  We present a study of the magnetic-field effect on spin correlations in the
charge ordered triangular Ising system LuFe2O4+{\delta} through single crystal
neutron diffraction. In the absence of a magnetic field, the strong diffuse
neutron scattering observed below the Neel temperature (TN = 240 K) indicates
that LuFe2O4+{\delta} shows short-range, two-dimensional (2D) correlations in
the FeO5 triangular layers, characterized by the development of a magnetic
scattering rod along the 1/3 1/3 L direction, persisting down to 5 K. We also
found that on top of the 2D correlations, a long range ferromagnetic component
associated with the propagation vector k1 = 0 sets in at around 240 K. On the
other hand, an external magnetic field applied along the c-axis effectively
favours a three-dimensional (3D) spin correlation between the FeO5 bilayers
evidenced by the increase of the intensity of satellite reflections with
propagation vector k2 = (1/3, 1/3, 3/2). This magnetic modulation is identical
to the charge ordered superstructure, highlighting the field-promoted coupling
between the spin and charge degrees of freedom. Formation of the 3D spin
correlations suppresses both the rod-type diffuse scattering and the k1
component. Simple symmetry-based arguments provide a natural explanation of the
observed phenomenon and put forward a possible charge redistribution in the
applied magnetic field.
