Energy Level Spectra of Transition Metal Ions In Diluted Magnetic Semiconductors
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ENERGY LEVEL SPECTRA OF TRANSITION METAL IONS IN DILUTED MAGNETIC SEMICONDUCTORS MURIELLE VILLERET*, S. RODRIGUEZ* AND E. KARTHEUSER** *Department of Physics, Purdue University, West Lafayette, IN 47907 "**Institut de Physique, Universite de Liege, B-4000 Liege, Belgium ABSTRACT We present a study of the low lying energy levels of Fe2t, Co2+, Ni2t and Cu2+ in diluted magnetic semiconductors such as Cd1 _xCoxTe and Cdj_xCoxSe and their counterparts. In the first of these compounds the magnetic ion sits on a site of symmetry Td while in the second the symmetry is trigonal (C3 v). We develop a formulation that permits a continuous variation from Td to C3V symmetry. Comparison with experimental data in Cd1 -xCoxSe shows that the C3v distortion amounts to about 10% of the crystal potential at the Co2t site. Our study of the energy 2 spectra of Fe + in Td and C3V crystal potentials reveals that, even in the cubic field, the levels exhibit an aniso~ropy which manifests it- ÷ self in an anisotropy of the magnetization, M, jn the regime in which M is not a linear function of the magnetic field B. The study includes all the levels in the lowest terms of the (3d)n (n=6,7,8,9) configurations. The calculations ýre carried out to second order in the spinorbit interaction and in B for the lowest orbital states and to first order in B for the excited states. The g-factors of all the levels are obtained including their anisotropy for the Co2 + and Cu2t r8 states. Diluted magnetic semiconductors (DMS's) [1] are materials obtained alloying a II-VI compound AB, where A and B are elements of the groups II and VI of the periodic table of the elements, respectively, with MBwhere M is a transition metal ion. Usually, the element M enters the structure substitutionally at A sites in the compound AB. The chemical formula of the resulting compound is A1-xMxB, x being the atomic concentration of M. The Mn-based DMS's have, until 2recently, received the greatest attention. Since the ground state of Mn + is 6S5 /2 , the crystal field has a negligible effect on 2 its magnetic properties and isolated Mn + ions in DMS's behave as if they were free. Other doubly-ionized transition metal ions exhibit ground terms possessing orbital as well as spin degeneracies. A systematic investigation of these transition ions in zinc-blende and wurtzite semiconductors has been carried out [2-3]. In the former, the symmetry of the site of the impurity is tetrahedral (group Td) whereas in the latter a slight distortion along 2 the [1111 direction yields trigonal symmetry (group C30). Excluding Mn +, all the doubly-ionized iron group ions have ground states that are either D or F terms. The values of L and S are symmetrical with respect to the halffilled 3d shell so that a study of ions whose shell is more than half-filled yields automatically information about those for which the 3d shell is less than half full. However, the order of the crystal-field-split levels is reversed and the spin-orbit coupling constant, X, changes sign. Therefore, we need only study four
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