Spin dynamics and unconventional Coulomb phase in Nd2Zr2O7

Spin ice and more generally Coulomb phases are emergent states of matter that attract sustained attention in phys-ics. Such systems lack long range order, yet the ground state is formed, at the classical level, by degenerate con-figurations which satisfy a local organizing principle. In the famous example of spin ice, this organization princi-ple is known as the “ice rule” and states that each tetrahedron (building the pyrochlore structure of these materi-als) should have two spins pointing in and two spins pointing out. Even more fascinating, the ice rule constraint can be interpreted as the divergence-free condition of an emergent fictitious magnetic field, while quantum fluctu-ations are expected to give rise to an emergent associated electric field. This is the starting point of theoretical approaches pointing to emergent electrodynamics in quantum spin ice and more generally U(1) quantum spin liquids [1]. The route to stabilize such quantum spin liquid phases is to introduce transverse couplings, as opposed to Ising coupling terms at play in classical Coulomb phases. However, if too large, these transverse terms are expected to stabilize ordered phases. In this context, the question whether classical ordered phases may be stabi-lized out of Coulombic phase via a Higgs mechanism, has become an important issue. In this presentation, we tackle this question experimentally in Nd2Zr2O7 [2]. This pyrochlore magnet is indeed an excellent candidate to explore this physics: its ground state is known to be antiferromagnetically ordered in the so-called all-in all-out (AIAO) state, but its paramagnetic phase above the ordering temperature remains enigmatic and could be a novel example of Coulomb phase [3]. Recently, it has been proposed that the transition from this possible Coulomb phase towards the AIAO phase could be driven by a Higgs mechanism [4]. We have performed a careful study of the dynamics and of the magnetic correlations below and above the transition temperature (TN = 300 mK) using high resolution inelastic and polarized neutron scattering experiments. We confirm the coulombic nature of the phase above the ordering temperature, yet its organizing principle is different from canonical spin ice. In addition, we show that in this Coulomb phase, the spin dynamics contains features typical of the low temperature AIAO phase, i.e. a gapped spin ice-like at mode and dispersing spin waves. Our observations suggest that the transition arises in the thermal regime of the Coulomb phase and is likely not a Higgs mechanism.

[1] M. J. P. Gingras et al., Rep. Prog. Phys., 77, 056501, 2014
[2] Petit et al., Nature Phys, 12,746, 2016
[3] M. Léger et al., Phys. Rev. Lett., 126, 247201, 2021
[4] J. Xu, et al., Phys. Rev. Lett., 124, 097203, 2020