In the temperature-concentration phase diagram of most iron-based superconductors, antiferromagnetic order is gradually suppressed to zero at a critical point, and a dome of superconductivity forms around that point. The nature of the magnetic phase and its fluctuations is of fundamental importance for elucidating the pairing mechanism. In Ba{1-x}KxFe2As2 and Ba{1-x}NaxFe2As2, it has recently become clear that the usual stripe-like magnetic phase, of orthorhombic symmetry, gives way to a second magnetic phase, of tetragonal symmetry, near the critical point, between x = 0.24 and x = 0.28. Here we report measurements of the electrical resistivity of Ba{1-x}KxFe2As2 under applied hydrostatic pressures up to 2.75 GPa, for x = 0.22, 0.24 and 0.28. We track the onset of the tetragonal magnetic phase using the sharp anomaly it produces in the resistivity. In the temperature-concentration phase diagram of Ba{1-x}KxFe2As2, we find that pressure greatly expands the tetragonal magnetic phase, while the stripe-like phase shrinks. This raises the interesting possibility that the fluctuations of the former phase might be involved in the pairing mechanism responsible for the superconductivity.
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