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A measure of monopole inertia in the quantum spin ice Yb2Ti2O7


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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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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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.

Corresponding author

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).

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