To understand the origin of muon spin relaxation and frequency shift in water with temperature, we performed weak transverse-field muon spin rotation and relaxation ($\mu \mathrm{SR}$) measurements over a temperature range of 220 K to 300 K. Using a conventional model with a phenomenological relaxation term, the spin relaxation of diamagnetic muons in frozen water (0.2473 $\pm$ 0.0061 MHz at 270 K) was found to be significantly higher than that in liquid water (0.0 $\pm$ 0.0020 MHz at 300 K). Furthermore, this conventional model reveals a non-negligible frequency shift below the freezing point. We propose a model that incorporates spin-dipole interactions between the muon in $\mathrm{MuOH}$ and the nearest-neighboring (first- and second-shell) protons of ${\mathrm{H}}_2\mathrm{O}$. This model reproduced the spectra well without the need for a phenomenological relaxation term. The validity of this model and quantitative information about spin-dependent interactions were tested using $\mathrm{MuOD}$ in ${\mathrm{D}}_2\mathrm{O}$ under identical field and temperature conditions. We also estimated the fractions of muons precessing with the Zeeman field versus those influenced by combined spin-dipole and Zeeman interactions in ${\mathrm{H}}_2\mathrm{O}$ and ${\mathrm{D}}_2\mathrm{O}$. This study provides deeper insights into $\mu \mathrm{SR}$ behavior in condensed matter, including water, hydrated samples, and aqueous solutions.

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• Electronic structure of atoms & molecules
• Muons
• Water
• Muon spin resonance