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

Abstract

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 $(1/T_{1}T)$ 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$A^{\prime \prime }{B}_2$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${}_7$.