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arXiv:cond-mat/0501069 · Nature Materials

Quantum criticality and universal scaling of a quantum antiferromagnet

B. Lake, D. M. Tennant, Chris D. Frost, S. E. Nagler

Published Mar 20, 2005• 340 citations
arXivHTMLPDF
DOI
10.1038/nmat1327

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In certain Mott-insulating dimerized antiferromagnets, triplet excitations of the paramagnetic phase display both three-particle and four-particle interactions. When such a magnet undergoes a quantum phase transition into a magnetically ordered state, the three-particle interaction becomes part of the critical theory provided that the lattice ordering wave vector is zero. One microscopic example is the staggered-dimer antiferromagnet on the square lattice, for which deviations from O(3) universality have been reported in numerical studies. Using both symmetry arguments and microscopic calculations, we show that a nontrivial cubic term arises in the relevant order-parameter quantum field theory, and we assess its consequences using a combination of analytical and numerical methods. We also present finite-temperature quantum Monte Carlo data for the staggered-dimer antiferromagnet which complement recently published results. The data can be consistently interpreted in terms of critical exponents identical to that of the standard O(3) universality class, but with anomalously large corrections to scaling. We argue that the cubic interaction of critical triplons, although irrelevant in two spatial dimensions, is responsible for the leading corrections to scaling due to its small scaling dimension.
Metallic quantum criticality is among the central themes in the understanding of correlated electronic systems, and converging results between analytical and numerical approaches are still under review. In this work, we develop a state-of-the-art large-scale quantum Monte Carlo simulation technique and systematically investigate the itinerant quantum critical point on a 2D square lattice with antiferromagnetic spin fluctuations at wavevector [Formula: see text]-a problem that resembles the Fermi surface setup and low-energy antiferromagnetic fluctuations in high-Tc cuprates and other critical metals, which might be relevant to their non-Fermi-liquid behaviors. System sizes of [Formula: see text] ([Formula: see text]) are comfortably accessed, and the quantum critical scaling behaviors are revealed with unprecedented high precision. We found that the antiferromagnetic spin fluctuations introduce effective interactions among fermions and the fermions in return render the bare bosonic critical point into a different universality, different from both the bare Ising universality class and the Hertz-Mills-Moriya RPA prediction. At the quantum critical point, a finite anomalous dimension [Formula: see text] is observed in the bosonic propagator, and fermions at hotspots evolve into a non-Fermi liquid. In the antiferromagnetically ordered metallic phase, fermion pockets are observed as the energy gap opens up at the hotspots. These results bridge the recent theoretical and numerical developments in metallic quantum criticality and can serve as the stepping stone toward final understanding of the 2D correlated fermions interacting with gapless critical excitations.
Near a quantum critical point (QCP), the low-temperature thermodynamics follows universal scaling laws. Using copper sulfate pentahydrate-a canonical spin-1/2 antiferromagnetic Heisenberg chain compound-we report the observation of a universal magnetocaloric effect (MCE) near a field-driven QCP. Remarkably, in the 1D quantum-critical regime, we obtain the universal magnetocaloric scaling function via adiabatic demagnetization measurements, which agrees with the analytical solutionof the critical 1D Fermi gas. This establishes the copper sulfate crystal as an ideal platform for studying quantum criticality and universal phenomena. Upon further cooling, our MCE and nuclear magnetic resonance measurements reveal a dimensional crossover to a 3D quantum-critical regime of the Bose-Einstein condensation (BEC) universality class, characterized by the scaling lawand a clear data collapse of the magnetic Grüneisen ratio with the 3D Bose-gas scaling function. Practically, this quantum-critical MCE enables cooling to 68.7 mK near the QCP and achieves a lowest temperature of 12.8 mK at zero field without the need for helium-3. Our work identifies a universal MCE in a common compound, establishing this magnon BEC system as a prototype quantum-critical coolant and a platform for next-generation millikelvin refrigeration.