  Periodic driving can be used to coherently control the properties of a
many-body state and to realize new phases which are not accessible in static
systems. For example, exposing materials to intense laser pulses enables to
provoke metal-insulator transitions, control the magnetic order and induce
transient superconducting behaviour well above the static transition
temperature. However, pinning down the responsible mechanisms is often
difficult, since the response to irradiation is governed by complex many-body
dynamics. In contrast to static systems, where extensive calculations have been
performed to explain phenomena such as high-temperature superconductivity,
theoretical analyses of driven many-body Hamiltonians are more demanding and
new theoretical approaches have been inspired by the recent observations. Here,
we perform an experimental quantum simulation in a periodically modulated
hexagonal lattice and show that anti-ferromagnetic correlations in a fermionic
many-body system can be reduced or enhanced or even switched to ferromagnetic
correlations. We first demonstrate that in the high frequency regime, the
description of the many-body system by an effective Floquet-Hamiltonian with a
renormalized tunnelling energy remains valid, by comparing the results to
measurements in an equivalent static lattice. For near-resonant driving, the
enhancement and sign reversal of correlations is explained by a microscopic
model, in which the particle tunnelling and magnetic exchange energies can be
controlled independently. In combination with the observed sufficiently long
lifetime of correlations, Floquet engineering thus constitutes an alternative
route to experimentally investigate unconventional pairing in strongly
correlated systems.
