Anisotropy of the Linear and Quadratic Magnetic Birefringence in Rare-Earth Semiconductors γ-Ln_2S_3 (Ln = Dy~(3+), Pr~(3+), Gd~(3+), La~(3+))

摘要

The field and angular dependence of the magnetic linear birefringence (MLB) in noncentrosymmetric cubic (symmetry class T_d) rare-earth (RE) semiconductors γ-Ln_2S_3 (Ln = Dy~(3+), Pr~(3+), Gd~(3+), La~(3+)) was studied. The field dependence of the MLB in Dy_2S_3 and Pr_2S_3 is a combination of two contributions, quadratic and linear with respect to the magnetic induction B, both possessing a strong anisotropy. The quadratic birefringence related to the Cotton-Mouton effect manifestations at a wavelength of λ = 633 nm is characterized in Dy_2S_3 by the value of β = 1.5 deg/(cm T~2) and the anisotropy parameter a = -0.7 and in Pr_2S_3, by β = 0.2 deg/(cm T~2) and a = 2. The non-reciprocal MLB caused by the magnetic-field-induced spatial dispersion reaches γ = 0.55 and 0.71 deg/(cm T) in Dy_2S_3 and Pr_2S_3, respectively. The relationship between parameters A and g of the γ_(ijkl) tensor describing contributions of the B_ik_j type to the dielectric tensor ε_(ij)(ω, k, B) is A = 2g in Dy_2S_3 (as well as in boracite crystals containing 3d ions), which is characteristic of the second-order magnetoelectric permittivity manifestations in the optical frequency range. In Pr_2S_3, the relationship A = 3.3g is evidence of manifestations of the additional quadrupole mechanism. A comparison of the Cotton-Mouton and Faraday effects in Ln_2S_3 and in magnetic semiconductors Cd_(1-x)Mn_xTe shows a principal difference between these systems and indicates that both phenomena in Ln_2S_3 are determined by the optical transitions in RE ions rather than by the interband or exciton transitions. This is also confirmed by the comparison of the Cotton-Mouton effect manifestations in Ln_2S_3, in dielectric Dy_3Ga_5O_(12) and Dy_3Al_5O_(12) single crystal cubic garnets, and in Dy_2O_3. An analysis of the non-reciprocal MLB mechanisms related to manifestations of the local interconfiguration optical transitions 4f~N → 4f~(N-1)5d in RE ions showed that this phenomenon, in contrast to the Cotton-Mouton and Faraday effects is caused by the presence of odd components of the crystal field acting upon the RE ion in Ln_2S_3. In Gd_2S_3, as well as in diamagnetic Ln_2S_3, neither the Cotton-Mouton effect nor the non-reciprocal MLB are manifested at T = 294 K, which is explained by different microscopic mechanisms of the magnetooptical phenomena for ions in the S-state and diamagnetic ions, on the one hand, and RE ions with nonzero orbital moment, on the other hand.