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arXiv:cond-mat/0303364 · Physical Review Letters

Extended Quantum Critical Phase in a Magnetized Spin- 1 2 Antiferromagnetic Chain

M. B. Stone, Daniel H. Reich, C. Broholm, Kim Lefmann, Christian Rischel, C.P. Landee, Mark M. Turnbull

Published Jul 17, 2003• 139 citations
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Abstract

Measurements are reported of the magnetic field dependence of excitations in the quantum critical state of the spin S=1/2 linear chain Heisenberg antiferromagnet copper pyrazine dinitrate (CuPzN). The complete spectrum was measured at k(B)T/J< or =0.025 for H=0 and H=8.7 T, where the system is approximately 30% magnetized. At H=0, the results are in agreement with exact calculations of the dynamic spin correlation function for a two-spinon continuum. At H=8.7 T, there are multiple overlapping continua with incommensurate soft modes. The boundaries of these continua confirm long-standing predictions, and the intensities are consistent with exact diagonalization and Bethe ansatz calculations.

DOI
10.1103/physrevlett.91.037205

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Measurements are reported of the magnetic field dependence of excitations in the quantum critical state of the spin S=1/2 linear chain Heisenberg antiferromagnet copper pyrazine dinitrate (CuPzN). The complete spectrum was measured at k(B)T/J< or =0.025 for H=0 and H=8.7 T, where the system is approximately 30% magnetized. At H=0, the results are in agreement with exact calculations of the dynamic spin correlation function for a two-spinon continuum. At H=8.7 T, there are multiple overlapping continua with incommensurate soft modes. The boundaries of these continua confirm long-standing predictions, and the intensities are consistent with exact diagonalization and Bethe ansatz calculations.
High-precision DC magnetization (M) measurements have been performed on a single crystal of copper pyrazine dinitrate (CuPzN) in magnetic fields H up to 14.7 T at temperatures down to 0.08 K. This material is one of the best realizations of a one-dimensional (1D) S = 1/2 Heisenberg antiferromagnet. At the base temperature, full saturation of M is observed above Hs = 13.97 T with the M(H) curve closely following a prediction based on the Bethe ansatz. The peak in M(T ), which appears at about 7 K in zero field, moves to lower temperatures with increasing H and vanishes into a temperature region well below 0.08 K at H ∼ Hs; as a result, M(T ) exhibits a strong upturn as T → 0 at this field, in agreement with a theoretical prediction. These results constitute an observation of field-induced quantum critical behavior in bulk magnetization.
Low-dimensional quantum magnets promote strong correlations between magnetic moments that lead to fascinating quantum phenomena. A particularly interesting system is the antiferromagnetic spin-1/2 Heisenberg chain because it is exactly solvable by the Bethe-Ansatz method. It is approximately realized in the magnetic insulator copper pyrazine dinitrate, providing a unique opportunity for a quantitative comparison between theory and experiment. We investigate its thermodynamic properties with a particular focus on the field-induced quantum phase transition. Thermal expansion, magnetostriction, specific heat, magnetization, and magnetocaloric measurements are found to be in excellent agreement with exact Bethe-Ansatz predictions. Close to the critical field, thermodynamics obeys the expected quantum critical scaling behavior, and in particular, the magnetocaloric effect and the Grüneisen parameters diverge in a characteristic manner. Beyond its importance for quantum magnetism, our study establishes a paradigm of a quantum phase transition, which illustrates fundamental principles of quantum critical thermodynamics.
