Electron spin dynamics in $\mathrm{C}{\mathrm{e}}^{3+}$ : YAG crystals: Hyperfine interaction of $4f$ and $5d$ electrons

The electron spin dynamics of $\mathrm{C}{\mathrm{e}}^{3+}$ ions in YAG crystals is studied by time-resolved photoluminescence spectroscopy with an alternating left and right circularly polarized continuous-wave laser modulation technique. The electron spin relaxation due to hyperfine interaction with randomly oriented nuclear spins can be efficiently suppressed by a weak external longitudinal magnetic field. The suppression of the hyperfine-induced spin relaxation makes the electron spin polarization increase from 0.001 to 0.016 for the lowest $4f$ state, and from 0.08 to 0.32 for the lowest $5d$ state. The suppression magnetic fields for the $4f$ electrons are several times weaker than that for the $5d$ electrons, dependent on the crystal orientation. The dispersion of the local hyperfine field distribution $\mathrm{\Delta }B$ is isotropic and equal to 4.0 mT for the $5d$ electrons, and anisotropic for the $4f$ electrons with $\mathrm{\Delta }{B}_{\left[001\right]}=0.8\mathrm{mT},\mathrm{\Delta }{B}_{\left[110\right]}=1.1\mathrm{mT},\mathrm{\Delta }{B}_{\left[1\overline{1}0\right]}=2.4\mathrm{mT}$. The hyperfine coupling strength for the $4f$ electrons is ∼4 times weaker than that for the $5d$ electrons.

Figure 1

Experimental setup for electron spin dynamics measurements. The sample $\mathrm{C}{\mathrm{e}}^{3+}$: YAG crystal is [111] oriented. Light vector $\mathit{k}\left|\right|$ magnetic field $\mathit{B}\left|\right|$ [111]. EOM: electro-optical modulator; G-L: Glan-laser polarizer. F1-500 nm long wave pass filter; F2-532 nm band pass filter with bandwidth 10 nm. APD: avalanche photodiode.

Figure 2

PL spectra of $\mathrm{C}{\mathrm{e}}^{3+}$ : YAG crystals under ${\sigma }^{+}$ and ${\sigma }^{-}$ circular polarization excitation at low temperature $T=5\mathrm{K}$. The longitudinal magnetic field (a) $B=0\mathrm{mT}$ and (b) $B=100\mathrm{mT}$. The excitation wavelength is 473 nm. The signal detection is fixed in the ${\sigma }^{+}$ polarization mode.

Figure 3

PL transients under periodic circularly polarized switching excitation at zero and weak external magnetic field $B=30\mathrm{mT}$ for low temperature $T=5\mathrm{K}$; signal detection is always in the ${\sigma }^{+}$ polarization mode.

Figure 4

(a) Optical transitions of $\mathrm{C}{\mathrm{e}}^{3+}$ ions in YAG crystals under circularly polarized light excitation. ↑, ↓ : electron spin; ${\tau }_{\mathrm{ph}}$ : the electron lifetime in the $5d{\left(1\right)}^{\mathrm{ph}}$ state; $\tau ,{\tau }_1$, and ${\tau }_2$ : the radiative lifetimes of the $5d$(1) state; ${\tau }_3$ : the time of the transition from $4f\left(n\right)$ to $4f$(1); ${\tau }_{\mathrm{s}}^{\mathrm{ph}},{\tau }_{\mathrm{s}}^{\mathrm{exc}},{\tau }_{\mathrm{s}}$, and ${\tau }_{\mathrm{s}}^e$ : spin-flip time of electrons in the $5d{\left(1\right)}^{\mathrm{ph}},5d$(1), $4f\left(n\right)$, and $4f$(1), respectively; $P_{\pm }$ : optical pumping rates. (b) Schematic of electron spin excitation and evolution dynamics.

Figure 5

External magnetic field dependence of the electron spin polarization of the $\mathrm{C}{\mathrm{e}}^{3+}$ ion in YAG crystals $\left(T=5\mathrm{K}\right)$. (a) ${\rho }_{\mathrm{s}}^{\mathrm{g}}$ : the electron spin polarization of the $4f$(1) state. (b) ${\rho }_{\mathrm{s}}^{\mathrm{exc}}$ : the electron spin polarization of the $5d$(1) state. (c) Calculated magnetic field dependence of $R_{\parallel }\left(\infty \right)$ according to Eq. (16) for an ensemble electron spin polarization that is instantaneously created. (d) Excitation power dependence of relaxation rates $1/{\tau }_R$ at $B=30\mathrm{mT}$.