Hyperfine interaction of ${\mathrm{Er}}^{3+}$ ions in ${\mathrm{Y}}_2\mathrm{Si}{\mathrm{O}}_5$: An electron paramagnetic resonance spectroscopy study

Electron paramagnetic resonance (EPR) spectroscopy of rare earth ions in crystals is a powerful tool to analyze the hyperfine structure of the rare earth ground state. This can be useful for coherent spectroscopy and quantum information applications where the hyperfine structure of the electronic levels is used. In this work, we give a detailed analysis of the hyperfine structure of the ground state $\left[{}^{4}I_{15∕2}\left(0\right)\right]$ of ${\mathrm{Er}}^{3+}$ ions in ${\mathrm{Y}}_2\mathrm{Si}{\mathrm{O}}_5$. The electronic Zeeman, hyperfine, and quadrupole matrices are obtained from angular variations of the magnetic field in three orthogonal crystal planes. An excellent agreement is obtained between experimental and simulated magnetic field positions and relative intensities of EPR lines.

Figure 1

Experimental and calculated EPR spectra at $7\mathrm{K}$ of ${\mathrm{Er}}^{3+}$ in ${\mathrm{Y}}_2\mathrm{Si}{\mathrm{O}}_5$ for sites 1 and 2 with the magnetic field $\mathbf{B}$ parallel to the $\mathit{b}$ axis. The spectra were recorded at $9.5\mathrm{GHz}$ with a microwave power of $20\mathrm{mW}$.

Figure 2

Angular variation of the position (in mT) of the central line of the EPR spectra of ${\mathrm{Er}}^{3+}$ in ${\mathrm{Y}}_2\mathrm{Si}{\mathrm{O}}_5$. The magnetic field $\mathbf{B}$ varies in three orthogonal crystallographic planes: $(\mathit{b},{\mathit{D}}_1)$, $({\mathit{D}}_1,{\mathit{D}}_2)$ and $({\mathit{b}}^{\prime },{\mathit{D}}_2)$. See text for definition of ${\mathit{b}}^{\prime }$. The two crystallographic sites as well as the inequivalent magnetic sites are shown. Calculated curves using Eq. (1) are represented by solid lines.

Figure 3

Angular variation of the positions (in mT) of the eight allowed hyperfine transitions for ${\mathrm{Er}}^{3+}$ in ${\mathrm{Y}}_2\mathrm{Si}{\mathrm{O}}_5$. The magnetic field $\mathbf{B}$ varies in the $({\mathit{D}}_1,{\mathit{D}}_2)$ plane. The two crystallographic sites are shown. Calculated curves are represented by solid lines.

Figure 4

Angular variation of the positions (in mT) of the eight allowed hyperfine transitions for ${\mathrm{Er}}^{3+}$ in ${\mathrm{Y}}_2\mathrm{Si}{\mathrm{O}}_5$. The magnetic field $\mathbf{B}$ varies in the $(\mathit{b},{\mathit{D}}_1)$ plane. The two crystallographic sites are shown. Calculated curves are represented by solid lines.

Figure 5

Angular variation of the positions (in mT) of the eight allowed hyperfine transitions for ${\mathrm{Er}}^{3+}$ in ${\mathrm{Y}}_2\mathrm{Si}{\mathrm{O}}_5$. The magnetic field $\mathbf{B}$ varies in the $({\mathit{b}}^{\prime },{\mathit{D}}_2)$ plane. See text for definition of ${\mathit{b}}^{\prime }$. The two crystallographic sites are shown. Calculated curves are represented by solid lines.

Figure 6

Angular variation of the six quadrupole splittings (in mT) of forbidden hyperfine transitions for ${\mathrm{Er}}^{3+}$ in ${\mathrm{Y}}_2\mathrm{Si}{\mathrm{O}}_5$. The magnetic field $\mathbf{B}$ varies in the $({\mathit{D}}_1,{\mathit{D}}_2)$ plane. The two crystallographic sites are shown. Calculated curves are represented by solid lines.

Figure 7

Angular variation of the six quadrupole splittings (in mT) of forbidden hyperfine transitions for ${\mathrm{Er}}^{3+}$ in ${\mathrm{Y}}_2\mathrm{Si}{\mathrm{O}}_5$. The magnetic field $\mathbf{B}$ varies in the $(\mathit{b},{\mathit{D}}_1)$ plane. The two crystallographic sites are shown. Calculated curves are represented by solid lines.

Figure 8

Angular variation of the six quadrupole splittings (in mT) of forbidden hyperfine transitions for ${\mathrm{Er}}^{3+}$ in ${\mathrm{Y}}_2\mathrm{Si}{\mathrm{O}}_5$. The magnetic field $\mathbf{B}$ varies in the $({\mathit{b}}^{\prime },{\mathbf{D}}_2)$ plane. See text for definition of ${\mathit{b}}^{\prime }$. The two crystallographic sites are shown. Calculated curves are represented by solid lines.

Figure 9

Orientations of the principal axes of the $\mathbf{g}$, $\mathbf{A}$, and $\mathbf{Q}$ interactions with respect to the $(D_1,D_2,b)$ axis set for sites 1 and 2 of ${\mathrm{Er}}^{3+}$ in ${\mathrm{Y}}_2\mathrm{Si}{\mathrm{O}}_5$.