First-Principles Study of the Crystal-Field and Racah Parameters of Cr3+ in Alumina

Abstract

The development of blue LEDs [1] enabled one to construct white LEDs by combining them with appropriate phosphors. Recently Mn4+-doped fluorides have been put into commercial use as the red phosphors for high color-rendering white LEDs [2]. However, in order to suppress the degradation due to high humidity and high temperature, a special surface treatment is required for these phosphors. Therefore, the search of other red phosphors activated by Mn4+ is still desired. For theoretical design of novel phosphors, non-empirical prediction of optical parameters such as the crystal-field and Racah parameters is quite important. The purpose of this study is to establish a first-principles approach to predict these parameters of transition metal ions in crystals.In this work, the crystal-field and Racah parameters of ruby (Cr3+ doped α-Al2O3) were evaluated based on the first-principles calculations using the relationship between the ligand-field theory and the molecular orbital (MO) theory derived by Sambe and Felton [3]. Two types of first-principles methods were adopted. One is the discrete-variational (DV)-Xα method [4], which is an MO calculation method based on the one-electron approximation. The other is the discrete variational multi-electron (DVME) method [5], which is a configuration-interaction (CI) calculation method based on the explicit many-electron wave functions. The estimation of the crystal-field and Racah parameters were performed in the following three approaches.(1) Estimation based only on the DV-Xα method(2) Estimation based only on the DVME method(3) Estimation based on the combination of the DVME method and the DV-Xα methodThe results show that the values of the crystal-field and Racah parameters obtained by the approach (3) are in the best agreement with the values obtained by fitting to the experimental data [6], indicating that CI calculations using some corrections based on the one-electron MO calculations are effective for the non-empirical estimation of the crystal-field and Racah parameters [7]. These results also provide theoretical basis for the configuration-dependent correction and the correlation correction introduced in our previous CI calculations of ruby [5]. This approach could be applied to prediction of d-d transitions of Mn4+ in crystals to find a suitable host for novel Mn4+-activated red phosphors for white LEDs.[1] I. Akasaki and H. Amano, Jpn. J. Appl. Phys. 45, 9001 (2006).[2] J. E. Murphy, F. Garcia-Santamaria, A. A. Setlur, and S. Sista, SID 2015 DIGEST, 927 (2015).[3] H. Sambe and R. Felton, Int. J. Quant. Chem., 10, 155 (1976).[4] H. Adachi, M. Tsukada, and C. Satoko, J. Phys. Soc. Jpn. 45, 875 (1978).[5] K. Ogasawara T. Ishii, I. Tanaka, and H. Adachi, Phys. Rev. B 61, 143 (2000).[6] W. M. Fairbank, Jr., G. K. Klauminzer, and A. L. Schawlow, Phys. Rev. B 11, 60 (1975).[7] K. Ogasawara, K.C. Mishra, and J. Collins, ECS J. Solid State Sci. Technol. 9, 016011 (2020).