Page 43 - ILLS Annual Report 2018

a)
Int.(a.u.) b) 0.04
0.02 0
E = 0 ± 0.06 meV
−2 −1 0 1 2 (H,H,0)
Figure 2
a)
3 2 1 0
−1 −2 −3
The quasi-elastic structure factor (a) and inelastic spectrum (b) of Pr2Hf2O7 measured at 0.05 K on IN5.
be oriented inward and the other two outward. This ‘2 in 2 out’ local constraint can be achieved in a number of ways that grows exponentially with the number of tetrahedra involved, so that no order can occur. A spin ice is therefore better viewed as a fluctuating fluid—a spin liquid—of correlated moments, despite its name being inherited from a form of crystalline water ice.
A famous example of exotic behaviour in spin-ice materials is that of magnetic monopoles. The magnetic moments in the material interact in such a manner that separate magnetic charges can emerge as ‘quasi- particles’ associated with excitations. But exotic as these phenomena may be, they can nevertheless
be fully described within the framework of classical magnetostatics.
An intriguing question, then, is what happens when quantum effects are thrown into the mix [2]? Theoretical work predicts that quantum-mechanical tunnelling between different spin-ice configurations can lead to excitations that are qualitatively different from those in classical spin ice.
In quantum spin ice, behaviour emerges that is described by quantum electromagnetism; that is, quantum fluctuations bring an emerging dynamic electromagnetic field into play (figure 1). This leads to a rich set of novel phenomena: not only should variants of magnetic monopoles appear
in quantum spin ices, but so should electric monopoles and excitations that behave like photons. The experimental realisation of a quantum spin ice is, however, challenging. Attempts to identify its manifestations in various pyrochlore materials have been made. As a result, spectacular results
of neutron scattering experiments hinting at ground states with quantum origins in rare-earth pyrochlores have been obtained over the past few years (see [3, 4], for example).
In the present study, high-quality single crystals of Pr2Hf2O7 were measured on IN5 at the ILL. The results reveal two important signatures of a quantum spin ice state. First, the mapping of the quasi-elastic structure factor at 0.05 K in this material reveals pinch points (figure 2a)—a signature of a classical spin ice—that are partially suppressed as expected in a quantum spin ice. The line shape of the pinch-point scattering was compared with calculations
of a lattice field theory of a quantum spin ice, in which low-energy gapless photon excitations explain the broadening of the curve. This result makes it possible
to estimate the speed of light associated with magnetic photon excitations. Second, the IN5 data also reveal a continuum of inelastic spin excitations (figure 2b) that resemble predictions of the fractionalised, topological excitations of a quantum spin ice. Complementary polarised-neutron measurements confirming the magnetic origin of these signals were made on the HYSPEC spectrometer at the Spallation Neutron Source (Oak Ridge National Laboratories, USA), using an array of polarisation analysers built at the Paul Scherrer Institute (Villigen, Switzerland). Taken together, these two signatures of a quantum spin ice ground state suggest that the low-energy physics of the magnetic pyrochlore Pr2Hf2O7 can be described by emergent quantum electrodynamics. Such observations constitute a concrete example of a three- dimensional quantum spin liquid—a topical state of matter that has so far mostly been observed in lower dimensions.
SCIENTIFIC HIGHLIGHTS
40-41
(0,0,L)
Intensity (a.u.)
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