Fig. 2: Thermodynamically optimized Boltzmann cryothermometry with Gd³⁺ in YAB:Pr³⁺, Gd³⁺.

a Splitting of the lowest excited ⁶P_7/2 spin-orbit level of Gd³⁺ into the different Kramers’ doublets at the present D₃ site symmetry in YAB. The doped Gd³⁺ ions are sixfold coordinated in the form of a twisted trigonal prism (inset). b Indirect upconversion excitation scheme for Gd³⁺ by energy transfer from the 4f¹5d¹-related electronic states of Pr³⁺. Both the ground state absorption (GSA) and the excited state absorption (ESA) of two 450 nm photons within the pulse period (T = 50 ms) of the used pulsed laser source are indicated. c High-resolution upconversion photoluminescence spectra of YAB: 0.7% Pr³⁺, 20% Gd³⁺ upon excitation of Pr³⁺ at 448 nm showing the temperature dependence of the two radiative transitions from the lower and higher crystal field states of the ⁶P_7/2 level. The arrows mark the two thermometrically employed transitions. d Boltzmann plot of the temperature-dependent LIR normalized to its value at 300 K. The fitted energy gap, statistical figures of merit, and expected onset temperature for Boltzmann behaviour (see Eq. (5)) are indicated