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

Andrej Kancko, Hironori Sakai, Cinthia Antunes Corrêa, Petr Proschek, Jan Prokleška, Tetiana Haidamak, Marc Uhlarz, Adam Berlie, Yo Tokunaga, Ross Harvey Colman

TL;DR

The study establishes NaCdCu$_2$F$_7$ as the first confirmed $S=\frac{1}{2}$ pyrochlore antiferromagnet hosting a random singlet ground state in three dimensions. Quenched A-site disorder induces a broad distribution of Cu$^{2+}$--F$^-$--Cu$^{2+}$ exchange energies, yielding a disorder-driven network of singlets and orphan spins that survive to at least $58$ mK, with no spin-glass freezing. Across DC/AC susceptibility, specific heat, $^{23}$Na NMR, and local-probe $\mu$SR, the data exhibit reliable power-law scaling and data collapse consistent with $P[\mathcal{J}]\sim \mathcal{J}^{-\alpha}$ and a gapless excitation spectrum, including a $T$-linear $C_{\rm mag}$ and a Curie-like tail in $\chi$. The results highlight the role of strong $S=\frac{1}{2}$ quantum fluctuations in stabilizing a 3D random-singlet phase and provide a benchmark for testing theories of disorder-driven quantum magnetism.

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 ($θ_{\mathrm{CW}}=-72$~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 $χ(T)$, $M(H)$, $C_{\mathrm{mag}}/T$, $^{23}$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, $P[\mathcal{J}] \sim \mathcal{J}^{-α}$. 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$_7$.

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

TL;DR

The study establishes NaCdCuF as the first confirmed pyrochlore antiferromagnet hosting a random singlet ground state in three dimensions. Quenched A-site disorder induces a broad distribution of Cu--F--Cu exchange energies, yielding a disorder-driven network of singlets and orphan spins that survive to at least mK, with no spin-glass freezing. Across DC/AC susceptibility, specific heat, Na NMR, and local-probe SR, the data exhibit reliable power-law scaling and data collapse consistent with and a gapless excitation spectrum, including a -linear and a Curie-like tail in . The results highlight the role of strong quantum fluctuations in stabilizing a 3D random-singlet phase and provide a benchmark for testing theories of disorder-driven quantum magnetism.

Abstract

We report a random singlet ground state in the Heisenberg pyrochlore antiferromagnet NaCdCuF. Cationic Na/Cd disorder on the pyrochlore site generates a broad distribution of Cu--F--Cu exchange couplings, introducing intrinsic magnetic bond disorder. Despite strong antiferromagnetic interactions (~K), no magnetic order or global spin freezing is observed in DC and AC susceptibility, specific heat or Na nuclear magnetic resonance to 120 mK, with muon spin relaxation experiments confirming persistent spin dynamics to 58 mK. -linear specific heat, a Curie-like susceptibility tail, and power-law scaling with data collapse in , , , Na and the muon spin polarization 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, . This behavior contrasts with previously-studied NaF pyrochlore fluorides, where magnetic bond disorder precipitates spin-glass freezing, underscoring the crucial role of strong quantum fluctuations in NaCdCuF.

Paper Structure

This paper contains 10 sections, 6 equations, 6 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Experimental methods
  3. Results
  4. Structural details
  5. Magnetic properties
  6. Specific heat
  7. Muon spin relaxation ($\mu$SR)
  8. Nuclear magnetic resonance (NMR)
  9. Scaling behaviour
  10. Conclusion

Figures (6)

  • Figure 1: (a) Cubic unit cell of NaCdCu$_2$F$_7$ with highlighted magnetic (blue) and non-magnetic (yellow) pyrochlore sublattices. Fluorine ions are ommitted for clarity. (b) Local environment around the magnetic Cu$^{2+}$ site - distorted CuF$_6$ octahedron (light blue), connected to a distorted (Na/Cd)F$_8$ cube (pink dodecahedron).
  • Figure 2: (a) Magnetic susceptibility $\chi(T)$ at $\mu_0 H$ = 0.67 T, decomposed into an orphan spin contribution $\chi_{\rm orp}$ and intrinsic susceptibility $\chi_{\rm int} = \chi - \chi_{\rm orp}$. (b) The inverse total susceptibility $\chi^{-1}(T)$, fitted to a Curie-Weiss law between 200 and 300 K. (c) Isothermal magnetization $M(H)$ between 1.8 and 20 K, with fits to Equation \ref{['eq1']} shown as solid lines. (d) Decomposition of the 1.8 K $M(H)$ curve into the fitted orphan spin $M_{\rm orp}$ and intrinsic $M_{\rm int}$ terms. (e) High-field magnetization between 1.35 and 50 K. (f) Real part (left) and imaginary part (right) of AC magnetic susceptibility, vertically offset for clarity.
  • Figure 3: (a) Specific heat $C_p$ and (b) $C_p/T$ of NaCdCu$_2$F$_7$ in fields of 0--9 T, with the non-magnetic analogue NaCdZn$_2$F$_7$ shown as a black solid line. (c) Magnetic specific heat $C_{\rm mag}$ after subtraction of phonon contribution. (d) Magnetic entropy change $\Delta S_{\rm mag}$ in % of Rln(2). (e) Fits of $C_{\rm mag}/T$ to Equation \ref{['eq2']}, with (e) a decomposition into the Schottky and power-law terms. (g) Zero-field dilution refrigerator (DR) and $^3$He specific heat $C_p$ with a power-law ($T = 200\!-\!650$ mK) and linear ($T<200$ mK) regime. (h) DR $C_p/T$ between 0--0.5 T.
  • Figure 4: (a) LF-dependence of the $T=58$ mK spectra, showing the ZF F-$\mu$-F oscillations (black), stretched-exponential relaxation of asymmetry at 200 G (red) and a purely exponential relaxation at 3000 G (green). Temperature dependence of (b) the ZF spectra, fitted to Equation \ref{['eq3']} and (c) the LF 200 G spectra, fitted to Equation \ref{['eq5']}. (d) Temperature dependence of the fitted ZF and LF muon relaxation rates $\lambda_{\rm LF}$ and $\lambda_{\rm ZF}$ (left axis), and the stretching exponent $\beta_{\rm LF}$ (right axis).
  • Figure 5: Temperature dependence of the $^{23}$NMR spectral intensity scaled by temperature $I \times T$ (a) at $\mu_0H$ = 0.67 T and (b) at $\mu_0H$ = 3 T. Temperature dependence of (c) the $^{23}$Na spin-lattice relaxation rate $1/T_1$ and (d) the stretching exponent $\beta_{\rm NMR}$.
  • ...and 1 more figures