Fig. 4: Determination of Er spin relaxation time.

a, b Double resonance spectra in the frequency range covering Ti ESR transitions \({{f}}_{{1}{,}{2}}^{{{{{{{\rm{Ti}}}}}}}}\) (a) without and (b) with simultaneous driving of Er at the ESR frequency of \({{f}}_{{3}}^{{{{{{{\rm{Er}}}}}}}}\). The peak intensities of \({{f}}_{{1}{,}{2}}^{{{{{{{\rm{Ti}}}}}}}}\) are related to the relative population of the Er spin states (insets). The spectra were normalized to the sum of their peak intensity. c ESR intensity ratios between \({\triangle I}_{{f}_{2}}^{{{{{{\rm{Ti}}}}}}}\) and \({\triangle I}_{{f}_{1}}^{{{{{{\rm{Ti}}}}}}}\) as a function of the driving strength V_rf2 at different Er ESR transition states (red, orange, and gray circles for \({{f}}_{{3}}^{{{{{{{\rm{Er}}}}}}}}\), \({{f}}_{{4}}^{{{{{{{\rm{Er}}}}}}}}\), and off-resonance, respectively). The solid curves show the correspondent simulation results by the rate equation model (Supplementary Section 9) for \({{f}}_{{3}}^{{{{{{{\rm{Er}}}}}}}}\) (red line), \({{f}}_{{4}}^{{{{{{{\rm{Er}}}}}}}}\) (orange line) and at an off-resonance frequency (gray line). The experimental points are given as black dots with error bars corresponding to 95% confidence interval. Set-point: I_dc = 15 pA, V_dc = 70 mV, V_rf = 30 mV, V_rf2 = 1–50 mV, B = 0.28 T, ϑ = 97°. d Schematics of the inversion recovery measurement in a pump-probe pulse scheme to determine the Er spin relaxation time \({T}_{1}^{{{{{{\rm{Er}}}}}}}\). Each sequence is composed of a pump pulse at the resonance frequency of \({{f}}_{{3}}^{{{{{{{\rm{Er}}}}}}}}\) (red box) and a probe pulse at the resonance frequency of \({{f}}_{{1}}^{{{{{{{\rm{Ti}}}}}}}}\) (blue box). The probe pulse follows the pump pulse after a delay time Δt. The population of the Er states after the pump pulse relaxes back to the thermal state following its T₁. e The experimental data for the inversion recovery measurement (blue circles) show the intensity of the ESR signal at the probe pulse \({{f}}_{{1}}^{{{{{{{\rm{Ti}}}}}}}}\) as a function of Δt. The black line shows the fit using an exponential function with \({T}_{1}^{{{{{{\rm{Er}}}}}}}\) of about 1 μs. Set-point: I_dc = 50 pA, V_dc = 70 mV, V_{rf pump} = 60 mV, V_{rf probe} = 100 mV, B = 0.28 T, ϑ = 97°.