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BaFe$_2$As$_2$ is the parent compound for a family of iron-basedhigh-temperature superconductors as well as a prototypical example of thespin-density wave (SDW) system. In this study, we perform an optical pump-probestudy of this compound to systematically investigate the SDW order across thepressure-temperature phase diagram. The suppression of the SDW order bypressure manifests itself by the increase of relaxation time together with thedecrease of the pump-probe signal and the pump energy necessary for completevaporization of the SDW condensate. We have found that the pressure-drivensuppression of the SDW order at low temperature occurs gradually in contrast tothe thermally-induced SDW transition. Our results suggest that thepressure-driven quantum phase transition in BaFe$_2$As$_2$ (and probably otheriron pnictides) is continuous and it is caused by the gradual worsening of theFermi-surface nesting conditions.

Ultrafast Relaxation Dynamics of Spin-Density Wave Order in BaFe$_2$As$_2$ under High Pressures