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A measure of monopole inertia in the quantum spin ice Yb2Ti2O7

Nature Physics volume 12, pages 361–366 (2016)Cite this article

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Abstract

An important and continuing theme of modern solid state physics is the realization of exotic excitations in materials, known as quasiparticles, that have no analogy in the actual physical vacuum of free space. Although they are not fundamental, such quasiparticles do constitute the most basic description of the excited states of the ‘vacuum’ in which they reside. In this regard the magnetic textures of the excited states of spin ices, magnetic pyrochlore oxides with dominant Ising interactions, have been proposed to behave as effective magnetic charge monopoles. Inelastic neutron scattering experiments have established the pyrochlore material Yb2Ti2O7 (YbTO) as a quantum spin ice, where, in addition to the Ising interactions, there are substantial transverse terms that may induce quantum dynamics and—in principle—coherent monopole motion. Here we report a combined time-domain terahertz spectroscopy (TDTS) and microwave cavity study of YbTO to probe its complex dynamic magnetic susceptibility. We find that the form of the susceptibility is consistent with that of a monopole gas, and a magnetic monopole conductivity can be defined and measured. Using the phase sensitive capabilities of these techniques, we observe a sign change in the reactive part of the magnetic response. In generic models of magnetic excitations this is possible only by introducing inertial effects, such as a mass-dependent term, to the equations of motion. Analogous to conventional electric charge systems, measurement of the conductivity’s spectral weight allows us to derive a value for the magnetic monopole mass. Our results support the idea of magnetic monopoles of quantum spin ice as the true coherently propagating quasiparticles of this system.

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Figure 1: Schematic of spin ice and experimental set-up.
Figure 2: Transmission as a function of temperature and field.
Figure 3: Real and imaginary parts of measured κ with fitting.
Figure 4: Temperature dependence of the fitting parameters for the extended Ryzhkin model describe in the main text.

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References

  1. Balents, L. Spin liquids in frustrated magnets. Nature 464, 199–208 (2010).

    Article  ADS  Google Scholar 

  2. Gingras, M. J. P. & McClarty, P. A. Quantum spin ice: a search for gapless quantum spin liquids in pyrochlore magnets. Rep. Prog. Phys. 77, 056501 (2014).

    Article  ADS  Google Scholar 

  3. Lacroix, C., Mendels, P. & Mila, F. (eds) Introduction to Frustrated Magnetism Vol. 164 (Springer Series in Solid-State Sciences, Springer, 2011).

    Book  Google Scholar 

  4. Gardner, J. S., Gingras, M. J. P. & Greedan, J. E. Magnetic pyrochlore oxides. Rev. Mod. Phys. 82, 53–107 (2010).

    Article  ADS  Google Scholar 

  5. Harris, M. J., Bramwell, S. T., McMorrow, D. F., Zeiske, T. & Godfrey, K. W. Geometrical frustration in the ferromagnetic pyrochlore Ho2Ti2O7 . Phys. Rev. Lett. 79, 2554–2557 (1997).

    Article  ADS  Google Scholar 

  6. Bramwell, S. T. & Gingras, M. J. P. Spin ice state in frustrated magnetic pyrochlore materials. Science 294, 1495–1501 (2001).

    Article  ADS  Google Scholar 

  7. Ryzhkin, I. A. Magnetic relaxation in rare-earth pyrochlores. J. Exp. Theor. Phys. 101, 481–486 (2005).

    Article  ADS  Google Scholar 

  8. Castelnovo, C., Moessner, R. & Sondhi, S. L. Magnetic monopoles in spin ice. Nature 451, 42–45 (2008).

    Article  ADS  Google Scholar 

  9. Ehlers, G. et al. Dynamical crossover in hot spin ice. J. Phys. Condens. Matter 15, L9–L15 (2003).

    Article  Google Scholar 

  10. Savary, L. & Balents, L. Spin liquid regimes at nonzero temperature in quantum spin ice. Phys. Rev. B 87, 205130 (2013).

