  We present the results of high-field magnetization and muon-spin relaxation
measurements on the coordination polymer CuF_2(H_2O)_2(pyrazine) in pressures
up to 22.5 kbar. We observe a transition from a quasi-two-dimensional to a
quasi-one-dimensional antiferromagnetic phase at 9.1 kbar, driven by a rotation
of the Jahn-Teller axis. Long-range antiferromagnetic ordering is seen in both
regimes, as well as a phase separation in the critical pressure region. The
magnetic dimensionality switching as pressure is increased is accompanied by a
halving of the primary magnetic exchange energy J and a fivefold decrease in
the ordering temperature T_N. J decreases gradually with pressure in the
two-dimensional phase, and then increases in the one-dimensional regime. We
relate both effects to the changes in the crystal structure with applied
pressure.
