The dynamic nuclear polarization (DNP) of lanthanum ($^{139}$La) nuclei has been studied in a magnetic field of 2.3 T and at a temperature of 1.5 K with a single crystal of lanthanum aluminate (LaAlO$_3$) doped with neodymium (Nd$^{3+}$) ions at a concentration of about 0.03 mol\% as a paramagnetic ion.
However, a fine optimization of the Nd in the crystals has not yet been attempted, and a lower Nd$^{3+}$ concentration is promising for a longer spin-lattice relaxation time (T$_1$), which is crucial for the realization of polarized $^{139}$La targets for time-reversal invariance searches in compound nuclear resonance with a slow neutron.
In a first attempt, we have successfully grown small single crystals with different Nd concentrations to optimize at the 0.01 mol\% level and have performed evaluation of 0.01 mol\% and 0.05 mol\% crystals by measuring maximum polarization and relaxation times in a simple DNP test using a one-shot dewar. However, crystals below 0.01 mol\% have such long relaxation times that polarization and relaxation times cannot be adequately measured, and a DNP system is required for long-term measurements.

In this paper, we report on future prospects based on the current state of research and development of the polarized $^{139}$La target at three points: crystal growth methods, simple DNP tests for crystal selection, and preparation of a DNP system for long-term measurements.