    Article  ADS  Google Scholar 

  11. Wan, Y. & Tchernyshyov, O. Quantum strings in quantum spin ice. Phys. Rev. Lett. 108, 247210 (2012).

    Article  ADS  Google Scholar 

  12. Hao, Z. H., Day, A. G. R. & Gingras, M. J. P. Bosonic many-body theory of quantum spin ice. Phys. Rev. B 90, 214430 (2014).

    Article  ADS  Google Scholar 

  13. Onoda, S. & Tanaka, Y. Quantum fluctuations in the effective pseudospin-12 model for magnetic pyrochlore oxides. Phys. Rev. B 83, 094411 (2011).

    Article  ADS  Google Scholar 

  14. Ross, K. A., Savary, L., Gaulin, B. D. & Balents, L. Quantum excitations in quantum spin ice. Phys. Rev. X 1, 021002 (2011).

    Google Scholar 

  15. Applegate, R. et al. Vindication of Yb2Ti2O7 as a model exchange quantum spin ice. Phys. Rev. Lett. 109, 097205 (2012).

    Article  ADS  Google Scholar 

  16. D’Ortenzio, R. M. et al. Unconventional magnetic ground state in Yb2Ti2O7 . Phys. Rev. B 88, 134428 (2013).

    Article  ADS  Google Scholar 

  17. Pan, L. D. et al. Low-energy electrodynamics of novel spin excitations in the quantum spin ice Yb2Ti2O7 . Nature Commun. 5, 4970 (2014).

    Article  ADS  Google Scholar 

  18. Hodges, J. A. et al. The crystal field and exchange interactions in Yb2Ti2O7 . J. Phys. Condens. Matter 13, 9301–9310 (2001).

    Article  ADS  Google Scholar 

  19. Malkin, B. Z. et al. Optical spectroscopy of Yb2Ti2O7 and Y2Ti2O7:Yb3+ and crystal-field parameters in rare-earth titanate pyrochlores. Phys. Rev. B 70, 075112 (2004).

    Article  ADS  Google Scholar 

  20. Ross, K. A. et al. Two-dimensional kagome correlations and field induced order in the ferromagnetic xy pyrochlore Yb2Ti2O7 . Phys. Rev. Lett. 103, 227202 (2009).

    Article  ADS  Google Scholar 

  21. Thompson, J. D. et al. Rods of neutron scattering intensity in Yb2Ti2O7: compelling evidence for significant anisotropic exchange in a magnetic pyrochlore oxide. Phys. Rev. Lett. 106, 187202 (2011).

    Article  ADS  Google Scholar 

  22. Ross, K. A. et al. Dimensional evolution of spin correlations in the magnetic pyrochlore Yb2Ti2O7 . Phys. Rev. B 84, 174442 (2011).

    Article  ADS  Google Scholar 

  23. Chang, L. J. et al. Higgs transition from a magnetic Coulomb liquid to a ferromagnet in Yb2Ti2O7 . Nature Commun. 3, 992 (2012).

    Article  ADS  Google Scholar 

  24. Ross, K. A. et al. Lightly stuffed pyrochlore structure of single-crystalline Yb2Ti2O7 grown by the optical floating zone technique. Phys. Rev. B 86, 174424 (2012).

    Article  ADS  Google Scholar 

  25. Hayre, N. R. et al. Thermodynamic properties of Yb2Ti2O7 pyrochlore as a function of temperature and magnetic field: validation of a quantum spin ice exchange Hamiltonian. Phys. Rev. B 87, 184423 (2013).

    Article  ADS  Google Scholar 

  26. Vandenborre, M. T. et al. Rare-earth titanates and stannates of pyrochlore structure; vibrational spectra and force fields. J. Raman Spectrosc. 14, 63–71 (1983).

