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At $x\approx0.25$$\mathrm{Ba}_{1-x}\mathrm{K}_{x}\mathrm{Fe}_{2}\mathrm{As}_{2}$ undergoes anovel first-order transition from a four-fold symmetric double-Q magnetic phaseto a two-fold symmetric single-Q phase, which was argued to occursimultaneously with the onset of superconductivity (B\"ohmer et al., Nat. Comm.6, 7911 (2015)). Here, by applying magnetic fields up to 10T, we investigate inmore detail the interplay of superconductivity with this magneto-structuraltransition using a combination of high-resolution thermal-expansion andheat-capacity measurements. We find that a magnetic field suppresses thereentrance of the single-Q orthorhombic phase more strongly than thesuperconducting transition, resulting in a splitting of the zero-fieldfirst-order transition. The suppression rate of the orthorhombic reentrancetransition is stronger for out-of-plane than for in-plane fields and scaleswith the anisotropy of the superconducting state. These effects are capturedwithin a phenomenological Ginzburg-Landau model, strongly suggesting that thesuppression of the reentrant orthorhombic single-Q phase is primarily linked tothe field-induced weakening of the superconducting order. Not captured by thismodel is however a strong reduction of the orthorhombic distortion forout-of-plane fields, which deserves further theoretical attention.

physical review. b./physical review. b

Interplay of stripe and double-Q magnetism with superconductivity in  $\mathrm{Ba}_{1-x}\mathrm{K}_{x}\mathrm{Fe}_{2}\mathrm{As}_{2}$ under the  influence of magnetic fields