A direct algebraic parametrization of the high-symmetry crystal-field Hamiltonians

作者：Mulak Maciej^*; Mulak Jacek

来源：Physica Status Solidi (B) Basic Research, 2015, 252(10): 2209-2214.

DOI：10.1002/pssb.201552176

• parametrization
• cubic and hexagonal crystal fields
• crystal-field Hamiltonian
• second moment of crystal-field splitting

An algebraic, calculational, non-fitting method of parametrization of the cubic and hexagonal crystal-field (CF) Hamiltonians (H-CF) with only two independent CF parameters B-40 and B-60 is proposed. It is based on the linear relation sigma(2)(J) = Sigma(k) A(k)(2) (J)S-k(2) between s2(J) the square of the second moment of the electron state |J > CF splitting and the squares of the multipolar CF strengths S-k(2) = 1/2k+1 Sigma(q) |B-kq|(2), where A(k) (J) = < J parallel to C-(k)parallel to J >. For a pair of |J(i)> and |J(j)> electron states an algebraic solution for S-4(2) and S-6(2), and hence for the B-40 and B-60 CF parameters can be gained. The necessary conditions for physical correctness of the solutions (S-k(2)>= 0) impose limitations on the observed sigma(2)(J(i))/sigma(2)(J(j)) ratios depending on the respective ratios A(k)(2) (J(i))/A(k)(2)(J(j)). These restrictions can be used to verify postulated CF splitting diagrams. In the high-symmetry crystal fields, the electron states with J = 2 or 5/2 undergo splitting only by the k = 4H(CF) multipole, and from their CF splitting second moments the B-40 parameter can be directly obtained. For J = 2, |B-40|= root 63/10 Delta(J)/A(4)(J)|, whereas for J = 5/2, |B-40| = root 7 Delta(J)|A(4)(J)J| where similar to is the energy gap between the two Stark's levels of the |J > state. The proposed method is demonstrated and discussed for several systems of RE3+ ions in some high-symmetry crystal matrices.

• 出版日期2015-10