${}_{}{}^{89}{}_{}{}^{}\mathrm{Y}$ NMR study of Zn-induced local moments and pair breaking in Y(${\mathrm{Ba}}_{1\mathrm{-}\mathit{y}}$${\mathrm{La}}_{\mathit{y}}$${)}_2$(${\mathrm{Cu}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Zn}}_{\mathit{x}}$${)}_4$${\mathrm{O}}_8$

${}_{}{}^{89}{}_{}{}^{}\mathrm{Y}$ NMR measurements have been carried out and modeled for underdoped Y(${\mathrm{Ba}}_{1\mathrm{-}\mathit{y}}$ ${\mathrm{La}}_{\mathit{y}}$ ${)}_2$(${\mathrm{Cu}}_{1\mathrm{-}\mathit{x}}$ ${\mathrm{Zn}}_{\mathit{x}}$ ${)}_4$ ${\mathrm{O}}_8$ superconductors. We find that the data are well described by Zn inducing a local moment, leading to a spin-density oscillation and an additional ${}_{}{}^{89}{}_{}{}^{}\mathrm{Y}$ hyperfine field. We find an exchange energy increasing from ∼50 to ∼104 meV as the hole concentration is increased and an induced local moment which declines from 1.35 to 1.06${\mathrm{\mu }}_{\mathit{B}}$. Magnetic pair breaking can fully account for the decrease in ${\mathit{T}}_{\mathit{c}}$ with Zn substitution for the La-free materials. With progressive underdoping, magnetic pair breaking is increasingly unable to account for the decline in ${\mathit{T}}_{\mathit{c}}$ with Zn substitution suggesting that Zn weakens the pairing interaction as in the spin-fluctuation pairing model.