Emergent excitations from a quantum spin ice
Quantum spin ice is an appealing proposal of a quantum spin liquid – systems where the magnetic moments of the constituent electron spins evade classical long-range order to form an exotic state that is quantum entangled and coherent over macroscopic length scales. Such phases of the solid state offer promising opportunities for future new quantum technologies, and will unlock further understanding of the behaviour of matter at this state.
A recent multi-partner neutron study led by Romain Sibille from the PSI , with measurements performed on the time-of-flight spectrometer IN5 and on the HYSPEC spectrometer at SNS, provide evidence for such a quantum spin ice ground state in the magnetic pyrochlore Pr2Hf2O7. This observation constitutes 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.
Discovered in the late 90s in magnetic pyrochlore compounds, classical “spin ices” are materials that contain magnetic moments distributed on a network of corner-sharing tetrahedra. Due to the structure of the material, each magnetic moment is constrained to align along the direction joining its position and the centres of two tetrahedra.
With ferromagnetic interactions, two of the four magnetic moments in each tetrahedron must be oriented inward and the two others outward. This ‘2 in 2 out’ local constraint can be achieved in a number of ways that grow 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 (SL) — of correlated moments, despite its name being inherited from a form of crystalline water ice, which is very different.
The quantum spin ice (QSI), a type of quantum spin liquid (QSL) where spin ice configurations tunnel among themselves, is a generalisation of the classical “spin ice” (CSI) integrating quantum fluctuations. Whereas in CSI the excitations are akin to charges with a mutual Coulomb interaction, in the QSI these charges interact through a dynamic electromagnetic field, emerging from these quantum fluctuations. A remarkable prediction for this exotic state of matter is the emergence of photon-like excitations.
Moreover, a QSI is expected to exhibit peculiar ‘fractionalised’ excitations – microscopic degrees of freedom that are split into parts due to the long-range quantum entanglement in the ground state. These are the magnetic monopoles of CSI, but they become quantum-coherent quasiparticle excitations, akin to spinons in quantum spin chains.
The experimental challenge the group faced was to find the proof of existence of such excitations in a Praseodymium-based pyrochlore – materials that were long-thought by theoreticians to host such an exotic state of matter, but were yet to be observed.
To find evidence of the QSI state, the team used neutron scattering to identify the suppression of the so-called “pinch points” at the Brillouin Zone centers across the material’s reciprocal space . This effect, which comes about as a result of the quantum fluctuations present in QSI is testable by measuring a quasi-elastic constant-energy neutron intensity map, where the emergent photons are indistinguishably hidden. Meanwhile, the fractionalised excitations appear as an inelastic continuum, providing another hint for a QSI state.
To directly measure these interactions and the spin-spin correlations in these intriguing materials, the group conducted neutron scattering experiments on the IN5 cold neutron time-of-flight instrument at the ILL, which perfectly matched the resolution and wave-vector dependency needs for this investigation.
Following this, a polarisation experiment conducted on HYSPEC (SNS) confirmed unambiguously the magnetic origin of the signal measured on the time-of-flight spectrometer at IN5 – providing confirmation of the quantum spin ice ground state in the magnetic pyrochlore Pr2Hf2O7.
Instrument: Disk chopper time-of-flight spectrometer IN5
Re.: Experimental signatures of emergent quantum electrodynamics in Pr2Hf2O7, Sibille R, Gauthier N, Yan H, Ciomaga Hatnean M, Ollivier J, Winn B, Filges U, Balakrishnan G, Kenzelmann M, Shannon N, Fennell T
Nature Physics, DOI: 10.1038/s41567-018-0116-x (2018). (Free view)
Additional readings: Spin ice goes quantum
Contact: Jacques Ollivier, ILL
Notes to Editors:
 About PSI - The Paul Scherrer Institute, PSI, is the largest research institute for natural and engineering sciences within Switzerland. Scientists perform world-class research for major challenges facing society, industry and science, in three main areas: Matter and Material; Energy and the Environment; and Human Health. See https://www.psi.ch/psi-home
 About ORNL – Oak Ridge National Laboratory (ORNL) operates two neutron source facilities, the High Flux Isotope Reactor and the Spallation Neutron Source. Built and funded by the U.S. Department of Energy (DOE) Office of Basic Energy Sciences (BES), the two facilities combined house 30 neutron scattering instruments, providing researchers with unmatched capabilities for understanding the structure and properties of materials, macromolecular and biological systems, and the fundamental physics of the neutron. More than 1,200 unique users from around the world use ORNL’s neutron sources annually. ORNL is managed and operated by UT-Battelle for DOE. For more information visit https://www.ornl.gov/
 About ILL – the Institut Laue-Langevin (ILL) is an international research centre based in Grenoble, France. It has led the world in neutron-scattering science and technology for almost 40 years, since experiments began in 1972. ILL operates one of the most intense neutron sources in the world, feeding beams of neutrons to a suite of 40 high-performance instruments that are constantly upgraded. Each year 1,200 researchers from over 40 countries visit ILL to conduct research into condensed matter physics, (green) chemistry, biology, nuclear physics, and materials science. The UK, along with France and Germany is an associate and major funder of the ILL.