Magnetic dipole and electric quadrupole transitions in the trivalent lanthanide series: Calculated emission rates and oscillator strengths

Given growing interest in optical-frequency magnetic dipole transitions, we use intermediate coupling calculations to identify strong magnetic dipole emission lines that are well suited for experimental study. The energy levels for all trivalent lanthanide ions in the $4f^{\text{n}}$ configuration are calculated using a detailed free ion Hamiltonian, including electrostatic and spin-orbit terms as well as two-body, three-body, spin-spin, spin-other-orbit, and electrostatically correlated spin-orbit interactions. These free ion energy levels and eigenstates are then used to calculate the oscillator strengths for all ground-state magnetic dipole absorption lines and the spontaneous emission rates for all magnetic dipole emission lines including transitions between excited states. A large number of strong magnetic dipole transitions are predicted throughout the visible and near-infrared spectrum, including many at longer wavelengths that would be ideal for experimental investigation of magnetic light-matter interactions with optical metamaterials and plasmonic antennas.

Figure 1

Plot of the magnetic dipole ground-state absorption lines and corresponding MD oscillator strengths for all trivalent lanthanide ions between 300 and $10000$ nm.

Figure 2

Magnetic dipole emission lines and corresponding vacuum emission rates for all trivalent lanthanide ions between 300 and 1700 nm. Strong emission lines with vacuum rates greater than 5 ${\mathrm{s}}^{-1}$ located above the dashed line are listed in Table .

Figure 3

Plot of all electric quadruple ground-state absorption lines and corresponding EQ oscillator strengths for all trivalent lanthanide ions between 300 and $10000$ nm.

Figure 4

Plot of all electric quadrupole emission lines and corresponding EQ vacuum emission rates for all trivalent lanthanide ions between 300 and 1700 nm.