  The helicity structure of the diffractive electroproduction of rho mesons, e
+ p -> e + rho + Y, is studied in a previously unexplored region of large
four-momentum transfer squared at the proton vertex, t: 0 < t' < 3 GeV^2, where
t' = |t| - |t|_min. The data used are collected with the H1 detector at HERA in
the kinematic domain 2.5 < Q^2 < 60 GeV^2, 40 < W < 120 GeV. No t dependence of
the r^04_00 spin density matrix element is found. A significant t dependent
helicity non-conservation from the virtual photon to the rho meson is observed
for the spin density matrix element combinations r^5_00+2r^5_11 and
r^1_00+2r^1_11. These t dependences are consistently described by a
perturbative QCD model based on the exchange of two gluons.
