Observation of Two-Magnon Bound States in the Two-Leg Ladders of $(Ca,La{)}_{14}{\mathrm{Cu}}_{24}{O}_{41}$

Phonon-assisted two-magnon absorption is studied in the spin- $1/2$ two-leg ladders of $(\mathrm{Ca},\mathrm{La}{)}_{14}{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}$ for $E\parallel c$ (legs) and $E\parallel a$ (rungs). We verify the theoretically predicted existence of two-magnon singlet bound states, which give rise to peaks at $\approx 2140$ and $2800{\mathrm{cm}}^{-1\mathrm{}}$. The two-magnon continuum is observed at $\approx 4000{\mathrm{cm}}^{-1\mathrm{}}$. Two different theoretical approaches (Jordan-Wigner fermions and perturbation theory) describe the data very well for $J_{\parallel }\approx 1020–1100{\mathrm{cm}}^{-1\mathrm{}}$, $J_{\parallel }{/J}_{\perp }\approx 1–1.2$. At high energies, the magnetic contribution to $\sigma \left(\omega \right)$ is strikingly similar in the ladders and in the undoped high- $T_c$ cuprates, which emphasizes the importance of strong quantum fluctuations in the latter.