Influence of thermal noise on the field-driven dynamics of the non-collinear antiferromagnet Mn3Sn

$\mathrm{Mn_3Sn}(0\overline{1}\overline{1}0)[0001]$ experiences a tensile strain when grown epitaxially on $\mathrm{MgO}(110)[001]$, and thus the energy landscape changes from six-fold symmetry to two-fold symmetry. External magnetic field further breaks the symmetry and the resulting energy landscape is sensitive to the field orientation relative to the easy axis. In the presence of thermal noise, the relaxation of the magnetic octupole moment in a strained Mn$_3$Sn film is composed of four distinct escape processes involving the two saddle points and two equilibrium states in the energy landscape. Here, we apply harmonic transition-state theory to derive analytical expressions for the inter-well escape time and octupole moment relaxation time, both influenced by an external symmetry-breaking magnetic field and finite thermal noise in the intermediate-to-high damping regime. The analytical predictions are in strong agreement with comprehensive numerical simulations based on coupled LLG equations. The results presented here are crucial toward realizing Mn$_3$Sn's applications in random number generation and probabilistic computing.