Abstract
Free magnetic moments usually manifest themselves in Curie laws, where weak external magnetic fields produce magnetizations that vary as the reciprocal of the temperature (1/T). For a variety of materials that do not display static magnetism, including doped semiconductors1 and certain rare-earth intermetallics2, the 1/T law is replaced by a power law T-α with α < 1. Here we show that a much simpler material system—namely, the insulating magnetic salt LiHoxY1-xF4—can also display such a power law. Moreover, by comparing the results of numerical simulations of this system with susceptibility and specific-heat data3, we show that both energy-level splitting and quantum entanglement are crucial to describing its behaviour. The second of these quantum mechanical effects—entanglement, where the wavefunction of a system with several degrees of freedom cannot be written as a product of wavefunctions for each degree of freedom—becomes visible for remarkably small tunnelling terms, and is activated well before tunnelling has visible effects on the spectrum. This finding is significant because it shows that entanglement, rather than energy-level redistribution, can underlie the magnetic behaviour of a simple insulating quantum spin system.
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References
Paalanen, M. A., Ruckenstein, A. E. & Thomas, G. A. Spins in Si:P close to the metal-insulator transition. Phys. Rev. Lett. 54, 1295–1298 (1985)
Schröder, A. et al. Onset of antiferromagnetism in heavy-fermion metals. Nature 407, 351–355 (2000)
Reich, D. H. et al. Dipolar magnets and glasses: Neutron scattering, dynamical, and calorimetric studies of randomly distributed Ising spins. Phys. Rev. B 42, 4631–4644 (1990)
Aharony, A. & Stephen, M. J. Percolation with long-range interactions. J. Phys. C 14, 1665–1670 (1981)
Reich, D. H., Rosenbaum, T. F. & Aeppli, G. Glassy relaxation without freezing in a random dipolar-coupled Ising magnet. Phys. Rev. Lett. 59, 1969–1972 (1987)
Ghosh, S., Parthasarathy, R., Rosenbaum, T. F. & Aeppli, G. Coherent spin oscillations in a disordered magnet. Science 296, 2195–2198 (2002)
Bhatt, R. N. & Lee, P. A. Scaling studies of highly disordered spin-1/2 antiferromagnetic systems. Phys. Rev. Lett. 48, 344–347 (1982)
Ma, S. K., Dasgupta, C. & Hu, C. K. Random antiferromagnetic chain. Phys. Rev. Lett. 43, 1434–1437 (1979)
Dasgupta, C. & Ma, S. K. Low temperature properties of the random Heisenberg antiferromagnetic chain. Phys. Rev. B 22, 1305–1319 (1980)
Fisher, D. S. Random transverse field Ising spin chains. Phys. Rev. Lett. 69, 534–537 (1992)
Fisher, D. S. Critical behaviour of random transverse-field Ising spin chains. Phys. Rev. B 51, 6411–6461 (1995)
Westerberg, E., Furusaki, A., Sigrist, M. & Lee, P. A. Random quantum spin chains: A real space renormalization group study. Phys. Rev. Lett. 75, 4302–4305 (1995)
Phillips, P., Izzo, D. & Kundu, K. Spin-lattice relaxation below 1 K: A new mechanism for unexpected nuclear spin relaxation. Phys. Rev. B 37, 10876–10879 (1988)
Hansen, P. E., Johansson, T. & Nevald, R. Magnetic properties of lithium rare-earth fluorides: Ferromagnetism in LiErF4 and LiHoF4 and crystal-field parameters at the rare-earth and Li sites. Phys. Rev. B 12, 5315–5324 (1975)
Bitko, D., Rosenbaum, T. F. & Aeppli, G. Quantum critical behaviour for a model magnet. Phys. Rev. Lett. 77, 940–943 (1996)
Magarino, J., Tuchendler, J., Beauvillain, P. & Laursen, I. EPR experiment in LiTbF4, LiHoF4, and LiErF4 at submillimeter frequencies. Phys. Rev. B 21, 18–28 (1980)
Van Vleck, J. H. Quantum mechanics—the key to understanding magnetism. Rev. Mod. Phys 50, 181–189 (1978)
Gunlycke, D., Kendon, V. M., Vedral, V. & Bose, S. Thermal concurrence mixing in a one-dimensional Ising model. Phys. Rev. A 64, 042302 (2001)
Wootters, W. K. Entanglement of formation of an arbitrary state of two qubits. Phys. Rev. Lett. 80, 2245–2248 (1998)
Osterloh, A., Amico, L., Falci, G. & Fazio, R. Scaling of entanglement close to a quantum phase transition. Nature 416, 608–610 (2002)
Arnesen, M. C., Bose, S. & Vedral, V. Natural thermal and magnetic entanglement in the 1D Heisenberg model. Phys. Rev. Lett. 87, 017901 (2001)
Osborne, T. J. & Nielsen, M. A. Entanglement, quantum phase transitions, and density matrix renormalization. Quant. Inform. Process. 1, 45–53 (2002)
Acknowledgements
We thank R. Parthasarathy for discussions. The work at the University of Chicago was supported by the MRSEC Program of the National Science Foundation, that in the University of Wisconsin by the Petroleum Research Fund and the National Science Foundation, and that in University College London by a Wolfson–Royal Society Research Merit Award and the Basic Technologies programme of the UK Research Councils.
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Ghosh, S., Rosenbaum, T., Aeppli, G. et al. Entangled quantum state of magnetic dipoles. Nature 425, 48–51 (2003). https://doi.org/10.1038/nature01888
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DOI: https://doi.org/10.1038/nature01888
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