  The viscosity of glass-forming liquids increases by many orders of magnitude
if their temperature is lowered by a mere factor of 2-3 [1,2]. Recent studies
suggest that this widespread phenomenon is accompanied by spatially
heterogeneous dynamics [3,4], and a growing dynamic correlation length
quantifying the extent of correlated particle motion [5-7]. Here we use a novel
numerical method to detect and quantify spatial correlations which reveal a
surprising non-monotonic temperature evolution of spatial dynamical
correlations, accompanied by a second length scale that grows monotonically and
has a very different nature. Our results directly unveil a dramatic qualitative
change in atomic motions near the mode-coupling crossover temperature [8] which
involves no fitting or indirect theoretical interpretation. Our results impose
severe new constraints on the theoretical description of the glass transition,
and open several research perspectives, in particular for experiments, to
confirm and quantify our observations in real materials.
