Crystal field and hyperfine structure of ${}^{167}\mathrm{Er}^{3+}$ in $\mathrm{YP}{\mathrm{O}}_4$:Er single crystals: High-resolution optical and EPR spectroscopy

We report on a high-resolution optical and magneto-optical spectroscopy, luminescence, and electron paramagnetic resonance (EPR) studies of yttrium orthophosphate single crystals doped with erbium, which are promising telecom-wavelength materials for applications in quantum electronics and quantum information processing. An observation of the hyperfine structure in optical spectra of ${}^{167}\mathrm{Er}$ isotope in ${\mathrm{Er}:\mathrm{YPO}}_4$ is presented. Energies and symmetries of 40 crystal-field levels of ${\mathrm{Er}}^{3+}$ in ${\mathrm{Er}:\mathrm{YPO}}_4$ and $g$ factors of some of them were determined and successfully modeled on the basis of crystal-field calculations. The obtained set of crystal-field parameters was used in modeling the hyperfine structure observed in the optical and EPR spectra of ${\mathrm{Er}:\mathrm{YPO}}_4$ single crystals.

Figure 1

Experimental setup for recording the absorption and luminescence spectra and kinetics of the luminescence (including in a magnetic field $\mathit{B}$). AOM – acousto-optic modulator, ADC – analog-to-digital converter, AWG – arbitrary-waveform generator, PMT – photomultiplier, D – detector (avalanche photodiode Thorlabs APD110C/M), Laser – dye TekhnoScan DYE-SF-077 or Ti:Sapphire (TIS-SF-777) or diode (CTL 1500 - TOPTICA Photonics AG) lasers. Green dashed lines denote USB2.0 connections and black dashed lines are for electrical 50-Ω connections between devices.

Figure 2

High-resolution ($0.01{\mathrm{cm}}^{-1}$) (a),(c),(e),(g) σ- and (b),(d),(f),(h) π-polarized transmission spectra of ${\mathrm{YPO}}_4$ single crystal doped with ${\mathrm{Er}}^{3+}$ in the regions of optical transitions from the ground state to the (a),(b) ${}^{4}I_{13/2}$, (c),(d) ${}^{4}I_{11/2}$, (e),(f) ${}^{4}I_{9/2}$, and (g),(h) ${}^{4}F_{9/2}$ CF multiplets at 5.3 K. Doping concentrations were (a),(b),(c),(d) 0.2 at.% and (e),(f),(g),(h) 0.4 at.%.

Figure 3

Luminescence spectra of the ${\mathrm{YPO}}_4:{\mathrm{Er}}^{3+}$ (0.2 at. %) single crystal in the regions of (a) ${}^{4}I_{13/2}\to {}^{4}I_{15/2}$ and (b) ${}^{4}I_{11/2}\to {}^{4}I_{15/2}$ optical transitions at different temperatures indicated above the spectra. Unpolarized (black lines), σ- (red line), and π- (blue line) polarized luminescence.

Figure 4

(a) Zeeman splitting of the spectral line $6531.6{\mathrm{cm}}^{-1}$ corresponding to the ${\mathrm{\Gamma }}_7^1\left({}^{4}I_{15/2}\right)\to {\mathrm{\Gamma }}_6^1({}^{4}I_{13/2}$) optical transition of ${\mathrm{Er}}^{3+}$ in ${\mathrm{YPO}}_4:\mathrm{Er}$ (0.01 at.%) subjected to a magnetic field $\mathbf{B}\left|\right|c, B=0.21\mathrm{T}$ in the σ (red lower trace) and π (blue upper trace) polarizations. Inset: Field dependences of the Zeeman splittings $\mathrm{\Delta }{\nu }_{\sigma }$ (red symbols) and $\mathrm{\Delta }{\nu }_{\pi }$ (blue symbols and line) in the σ and π polarizations, respectively. $T=5\mathrm{K}$. (b) Scheme showing Zeeman splitting of the corresponding Kramers doublets and allowed transitions between them.

Figure 5

(a) EPR spectra of the ${\mathrm{YPO}}_4$:Er (0.1%) single crystal in the $\mathbf{B}\left|\right|c$ orientation of an external magnetic field, at the frequencies (1) 9.4 GHz; (2) 36.3 GHz, (3) 48 GHz, (4) 60.2 GHz. $T=5\mathrm{K}$ (1), $T=4.2\mathrm{K}$ (2–4). Inset: spectrum 1 in more detail; blue vertical lines represent positions of the calculated hyperfine components. (b) Calculated hyperfine energy levels corresponding to the ground ${}^4{I}_{15/2}\left({\mathrm{\Gamma }}_7^1\right)$ Kramers doublet in a magnetic field. The arrows indicate EPR transitions at the frequency 9.4 GHz. The calculations are detailed in Sec. 4.

Figure 6

The $6531.6{\mathrm{cm}}^{-1}$ absorption line of ${\mathrm{Er}}^{3+}$ in ${\mathrm{Er}:\mathrm{YPO}}_4$ registered at $T=5\mathrm{K}, B=0$ (a),(b) by a tunable single-frequency laser, Er concentration 0.005 at.% and (c),(d) by a high-resolution Fourier spectrometer, thick solid, dash-dotted, and thin solid spectral traces represent the data for 0.1, 0.2, and 0.4 at.% of erbium, respectively. (a),(c) σ and (b),(d) π polarizations. Bars in (a) and (b) represent the calculated hyperfine structure in the spectra of ${}^{167}\mathrm{Er}^{3+}$; the dashed lines in (c) and (d) show the results of modeling (the linewidth of $7\times 10–3{\mathrm{cm}}^{-1}$ was attributed to each hyperfine component of the line, to account for the inhomogeneous broadening, see the text).

Figure 7

The calculated ($B=0$) hyperfine structure schemes of the ground Kramers doublet (left) and of the lowest-energy Kramers doublet in the ${}^{4}I_{13/2}$ multiplet (right) of ${}^{167}\mathrm{Er}$ in ${\mathrm{YPO}}_4$, involved in the formation of HFS of the spectral line $6531.6{\mathrm{cm}}^{-1}$. Doublet (singlet) hyperfine levels are represented by solid (dotted) lines.

Figure 8

${}^{4}I_{13/2}\to {}^{4}I_{15/2}$ luminescence excitation and decay of ${\mathrm{Er}}^{3+}$ in ${\mathrm{YPO}}_4$:Er (0.1 at.%) at $T=5\mathrm{K}$. Inset: Luminescence decay in a logarithmic scale and exponential approximation (red line) with lifetime $5.1\pm 0.2\mathrm{ms}$.