[Paper Review] Ground state and excitation properties of the quantum kagomé system ZnCu$_{3}$(OH)$_{6}$Cl$_{2}$ investigated by local probes

Oren Ofer, Amit Keren+6 more|arXiv (Cornell University)|Oct 19, 2006

Advanced Condensed Matter Physics3 citations

TL;DR

This study investigates the quantum kagomé magnet ZnCu₃(OH)₆Cl₂ using local probes—muon spin rotation (μSR), nuclear magnetic resonance (NMR), and magnetization—to determine its ground state and excitation spectrum. The results show no magnetic order, no spin-Peierls transition, and a gapless spin excitation spectrum with density of states scaling as E¹/⁴, indicating a likely algebraic spin liquid ground state.

ABSTRACT

We characterize the ground state and excitation spectrum of the $S=1/2$, nominally pure and perfect kagomé system ZnCu$_{3}$(OH)$_{6}$Cl$_{2}$ using the following measurements: magnetization, muon spin rotation frequency shift $K$, transverse relaxation time $T_{2}^{\ast}$, and zero field relaxation, and Cl nuclear spin-lattice relaxation $T_{1}$. We found no sign of singlet formation, no long range order or spin freezing, and no sign of spin-Peierls transition even at temperatures as low as 60 mK. The density of states has $E^{1/4}$ energy dependence with a negligible gap to excitation.

Motivation & Objective

• To resolve the long-standing theoretical debate on the ground state of S=1/2 quantum kagomé systems by experimentally probing ZnCu₃(OH)₆Cl₂.
• To determine whether the system exhibits magnetic order, spin-Peierls distortion, or singlet formation at low temperatures.
• To measure the spin excitation spectrum and determine the presence or absence of a gap in the energy spectrum.
• To use local probes to overcome limitations of bulk measurements and provide direct insight into local spin dynamics and electronic correlations.

Proposed method

• Conducted DC magnetization measurements using a SQUID magnetometer from 2 K to 280 K to assess magnetic susceptibility and Curie-Weiss behavior.
• Performed muon spin rotation (μSR) experiments at PSI using GPS and LTF spectrometers to measure muon spin relaxation (T₂*) and frequency shift (K), probing local magnetic fields and spin dynamics.
• Acquired ³⁵Cl and ³⁷Cl nuclear spin-lattice relaxation rates (T₁⁻¹) via NMR using saturation recovery sequences at 8.15 T to probe electronic spin fluctuations.
• Used the ratio (T₁γ²)⁻¹ for ³⁵Cl and ³⁷Cl to distinguish between magnetic and quadrupolar relaxation mechanisms, confirming magnetic origin.
• Fitted the spin-lattice relaxation data to the theoretical expression 1/T₁ = 1/T₁ⁿ + γ²A²∫ρ²(E)n(E)[n(E)+1]dE, assuming a power-law density of states ρ(E) ∝ E^α.
• Employed the Bose-Einstein occupation factor n(E) and hyperfine coupling to model relaxation in terms of bosonic excitations, with α and Δ as fit parameters.

Experimental results

Research questions

• RQ1 Does the S=1/2 kagomé system ZnCu₃(OH)₆Cl₂ exhibit long-range magnetic order or spin freezing down to 60 mK?
• RQ2 Is the ground state a spin liquid with a gapless excitation spectrum, or does it form a singlet ground state with a finite gap?
• RQ3 Is there evidence of a spin-Peierls distortion or lattice dimerization in the system?
• RQ4 What is the functional form of the spin excitation density of states, and does it support a gapless or gapped spectrum?

Key findings

• No magnetic ordering or spin freezing was observed down to 60 mK, as indicated by the absence of a susceptibility peak and constant magnetization behavior.
• The muon spin shift (K) and transverse relaxation (T₂*) showed no temperature-dependent anomalies, ruling out long-range order or spin-Peierls transitions.
• ³⁵Cl and ³⁷Cl NMR relaxation data revealed a magnetic relaxation mechanism, with the ratio (T₁γ²)⁻¹ for ³⁵Cl and ³⁷Cl matching the expected value for magnetic fluctuations (0.75(10) vs. 0.69).
• The spin-lattice relaxation rate 1/T₁ showed a sharp decrease below 50 K, indicating suppression of electronic spin fluctuations at low temperatures.
• Fitting the relaxation data to the theoretical model yielded a power-law density of states ρ(E) ∝ E^α with α = 0.23(1), consistent with E¹/⁴ dependence.
• The spin gap was found to be negligible, with Δ = 0.5(2) K, much smaller than the exchange energy scale J = 209 K, indicating a gapless excitation spectrum.