Theory and Operation of Proton Spin Refrigerators: Sizable Proton Polarizations

Abstract

The enhancement of proton spin polarization by the spin-refrigerator method, in crystals of Y ${\left({\mathrm{C}}_2{\mathrm{H}}_5\mathrm{S}{\mathrm{O}}_4\right)}_3$ ·9 ${\mathrm{H}}_2$O containing a few percent ${\mathrm{Yb}}^{3+}$, is studied experimentally and theoretically. The spin refrigerator is operated simply by rotating the crystal in a magnetic field at liquid-helium temperatures, or by subjecting the crystal to a pulsed rotating field. The proton polarization comes about because the Yb spins have both anisotropic $g$ value ($g_{\mathrm{II}}=3.4, g_{\perp }\approx 0$) and relaxation rate (${T_{1e}}^{-1\mathrm{}}\propto {cos}^2\theta {sin}^2\theta$), so the Yb spin polarization at $\theta =45\mathrm{}°$ can be transferred by cross-relaxation to the protons at $\theta =90\mathrm{}°$ by rapid rotation of the crystal or field between these two orientations. A unified theory involving electronic and nuclear spin-lattice relaxation, cross-relaxation, and nuclear spin diffusion explains the results of both types of spin refrigerator, and predicts that polarizations as high as 70% may be achieved at higher operating speeds. Proton polarizations as high as 35% are reported, suggesting application to polarized targets.