Dynamic kagome ice state

Coulomb phases form a novel exotic state of matter which, because of frustration, lacks long range order, yet is described by a local organizing principle.
Spin ice is the emblematic example of this physics: in a lattice where magnetic ions occupy the vertices of corner sharing tetrahedra (pyrochlore lattice), the combination of strong Ising anisotropy along local <111> axes with ferromagnetic interactions leads to the so called ice rule (2 spins point in and 2 spins point out in each tetrahedron). Kagome ice is another example, in 2 dimensions, with a lattice made of corner sharing triangles. In this case, the organizing principle is the kagome ice rule, 2 spins pointing into each triangle, and 1 out, or vice versa.
The pyrochlore and kagome lattices are intimately related: along the [111] direction, the pyrochlore lattice can be viewed as a stacking of kagome layers separated by the apical spins. Applying a magnetic field along [111] in spin ice freezes out the apical spins, decouples the kagome layers and operates a dimension reduction.
In this context, we report here the effect of a [111] magnetic field on Nd₂Zr₂O₇. In this pyrochlore compound, classical spin ice physics is considerably modified by the existence of transverse terms in the Hamiltonian: spin ice signatures are transferred in the excitation spectrum, taking the form of a flat spin ice mode [1]. Correspondingly, we show that above 0.25 T, a flat dynamic kagome ice mode forms in the excitation spectrum, featuring a “dynamic kagome ice” state [2]. Mean-field calculations using the XYZ Hamiltonian [3] account qualitatively for our observations, although some discrepancies point to the existence of more complex processes. More generally, our study highlights the key role of transverse terms in the physics of pyrochlore magnets.
[1] Petit et al. Nature Phys. 12, 746 (2016)
[2] Lhotel et al. Nature Commun. 9, 3786 (2018)
[3] Huang et al. Phys. Rev. Lett. 112, 167203 (2014), Benton Phys. Rev. B 94, 104430 (2016)