Crystal-field Splitting for Low Symmetry Systems in ab Initio Calculations

In the framework of the LDA+U approximation we propose the direct way of calculation of crystal-field excitation energy and apply it to La and Y titanates. The method developed can be useful for comparison with the results of spectroscopic measurements because it takes into account fast relaxations of electronic system. For titanates these relaxation processes reduce the value of crystal-field splitting by ∼30% as compared with the difference of LDA one electron energies. However, the crystal-field excitation energy in these systems is still large enough to make an orbital liquid formation rather unlikely and experimentally observed isotropic magnetism remains unexplained. © 2005 The American Physical Society.We would like to thank I.V. Solovyev, D.E. Kondakov, M.A. Korotin, A.I. Poteryaev, S. Okatov, and A.I. Lichtenstein for very useful discussion of calculation details. We also acknowledge fruitful communications with G. Khaliullin, M. Haverkort, M. Grüninger, M. Cwik, E. Müller-Hartmann, M. Braden, and especially L.H. Tjeng. This work is supported by the Russian Foundation for Basic Research under Grant Nos. RFFI-04-02-16096 and RFFI-03-0239024, the Dynasty Foundation and International Center for Fundamental Physics in Moscow program for young scientists, Russian Science Support Foundation program for best Ph.D. students of Russian Academy of Sciences, Netherlands Organization for Scientific Research through NWO 047.016.005 and by the Deutsche Forschungsgemeinschaft through SFB 608