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Spin-gap evolution upon Ca doping in the spin-ladder series Sr<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mrow /><mml:mrow><mml:mn>14</mml:mn><mml:mo>−</mml:mo><mml:mi>x</mml:mi></mml:mrow></mml:msub></mml:math>Ca<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mrow /><mml:mi>x</mml:mi></mml:msub></mml:math>Cu<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mrow /><mml:mn…
The spin-gap evolution upon Ca doping in Sr${}_{14\ensuremath{-}x}$Ca${}_{x}$Cu${}_{24}$O${}_{41}$ was systematically investigated using inelastic neutron scattering. We discover that the singlet-triplet spin-gap excitation survives in this series with $x$ up to 13, indicating the singlet dimer ground state in these compounds. This observation corrects the previous speculation that the spin gap …