Zero field splitting fluctuations induced phase relaxation of Gd³⁺ in frozen solutions at cryogenic temperatures

Distance measurements using double electron-electron resonance (DEER) and Gd³⁺ chelates for spin labels (GdSL) have been shown to be an attractive alternative to nitroxide spin labels at W-band (95 GHz). The maximal distance that can be accessed by DEER measurements and the sensitivity of such measurements strongly depends on the phase relaxation of Gd³⁺ chelates in frozen, glassy solutions. In this work, we explore the phase relaxation of Gd³⁺-DOTA as a representative of GdSL in temperature and concentration ranges typically used for W-band DEER measurements. We observed that in addition to the usual mechanisms of phase relaxation known for nitroxide based spin labels, GdSL are subjected to an additional phase relaxation mechanism that features an increase in the relaxation rate from the center to the periphery of the EPR spectrum. Since the EPR spectrum of GdSL is the sum of subspectra of the individual EPR transitions, we attribute this field dependence to transition dependent phase relaxation. Using simulations of the EPR spectra and its decomposition into the individual transition subspectra, we isolated the phase relaxation of each transition and found that its rate increases with |m_s|. We suggest that this mechanism is due to transient zero field splitting (tZFS), where its magnitude and correlation time are scaled down and distributed as compared with similar situations in liquids. This tZFS induced phase relaxation mechanism becomes dominant (or at least significant) when all other well-known phase relaxation mechanisms, such as spectral diffusion caused by nuclear spin diffusion, instantaneous and electron spin spectral diffusion, are significantly suppressed by matrix deuteration and low concentration, and when the temperature is sufficiently low to disable spin lattice interaction as a source of phase relaxation.