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We characterize the magnetic properties for thulium ion energy levels in theY$_3$Ga$_5$O$_{12}$ (Tm:YGG) lattice with the goal to improve decoherence andreduce line-width broadening caused by local host spins and crystalimperfections. More precisely, we measure hyperfine tensors for the lowestlevel of the, $^3$H$_6$, and excited, $^3$H$_4$, states using a combination ofspectral hole burning, absorption spectroscopy, and optically detected nuclearmagnetic resonance. By rotating the sample through a series of angles with anapplied external magnetic field, we measure and analyze the orientationdependence of the Tm$^{3+}$ ion's spin-Hamiltonian. Using thisspin-Hamiltonian, we propose a set of orientations to improve materialproperties that are important for light-matter interaction and quantuminformation applications. Our results yield several important external fielddirections: some to extend optical coherence times, another to improve spininhomogeneous broadening, and yet another that maximizes mixing of the spinstates for specific sets of ions, which allows improving optical pumping andcreation of lambda systems in this material.

Measurement of the Thulium Ion Spin Hamiltonian Within a Yttrium Gallium Garnet Host Crystal