  Understanding defect-phonon interactions in solid-state devices is crucial
for improving our current knowledge of quantum platforms. In this work, we
develop first-principles calculations for a defect composed of two spin-$1/2$
particles that interact with phonon modes in a one-dimensional lattice. We
follow a bottom-up approach that begins with a dipolar magnetic interaction to
ultimately derive the spectral density function and time-local master equation
that describes the open dynamics of the defect. We provide theoretical and
numerical analysis for the non-Markovian features of the defect-phonon dynamics
induced by a pure dephasing channel acting on the Bell basis. Finally, we
analyze two measures of non-Markovianity based on the canonical rates and
Coherence, shedding more light on the role of the spectral density function and
temperature; and envisioning experimental realizations.
