Optical properties of Co3+ doped in α-Al2O3 with Considering Lattice Relaxation Effect

Search of new luminescence materials to improve the current white-ight emitting diode (LED) is still ongoing. Several investigations such as the ion dependence, the host crystal dependence has been done previously. Since we want to get a complete picture of ion-host combination dependence, we investigated α-Al2O3: TM3+. In this work we estimated the optical properties of α-Al2O3 doped with Co3+. We constructed model clusters consisting of 7 atoms. The lattice relaxation effects due to the Co3+ substitution were calculated using Shannon’s crystal radii method and geometry optimizations in the Cambridge Serial Total Energy Package (CASTEP) method. The one-electron Discrete Variational-Xα (DV-Xα) method was used to estimate the molecular orbital energies, while the many-electron Discrete Variational Multielectron (DVME) method was used to estimate the d-d absorption spectra. Since Co3+ belongs to 3d 6 configuration, there are two possible spin states i.e., high-spin (HS) and low-spin (LS) states.


Introduction
Up to recently, transition metal (TM) ions doped compounds have attracted great interest due to a wide variety of applications such as phosphors used in white light emitting diode (LED). However, search of new luminescence materials to improve the current white-LED is still ongoing. In our previous studies, we performed several investigations such as the ion dependence and the host crystal dependence. In the case of ion dependence, we found out that the U-and Y-band increase in the order of V 2+ , Cr 3+ and Mn 4+ [1][2][3]. On the other hand, in the case of host crystal dependence, we found out that when the Mn-F bond length decreased, the U-and Y-band energies increased whereas the R-line energy decreased [4,5]. Nevertheless, similar study for α-Al2O3: TM 3+ ions i.e., Ti 3+ . V 3+ , Cr 3+ , Mn 3+ , Fe 3+ , and Co 3+ need to be conducted to understand the complete picture of TM ions in the octahedral system. Therefore, we have reported a study on the optical properties of α-Al2O3: V 3+ and Mn 3+ using similar method [6,7]. In the case of α-Al2O3: V 3+ , since V 3+ belongs to 3d 2 configuration, there are  several transitions which occur from 3 T1a ground state to 1 T2, 1 E, 1 A1, 3 T2, and 3 T1b states. The transition energies from 3 T1a to the singlet states are observed as weak and sharp lines, while the transition energies from 3 T1a to the triplet states are observed as strong and broad bands. Our results point out the importance of lattice-relaxation consideration to produce the optical properties of α-Al2O3: V 3+ accurately. On the other hand, in the case ofα-Al2O3: Mn 3+ , since Mn 3+ belongs to 3d 4 configuration, there are two possible spin states i.e., high-spin (HS) and low-spin (LS) states. In the HS state, the spin-allowed transition is occurred from the 5 E ground state to 5 T2 states ( 5 E → 5 T2). On the other hand, in the LS state, the spin-allowed transition was occurred from the 3 T1 ground state to 3 E state ( 3 T1 → 3 E). Nevertheless, we limit our work in the LS state.
In this work, we want to do similar investigation for α-Al2O3: Co 3+ . The lattice relaxation effects due to the Co 3+ substitution were calculated using Shannon's crystal radii method and geometry optimizations in the Cambridge Serial Total Energy Package (CASTEP) method. The one-electron Discrete Variational-Xα (DV-Xα) method was used to estimate the molecular orbital energies, while the many-electron Discrete Variational Multielectron (DVME) method was used to estimate the d-d absorption spectra.

Methods
In this work, we used 7-atoms model clusters constructed from α-Al2O3 crystal structure [8], CoO6 9-. The lattice relaxation effect was estimated by Shannon's crystal radii [9,10] and geometry optimization using CASTEP code [11][12][13]. The detailed procedures were explained in Ref. 14. Table 1 shows the Co-O bond length of α-Al2O3: Co 3+ calculated using different computational methods. There are two different bond lengths; the shorter bonds indicated by (d1) and the longer bonds indicated by (d2). The lattice relaxation ratios described as the ratio between the bond length after relaxation process and the original bonds were shown in the right columns. It shows that d1 increases when model clusters with considering lattice relaxation effect calculated by both Shannon's crystal radii and the geometry optimization using CASTEP code were used. On the other hand, d2 increased when we used the model clusters with considering lattice relaxation effect calculated by Shannon's crystal radii, and then decreased when we used the model clusters with considering lattice relaxation effect calculated by the geometry optimization using CASTEP code.
In order to calculate the molecular orbital (MO) energies of α-Al2O3: Co 3+ , We used the one-electron calculations DV-Xα method. The detailed procedure is described in Ref. 15. In this case, only one electron and nuclei are considered, while the other electrons are treated just as potentials. On the other hand, the many-electron calculations DVME method was utilized to calculate the absorption spectra of α-Al2O3: Co 3+ . The detailed procedure is described in Ref. 16. Here, four electrons occupying the impurity levels are treated explicitly. Both above mentioned methods are first-principles calculations which performed without referring to any experimental parameter. The calculations carried in this work were performed under low spin (LS) state.  Figure 1. The molecular orbital (MO) energies of α-Al2O3: Co 3+ estimated without and with lattice relaxation effect. Figure 1 shows the molecular orbital of α-Al2O3: Mn 3+ calculated using different computational methods. The 7-atom model cluster (CoO6 9-) were used in the calculations. Two different types of lattice relaxation estimation i.e., Shannon's crystal radii method and CASTEP method are compared. The conduction band and the valence band are indicated by dashed and solid lines, respectively. The impurity levels consist of t2g and eg which their difference energy is called as crystal field splitting (10Dq). In this case, the lowest impurity levels were set to zero. The results show that the 10Dq were found to be 1.78, 1.75, and 1.92 eV calculated using no-relax, Shannon's crystal radii, and CASTEP methods, respectively. As we can see, the crystal field splitting calculated based on the model cluster with considering lattice relaxation effect using CASTEP code has the highest 10Dq. It might be understood since the t2g and eg levels split largely.  17 are shown at the lowest panel. In the experimental spectra, two broad peaks were observed either in the σ or in the π spectrum. The first peak appears at ca. 2 eV, while the second peak appears at ca. 2.8 eV. Our results show that the calculated absorption spectra obtained using the model clusters without considering lattice relaxation effect and with considering lattice relaxation effect estimated based on Shannon's crystal radii were identical. The tendency of the absorption spectra was changed significantly when we used the model cluster with considering lattice relaxation effect estimated based on the geometry optimization using CASTEP code. Figure 3 magnifies the absorption spectra of α-Al2O3: Co 3+ estimated with considering lattice relaxation effect calculated by the geometry optimization using CASTEP code. The peaks positions agree with the observed absorption spectra reported from Ref. 17.

Conclusion
In this work, the optical properties of α-Al2O3: Co 3+ have been successfully estimated by firstprinciples calculations DV-Xα and DVME method. The lattice relaxation effect was investigated thoroughly by comparing two different methods using Shannon's crystal radii method and firstprinciples band structure calculations CASTEP. The estimated absorption spectra shows that the results based on 7-atom model cluster with considering lattice relaxation effect using CASTEP improves the agreement with the experimental data.