  The magnetic properties tuning and volume dependence in the series of
quaternary full Heusler alloys with formula Co2Cr1-xYGa (Y = Ti, V, Mn, Fe, Co,
Ni) were studied with a detailed first-principles exploration. We employ the
density functional KKR method with the coherent potential approximation,
estimating effective Heisenberg exchange constants via the magnetic force
theorem together with mean-field Curie temperature (TC) and magnetic moment for
compositions in the whole concentration range. The volumetric dependency of
these magnetic properties is studied, particularly the pressure derivatives of
TC at equilibrium. Our ternary alloy calculations show good agreement with
local-density and generalized gradient approximations in the literature. The
quaternary alloys show a wide range of tunable magnetic properties, where
magnetic moments range from 0.8 to 4.9 mu_B, TC from 130 K to 1250 K, and
dTC/dV values range from -7 to +6.3 K A-3.
