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Muon spin rotation and infrared spectroscopy study of magnetism and superconductivity in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>Ba</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mo>โ</mml:mo><mml:mi>x</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi mathvariant="normal">K</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:msub><mml:mi>Fe</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi>As</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:mrow></mml:math>
Using muon spin rotation and infrared spectroscopy, we study the relation between magnetism and superconductivity in ${\mathrm{Ba}}_{1\ensuremath{-}x}{\mathrm{K}}_{x}{\mathrm{Fe}}_{2}{\mathrm{As}}_{2}$ single crystals from the underdoped to the slightly overdoped regime. We find that the Fe magnetic moment is only moderately suppressed in most of the underdoped region where it decreases more slowly than โฆ