  Contradictory results on the ferroelectric response of type II multiferroic
YBaCuFeO$_{5}$, in its incommensurate phase, has of late, opened up a lively
debate. There are ambiguous reports on the nature of the spiral magnetic state.
Using first-principles DFT calculations for the parent compound within
LSDA+U+SO approximation, the multiferroic response and the nature of spiral
state is revealed. The helical spiral is found to be more stable below the
transition temperature as spins prefer to lie in ab plane. The
Dzyaloshinskii-Moriya (DM) interaction and the spin current mechanism were
earlier invoked to account for the electric polarisation in this system.
However, the DM interaction is found to be absent, spin current mechanism is
not valid in the helical spiral state and there is no electric polarisation
thereof. These results are in good agreement with the recent single-crystal
data. We also investigate the magnetic transitions in
YBa$_{1-x}$Sr$_x$CuFeO$_5$ for the entire range $0\le x\le 1$ of doping. The
exchange interactions are estimated as a function of doping and a quantum Monte
Carlo (QMC) calculation on an effective spin Hamiltonian shows that the
paramagnetic to commensurate phase transition temperature increases with doping
till $x=0.5$ and decreases beyond. Our observations are consistent with
experimental findings.
