  The 1111 compounds with an alternating sequence of fluorite and antifluorite
layers serve as structural hosts for the vast family of Fe-based
superconductors. Here, we use neutron powder diffraction and
density-functional-theory (DFT) band-structure calculations to study magnetic
order of Eu2+ in the [EuF]+ fluorite layers depending on the nature of the
[TAs]- antifluorite layer that can be non-magnetic semiconducting (T = Zn),
magnetic semiconducting (T = Mn), or magnetic metallic (T = Fe).
Antiferromagnetic transitions at TN ~ 2.4 - 3 K due to an ordering of the Eu2+
magnetic moments were confirmed in all three EuTAsF compounds. Whereas in
EuTAsF (T = Zn and Mn), the commensurate k1 = (1/2 1/2 0) stripe order pattern
with magnetic moments within the ab-plane is observed, the order in EuFeAsF is
incommensurate with k = (0 0.961(1) 1/2) and represents a cycloid of Eu2+
magnetic moments confined within the bc-plane. Additionally, the Mn2+
sublattice in EuMnAsF features a robust G-type antiferromagnetic order that
persists at least up to room temperature, with magnetic moments along the
c-direction. Although DFT calculations suggest stripe antiferromagnetic order
in the Fe-sublattice of EuFeAsF as the ground state, neutron diffraction
reveals no evidence of long-range magnetic order associated with Fe. We show
that the frustrating interplane interaction J3 between the adjacent [EuF]+
layers is comparable with in-plane J1-J2 interactions already in the case of
semiconducting fluorite layers [TAs]- (T = Zn and Mn) and becomes dominant in
the case of the metallic [FeAs]- ones. The latter, along with a slight
orthorhombic distortion, is proposed to be the origin of the incommensurate
magnetic structure observed in EuFeAsF.

Strongly Correlated Electrons