Isotope Dependence of the Spin Gap in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>YBa</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi>Cu</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi>O</mml:mi></mml:mrow><mml:mrow><mml:mn>8</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>as Determined by Cu NQR Relaxation

We performed high accuracy ${}^{63}\mathrm{Cu}$ NQR spin-lattice relaxation and SQUID magnetization measurements on ${}^{16}\mathrm{O}$ and ${}^{18}\mathrm{O}$ exchanged ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{4}{\mathrm{O}}_{8}$ to determine the isotope shift of the temperature of the opening of the spin gap, ${T}^{*}$, and the superconducting transition temperature, ${T}_{c}$. The corresponding isotope exponents are ${\ensuremath{\alpha}}_{{T}^{*}}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.061(8)$ and ${\ensuremath{\alpha}}_{{T}_{c}}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.056(12)$ which are the same within the error bars and suggest a common origin for the superconducting and the spin gap.

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