We present a 13C^{13}\text{C}13C NMR study of the magnetic field driven transition to complete polarization of the S=12S=\frac{1}{2}S=21​ antiferromagnetic Heisenberg chain system copper pyrazine dinitrate Cu(C4H4N2)(NO3)2\text{Cu}({\text{C}}_{4}{\text{H}}_{4}{\text{N}}_{2}){({\text{NO}}_{3})}_{2}Cu(C4​H4​N2​)(NO3​)2​ (CuPzN). The static local magnetization as well as the low-frequency spin dynamics, probed via the nuclear spin-lattice relaxation rate ${T}_{1}^{\ensuremath{-}1}$, were explored from the low to the high field limit and at temperatures from the quantum regime (kBT⪡J)({k}_{B}T⪡J)(kB​T⪡J) up to the classical regime (kBT⪢J)({k}_{B}T⪢J)(kB​T⪢J). The experimental data show very good agreement with quantum Monte Carlo calculations over the complete range of parameters investigated. Close to the critical field, as derived from static experiments, a pronounced maximum in ${T}_{1}^{\ensuremath{-}1}$ is found which we interpret as the finite-temperature manifestation of a diverging density of zero-energy magnetic excitations at the field-driven quantum critical point.
A comprehensive comparison between the magnetic field- and temperature-dependent low-frequency spin dynamics in the antiferromagnetic spin-1/2 Heisenberg chain system copper pyrazine dinitrate, probed via the 13C^{13}\mathrm{C}13C nuclear magnetic resonance relaxation rate ${T}_{1}^{\ensuremath{-}1}$, and the field theoretical approach in the Luttinger liquid regime was performed. We found very good agreement between experiment and theory in the investigated temperature and field range. Our results demonstrate how spin-spin interactions strongly affect the spin dynamics of Heisenberg spin chain compounds in the vicinity of the quantum critical point.
The T=0T=0T=0 dynamical properties of the one-dimensional (1D) s=12s=\frac{1}{2}s=21​ Heisenberg antiferromagnet in a uniform magnetic field are studied via the Bethe ansatz for cyclic chains of N sites. The ground state at magnetization 0<Mz<N/2,0<{M}_{z}<N/2,0<Mz​<N/2, which can be interpreted as a state with 2Mz{2M}_{z}2Mz​ spinons or as a state of $N/2\ensuremath{-}{M}_{z}$ magnons, is reconfigured here as the vacuum for a different species of quasiparticles, the psinons and antipsinons. We investigate three kinds of quantum fluctuations, namely the spin fluctuations parallel and perpendicular to the direction of the applied magnetic field and the dimer fluctuations. The dynamically dominant excitation spectra are found to be sets of collective excitations composed of two quasiparticles excited from the psinon vacuum in different configurations. The Bethe ansatz provides a framework for (i) the characterization of the new quasiparticles in relation to the more familiar spinons and magnons, (ii) the calculation of spectral boundaries and densities of states for each continuum, (iii) the calculation of transition rates between the ground state and the dynamically dominant collective excitations, (iv) the prediction of line shapes for dynamic structure factors relevant for experiments performed on a variety of quasi-1D antiferromagnetic compounds, including KCuF3,{\mathrm{KCuF}}_{3},KCuF3​, Cu(C4H4N2)(NO3)2,\mathrm{Cu}({\mathrm{C}}_{4}{\mathrm{H}}_{4}{\mathrm{N}}_{2})({\mathrm{NO}}_{3}{)}_{2},Cu(C4​H4​N2​)(NO3​)2​, and CuGeO3.{\mathrm{CuGeO}}_{3}.CuGeO3​.
Spectral properties of the spin-1/2 antiferromagnetic Heisenberg chain in a magnetic field are investigated by using exact Bethe-ansatz solutions. We argue that not only quasiparticles called psinon and antipsinon but also a quasiparticle representing a 2-string in the Bethe ansatz plays an important role for dynamical properties in a magnetic field. Combined with psinon and antipsinon, the quasiparticle for a 2-string forms a continuum in the high-energy regime for transverse dynamical structure factor S +− ( κ,ω ). In the zero-field limit, the continuum is located on the mode of the lowest excited states in zero field called the des Cloizeaux-Pearson mode. In a magnetic field, the continuum separates from other low-energy continua, and reduces to the mode of bound states of overturned spins from the fully polarized state near the saturation field. We confirm the relevance through comparisons with available experimental results on the quasi-one-dimensional antiferromagnet CuCl 2 ·2N(C 5 D 5 ).