A general way of analyzing EPR spectroscopy for a pair of magnetically equivalent lanthanide ions in crystal: A case study of BaY_2F_8:Yb~(3+) crystal

摘要

Electron paramagnetic resonance (EPR) is an important tool to study the complex interactions (e.g., exchange and magnetic dipole-dipole interactions) for a pair of lanthanide (Ln) ions in crystals. How to analyze these EPR spectra and obtain the strength of each interaction is a challenge for experimentalists. In this work, a general way of calculating the EPR lines for two magnetically equivalent Ln ions is given by us to solve this problem. In order to explain their EPR spectra and obtain exchange interaction parameters J_i (i = x, y, z) between them, we deduce the analytic formulas for computing the angular dependent EPR lines for such Ln pairs under the condition of weak coupling (|j_i| hv, where v is the microwave frequency in the EPR experiment) and set up the spin-Hamiltonian energy matrix that should be diagonalized to obtain these lines if intermediate (|j_i| ～ hv) and strong (|j_i| > hv) couplings are encountered. To verify our method, the experimental EPR spectra for the Yb~(3+) doped BaY_2F_8 crystal are considered by us and the EPR lines from the isolated Yb~(3+) ion and Yb~(3+)-Yb~(3+) pair with distance R equal to 0.371 nm are identified clearly. Moreover, exchange interaction parameters (J_x ≈ -0.04 cm~(-1), J_y ≈-0.24 cm~(-1), and J_z ≈-0.1 cm~(-1)) for such a pair are also determined by our calculations. This case study demonstrates that the theoretical method given in this work would be useful and could be applied to understand interactions between Ln ions in crystals.