  The accurate thermoelastic properties and thermal conductivity are crucial in
understanding the thermal evolution of the Martian core. A fitting method based
on the ab initio calculated pressure-volume-temperature data is proposed in the
formulation of the equation of state with high accuracy, by which the pressure
and temperature dependent thermoelastic properties can be directly calculated
by definitions. The ab initio results show that the liquid Fe0.75S0.25 under
Martian core condition is thoroughly in the ferromagnetic state, without
existing spin crossover. The liquid Fe0.75S0.25 in magnetic calculation owns a
low thermal conductivity (21~23 W/m/K) when compared with non-magnetic
calculation at the same state. Based on the Insight estimated and ab initio
calculated properties of the Martian core, the iron snow model is verified when
the current temperature at the core-mantle boundary is below the core melting
temperature, and the simply secular cooling model is verified on the contrary.
