Pyrochlores magnets, spin ice and quantum spin ice physics: the neutron scattering perspective
Sylvain PETIT1, Elsa LHOTEL2, Mélanie LEGER1,2 Monica CIOMAGA HATNEAN3, Jacques OLLIVIER4, Andrew R. WILDES4, Stéphane RAYMOND5, Eric RESSOUCHE5, Geetha BALAKRISHNAN3
1Institut Néel, CNRS and Université Grenoble Alpes, 38000 Grenoble, France
2Laboratoire Léon Brillouin, Université Paris-Saclay, CNRS, CEA, CE-Saclay, 91191 Gif-sur-Yvette, France
3Department of Physics, University of Warwick, Coventry, CV4 7AL, United Kingdom
4Institut Laue Langevin, F-38042 Grenoble, France
5Université Grenoble Alpes, CEA, IRIG, MEM, MDN, 38000 Grenoble, France
Magnetic frustration, the inability of a system to simultaneously satisfy all of its interactions, is the subject of much research in condensed matter physics. This phenomenon, which can be related to the topology of the crystalline network or to the competition between interactions, constitutes the source of new exotic states of matter, the description of which goes beyond the classical models. Spin ice and its quantum analogues are an emblematic example of this physics. The crystallographic structure of these materials is based on a pyrochlore-type network, formed by a set of tetrahedra connected by their vertices, each node being occupied by a magnetic rare earth ion (Tb, Dy, Ho, Pr, etc.). In these compounds, the relevant electronic orbitals have the shape of a very thin needle, elongated towards the centres of each tetrahedra. The magnetic moment of each ion can then only point inward or outward, much like the ±1 states of an Ising variable. The classical ground state of such a system is very peculiar in that it is infinitely degenerate. Indeed, the only prescription for constructing it is to follow a local organizing principle, which states that each tetrahedron must have two spins “in" and two "out". In recent years, theoretical physicists have proposed a new vision of the problem, noting that the "two in-two out" rule is actually analogous to the conservation law of a fictitious magnetic flux (div B=0) in electromagnetism . The analogy is complete when quantum fluctuations are incorporated. Indeed, the fluctuations of the fictitious magnetic field B, create by virtue of the Lenz law curl E=- dB/dt an "emergent" electric field E. According to theoretical predictions, a quantum spin ice should have a particular excitation spectrum characterized by a photon-like mode. Using examples from the literature and from our own recent research, we will show in this presentation how inelastic neutron scattering has contributed to a better understanding of this physics. We will especially discuss the case of Tb2Ti2O7, Pr2Zr2O7, Er2Ti2O7, as well as Nd2Zr2O7.
 Quantum spin ice: a search for gapless quantum spin liquids in pyrochlore magnets, M.J.P. Gingras and P.A. McClarty, Rep Prog Phys 77 (2017) 056501.