Random singlet physics in the $S = \frac{1}{2}$ pyrochlore antiferromagnet NaCdCu$_2$F$_7$

We report a random singlet ground state in the $S=\frac{1}{2}$ Heisenberg pyrochlore antiferromagnet NaCdCu$_2$F$_7$. Cationic Na$^+$/Cd$^{2+}$ disorder on the pyrochlore $A$ site generates a broad distribution of Cu$^{2+}$--F$^-$--Cu$^{2+}$ exchange couplings, introducing intrinsic magnetic bond disorder. Despite strong antiferromagnetic interactions ($\theta_{\mathrm{CW}}=-72$~K), no magnetic order or global spin freezing is observed in DC and AC susceptibility, specific heat or $^{23}$Na nuclear magnetic resonance to 120 mK, with muon spin relaxation experiments confirming persistent spin dynamics to 58 mK. $T$-linear specific heat, a Curie-like susceptibility tail, and power-law scaling with data collapse in $\chi(T)$, $M(H)$, $C_{\mathrm{mag}}/T$, $^{23}$Na $(1/T_1T)$ and the muon spin polarization $P(t)$ reveal a disorder-driven network of random singlets and orphan spins. Scaling across multiple bulk and local probes is consistent with a broad distribution of exchange energies, $P[\mathcal{J}] \sim \mathcal{J}^{-\alpha}$. This behavior contrasts with previously-studied Na$A''B_2$F$_7$ pyrochlore fluorides, where magnetic bond disorder precipitates spin-glass freezing, underscoring the crucial role of strong $S=\frac{1}{2}$ quantum fluctuations in NaCdCu$_2$F$_7$.