Theory and Operation of Proton Spin Refrigerators: Sizable Proton Polarizations

The enhancement of proton spin polarization by the spin-refrigerator method, in crystals of Y (C₂H₅SO₄)₃ ·{}9 H₂O containing a few percent Yb³⁺, 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 (gII=3.4, g_⊥≈0) and relaxation rate (T₁ₑ^-1∝cos²θsin²θ), so the Yb spin polarization at θ=45^∘ can be transferred by cross-relaxation to the protons at θ=90^∘ 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.