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 Ba1−xKxFe2As2 and Ba1−xNaxFe2As2, 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 Ba1−xKxFe2As2 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 Ba1−xKxFe2As2, 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. The phase diagram of iron-based superconductors of the BaFe 2 As 2 family is characterized by competing antiferromagnetic (AF) order and superconductivity. Usually, the AF order decreases with concentration (doping) and a dome of superconductivity surrounds the critical point.1 The AF order is a stripe-like spin-density wave, with a wavevector Q = (π, 0) and the magnetic moments lie in the plane. At the magnetic transition temperature, or slightly above it, the lattice changes from tetragonal at high temperature to orthorhombic at low temperature. 2,3In Ba 1−x X x Fe 2 As 2 , where X = K or Na, the phase diagram was recently found to be richer than this simple picture. Resistivity measurements under pressure revealed the existence of an internal transition inside the AF phase of Ba 1−x K x Fe 2 As 2 .4 As the onset temperature T N of the orthorhombic AF phase (o-AF) is suppressed with hydrostatic pressure P , an additional phase transition to a "new phase" appears below a transition temperature T 0 < T N , for 0.16 < x < 0.21, when P > 0.9 GPa.

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