Common Energy Scale for Magnetism and Superconductivity in Underdoped Cuprates: A Muon Spin Resonance Investigation of(CaxLa1−x)(Ba1.75−xLa0.25+x)Cu3Oy

We characterize the spontaneous magnetic field, and determine the associated temperature $T_g$, in the superconducting state of $\left({\mathrm{Ca}}_x{\mathrm{La}}_{1-x}\right)\left({\mathrm{Ba}}_{1.75-x}{\mathrm{La}}_{0.25+x}\right){\mathrm{Cu}}_3{\mathrm{O}}_y$ using zero and longitudinal field muon spin resonance measurements for various values of $x$ and $y$. Our major findings are (i) $T_g$ and $T_c$ are controlled by the same energy scale, (ii) the phase separation between hole poor and hole rich regions is a microscopic one, and (iii) spontaneous magnetic fields appear gradually with no moment size evolution.