local charge density for the Fe-d minority spin states on the FeS 4 layer of the FeS 6 octahedron (the layer represented by the red line in figure 4(a)). The local charge density of Fe in figure 4(b) shows a typical Fe-t 2g (≈d x z -type) state. The lobe axes are not on the FeS 4 layer plane, but tilted towards the x z-plane, as shown in figure 4(a). This is become ≈Fe 3+ and ≈Cu 1+ , respectively. Thus, distinctly from the case of FeCr 2 Se 4 , Fe ions in Fe 0.5 Cu 0.5 Cr 2 Se 4 are not Jahn-Teller active and so no cooperative Jahn-Teller orbital ordering occurs. Since Fe and Cr spins are antiferromagnetically coupled, the total magnetic moment becomes 7.0 µ B per unit cell.    [23] and the Mössbauer spectroscopy study [24]. configurations, whereas the metallic-like bonding (strongly hybridized states) will smear out the multiplet features. It is surprising that finite XMCD signals are observed in both the Fe 2p and Cr 2p XMCD spectra of FeCr 2 Se 4 . Normally, an AF system does not show the XMCD effect. So the existence of the finite XMCD effect in FeCr 2 Se 4 implies that it has a ferromagnetic component at T ≈ 80 K, where the XMCD data were obtained. The existence of nonzero XMCD signals in FeCr 2 Se 4 seems to be consistent with its ferrimagnetic behavior below 75 K [7]. Further, the much smaller intensity of the XMCD spectrum of FeCr 2 Se 4 , as compared to FeCr 2 S 4 , is qualitatively consistent with the much smaller bulk magnetic moment of FeCr 2 Se 4 than that of Fe 0.9 Cu 0.1 Cr 2 S 4 . The nearly identical XMCD lineshapes for Fe 0.9 Cu 0.1 Cr 2 S 4 and FeCr 2 Se 4 imply similar local electronic structures between X = S and X = Se, as explained below. distributions of the corresponding photoelectrons. 5 These PSWs were determined by employing resonant PES (RPES) [18,25] near the Cr 2p and Fe 2p absorption edges. The details of the extraction procedure for each PSW are explained in [18]. The overall features are very similar to each other. The Cr 3d PES spectra exhibit rather sharp peaks, corresponding to the occupied t 3 2g -electrons, while the Fe 3d PES spectra are much broader. These differences again indicate that the Fe 3d-electrons are strongly hybridized with the other valence electrons. Then the strong hybridization will result in metallic-like bonding in Fe 3d-X p-electrons (X = S, Se). In this work, we have found that the electronic structures of Fe 3d and Cr 3d states of FeCr 2 Se 4 and FeCr 2 S 4 are very similar to each other. In view of the different crystal structures for FeCr 2 Se 4 (monoclinic) and FeCr 2 S 4 (spinel), this finding is unexpected. Note that the local environments of Fe ions are different: octahedral (O h ) for FeCr 2 Se 4 and tetrahedral (T d ) for FeCr 2 S 4 . Therefore, the similarity in electronic structures of Fe 3d states of FeCr 2 Se 4 and FeCr 2 S 4 might be due to the metallic-like bonding between Fe 3d states and S 3p or Se 4p states in FeCr 2 X 4 (X = S, Se); thereby the effect of the local atomic-like environments is weakened. As to the similarity in the Cr 3d electronic structures, it can be understood based on the same local O h environment of Cr ions in both FeCr 2 Se 4 and FeCr 2 S 4 .

Conclusions
We have studied the electronic structures of the Cr-based chalcogenide magnetic semiconductors FeCr 2 Se 4 and Fe 0.5 Cu 0.5 Cr 2 Se 4 by using the FLAPW band method in both the GGA and GGA + U schemes. Insulating ground states of FeCr 2 Se 4 and Fe 0.5 Cu 0.5 Cr 2 Se 4 are r Figure 8. Comparison of the valence-band PES spectra of FeCr 2 Se 4 and Fe 0.9 Cu 0.1 Cr 2 S 4 . These PES spectra represent roughly the partial spectral weight (PSW) distributions of the Cr 3d (top), Fe 3d (middle) and Se/S p + Fe/Cr 3d (bottom) states, respectively. described well by the GGA + U . We have shown that the Jahn-Teller interaction in FeCr 2 Se 4 is not large enough to induce the insulating ground state. The Coulomb correlation effects between d-electrons of Fe and Cr should be incorporated to get the AF insulating ground state with the orbital ordering in FeCr 2 Se 4 .
The electronic structure of FeCr 2 Se 4 has also been investigated experimentally by employing XAS, XMCD and PES. It is found that the electronic structure of FeCr 2 Se 4 is very similar to that of FeCr 2 S 4 . The valence states of Cr and Fe ions are nearly trivalent (Cr 3+ ) and divalent (Fe 2+ ), respectively. On the other hand, the Fe 2p XAS spectrum of FeCr 2 Se 4 does not exhibit the multiplet structures, similarly as in Fe metal, indicating the strong hybridization between the Fe 3d and Se p electrons.