    Article  ADS  Google Scholar 

  27. Bovo, L. et al. Brownian motion and quantum dynamics of magnetic monopoles in spin ice. Nature Commun. 4, 1535 (2013).

    Article  ADS  Google Scholar 

  28. Gardner, J. S., Ehlers, G., Rosov, N., Erwin, R. W. & Petrovic, C. Spin–spin correlations in Yb2Ti2O7: a polarized neutron scattering study. Phys. Rev. B 70, 180404 (2004).

    Article  ADS  Google Scholar 

  29. Hohenberg, P. C. & Brinkman, W. F. Sum rules for the frequency spectrum of linear magnetic chains. Phys. Rev. B 10, 128–131 (1974).

    Article  ADS  Google Scholar 

  30. Zaliznyak, I. A. & Lee, S.-H. Magnetic Neutron Scattering in Modern Techniques for Characterizing Magnetic Materials (Springer, 2005).

    Google Scholar 

  31. Onodera, Y. Breakdown of Debye’s model for dielectric relaxation in high frequencies. J. Phys. Soc. Jpn 62, 4104–4107 (1993).

    Article  ADS  Google Scholar 

  32. Bramwell, S. T., Field, M. N. & Parkin, I. P. Bulk magnetization of the heavy rare earth titanate pyrochlores—a series of model frustrated magnets. J. Phys. Condens. Matter 12, 483–495 (2000).

    Article  ADS  Google Scholar 

  33. Tokiwa, Y. et al. Thermal conductivity of quantum magnetic monopoles in the frustrated pyrochlore Yb2Ti2O7. Preprint at http://arXiv.org/abs/1504.02199 (2015).

  34. Wan, Y., Carrasquilla, J. & Melko, R. G. Spinon walk in quantum spin ice. Preprint at http://arXiv.org/abs/1510.00979 (2015).

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Acknowledgements

This work at JHU was supported by the Gordon and Betty Moore Foundation through Grant GBMF2628 to N.P.A. The microwave cavity work was supported by the DOE through DE-FG02-08ER46544. N.J.L. had additional support through the ARCS Foundation. The crystal growth work at McMaster was supported by NSERC. We would like to thank L. Balents, C. Broholm, N. Drichko, M. Gingras, Z. Hao, S. M. Koohpayeh, J. Lynn, G. Luke, M. Mourigal, M. Robbins, L. Savary, R. Singh, O. Tchernyshyov, M. Valentine and Y. Wan for helpful conversations and E. Kermarrec for help with the crystal preparation.

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Authors and Affiliations

  1. Department of Physics and Astronomy, Institute for Quantum Matter, Johns Hopkins University, Baltimore, Maryland 21218, USA

    LiDong Pan, N. J. Laurita, Kate A. Ross & N. P. Armitage

  2. NIST Center for Neutron Research, NIST, Gaithersburg, Maryland 20899, USA

    Kate A. Ross

  3. Department of Physics and Astronomy, McMaster University, Hamilton, Ontario L8S 4M1, Canada

    Bruce D. Gaulin

  4. Brockhouse Institute for Materials Research, McMaster University, Hamilton, Ontario L8S 4M1, Canada

    Bruce D. Gaulin

  5. Canadian Institute for Advanced Research, 180 Dundas St. W, Toronto, Ontario M5G 1Z8, Canada

    Bruce D. Gaulin

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Contributions

L.P. performed the terahertz experiments and data analysis. N.J.L. performed the microwave measurements and analysis. K.A.R. and B.D.G. provided the high-quality single crystals. N.P.A. directed the project. All authors contributed to discussions on data analysis and writing of the manuscript.

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Correspondence to N. P. Armitage.

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The authors declare no competing financial interests.

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Pan, L., Laurita, N., Ross, K. et al. A measure of monopole inertia in the quantum spin ice Yb2Ti2O7. Nature Phys 12, 361–366 (2016). https://doi.org/10.1038/nphys3608

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