Neutron Scattering Revealing Kagome Spin Ice in a Frustrated Intermetallic Compound

Abstract

Frustrated magnetic structures hold configurations wherein localized magnetic moments or spins interact through competing exchange interactions, rendering macroscopic degeneracy of exotic ground states like spin ice and providing an excellent platform for discovering novel states and properties. One example is the pyrochlore spin ice, in which four nearest-neighbor Ising-like spins on the vertices of the corner-sharing tetrahedra are forced to form the local “2-in-2-out” configuration for each tetrahedron, which forms spin ice in analogy to the water ice[1]. In two dimensions (2D), ice rules can be similarly defined for in-plane Ising like classical spins residing on the kagome lattice, which require “2-in-1-out” or “1-in-2-out” local arrangements of the spins on its triangles[2]. A √3×√3 ground state can be selected by further neighbor exchange couplings or the long-range dipolar interaction. As a result, kagome spin ices show a characteristic multi-stage ordering behavior under changing temperature. Experimentally, kagome spin ices have only been realized in artificial spin ice systems formed by nanorods of ferromagnets organized into honeycomb networks[3-5]. However, the large magnetic energy scales and system sizes make it challenging to explore the rich phase diagram of spin ices in the thermodynamic limit.Neutron scattering, though measuring the energy and momentum of in-coming and out-going neutrons, offers one of the most powerful tools in the study of magnetic structures and dynamics of magnets. Through neutron scattering and other experimental and theoretical approaches, we discover that the intermetallic compound HoAgGe is a naturally existing kagome spin ice that exhibits a fully ordered ground state[6]. The multi-stage ordering behavior was confirmed by Single-crystal neutron diffraction: below 11.6 K the Ho spins enter a partially ordered state with one-third of them still fluctuating, while below ~7 K, all spins order into the √3×√3 ground state of the kagome ice with crystalized magnetic monopoles. All these observations are in good agreement with Monte Carlo simulations of a classical spin model including both dipolar interactions and up to 4th nearest-neighbor exchange couplings on the noncentrosymmetric kagome lattice of HoAgGe. **