  Mn-based full Heusler compounds possess well-defined local atomic Mn moments,
and thus the correlation effects between localized d electrons are expected to
play an important role in determining the electronic and magnetic properties of
these materials. Employing ab-initio calculations in conjunction with the
constrained random-phase approximation (cRPA) method, we calculate the strength
of the effective on-site Coulomb interaction parameters (Hubbard U and Hund
exchange J) in the case of X2MnZ full Heusler compounds with X being one of Ni,
Pd or Cu, and Z being one of In, Sn, Sb or Te. We show that the Z element (or
sp element) in Heusler compounds significantly reduces the strength of the
Hubbard U parameter for Mn 3d electrons compared to the elementary bulk Mn. On
the contrary, the effect of the sp-atom on the strength of the U parameter of
Ni, Cu or Pd valence d electrons is not so substantial with respect to the
elementary bulk values. The U values for all transition metal atoms decrease
with increasing sp electron number in the In-Sn-Sb-Te sequence. Our cRPA
calculations reveal that despite their well-defined local magnetic moments, the
Mn-based full Heusler alloys fall into the category of the weakly correlated
materials.
