Antiferromagnetic Ordering Effect on the Infrared Absorption Spectrum of CoF2

Abstract

The ground state of the free Co2+ ion, 4F(3d7), splits into an orbital triplet 4T1, another triplet 4T2, and a singlet 4A2 in a cubic field. Among these states, the 4T1 state has the lowest energy. The degeneracy of the ground state 4T1 is further lifted by the spin-orbit interaction and the crystalline field with rhombic symmetry and thus the fine structure multiplet consists of six Kramers' doublets. Newman and Chrenko1 observed several absorption peaks in the 0.15 to 0.20 eV range both above and below the Néel temperature (TN=38°K). These peaks correspond to transitions within the ground state multiplet. Changes in the spectrum below TN appear in the number of the peaks and their intensities. Recently, Dietz2 has found out that these are magnetic dipole transitions. The explanation of these experimental facts by the crystal field theory is reported. Nakamura and Taketa3 pointed out an important role of the rhombic crystal field in understanding the anomalous behavior of the temperature dependence of the magnetic anisotropy. We show that the rhombic component of the crystal field is also important in explaining the number of peaks and their relative intensities. The numerical values of the axial crystal field Δ, the rhombic crystal field Γ, the over-all spin-orbit coupling constant λ, effective Lande factors −ρ and −η, and the exchange integral J are determined from the experimental data of peak positions above TN and the temperature dependence of the magnetic anisotropy χ∥−χ⊥.4 For this purpose the expressions for χ∥ and χ⊥ are derived, taking the effect of the unquenched orbital angular momentum into account. Better agreement with observed anisotropy are obtained by our theory than by Nakamura and Taketa's. The values of parameters thus obtained are: Δ = −707 cm−1, Γ = −183 cm−1, λ = −157 cm−1, ρ = 1.125, η = 1.59, and J = 2.6 cm−1. By using these values, g values are calculated. The result is gx = 6.18, gy = 4.07, and gz = 2.03, where y and z axes are taken along the c axis and the line connecting two nearest neighbor F− ions, respectively. These values are very close to the observed ones.5 And further, we predict the energy separation of the lowest two Kramers' doublets to be 175 cm−1 (255°K). This is in good agreement with the observed value of 240°K determined from the Shottky-type anomaly in the specific heat measurement, although the observed value is rather uncertain.6 The magnitude of the splitting of each peak by the molecular field, intensities of the split peaks, and the dichroic behavior for polarized light are also calculated. The comparison with the observed spectrum below TN shows that the number of peaks in the observed spectrum exceeds that given by the theory and that observed intensities below TN are not explained by the theory. The former disagreement is expected to be resolved by taking into account a simultaneous excitation to different excited states of two adjacent Co ions coupled by the exchange interaction, instead of molecular field approximation. Finally, the expression for the antiferromagnetic resonance frequency is derived. The contribution from the anisotropy due to the crystal field is quite large. The frequency is estimated to be 21 cm−1.