Realization of the kagome spin ice state in a frustrated intermetallic compound

The article presents the discovery and detailed investigation of HoAgGe, an intermetallic compound that naturally exhibits a kagome spin ice state, a rare and exotic magnetic phase characterized by frustrated spins arranged on a two-dimensional kagome lattice. In this system, spins follow local "ice rules" similar to those in water ice, requiring each spin triangle to have a single magnetic monopole, resulting in a highly degenerate ground state with residual entropy. Unlike previous kagome spin ices realized only in artificial nanostructures or under specific magnetic fields in pyrochlore materials, HoAgGe shows intrinsic kagome spin ice behavior in a bulk crystalline material. 

The authors used a combination of magnetometry, thermodynamic measurements, single-crystal neutron diffraction, and Monte Carlo simulations to study HoAgGe. They found that the Ho³⁺ ions form a distorted kagome lattice in the plane with strong in-plane anisotropy. Magnetic susceptibility measurements revealed two characteristic temperatures indicating complex magnetic ordering. Magnetization curves exhibited multiple plateaus at low temperatures, corresponding to successive metamagnetic transitions consistent with the kagome ice rule. Neutron diffraction identified a √3 × √3 magnetic unit cell below 11.6 K with partially ordered spins forming clockwise and counterclockwise hexagons, while some spins remained fluctuating. At lower temperatures near 7 K, the system transitions into a fully ordered ground state matching the theoretically predicted kagome spin ice configuration. When magnetic fields are applied along the b axis, the system undergoes a sequence of field-induced phase transitions with shrinking magnetic unit cells and symmetry changes, further confirming the kagome spin ice nature. 

All magnetic distribution models, measured under different temperatures and intensities of the external magnetic field, were obtained through representation analysis and magnetic structure refinement using our program, Jana2006. Additionally, the experimental research into these magnetic structures has led to essential enhancements in the program.

Popis

Magnetic structures of HoAgGe versus temperature and field with H//b.(A) Integrated intensity of the magnetic peak (1/3, 1/3, 0) (fig. S4A) from 13 K down to 3.8 K according to the neutron diffraction, with the integrated intensity of nuclear site (1, 0, 0) as an inset. (B) Refined magnetic structures of HoAgGe at 10 K. The magnetic unit cell is indicated by the green rhombus, with the three inequivalent Ho sites Ho1, Ho2, and Ho3 labeled by 1, 2, and 3, respectively, for simplicity. (C) Counterclockwise hexagons of spins in the partially ordered structure of HoAgGe at 10 K, with 1/3 spins not participating in the long-range order. (D) Integrated intensity of magnetic peak (–1/3, 2/3, 1) (fig. S4B) and (1/3, 4/3, 1) versus field at 4 K. (E) Refined magnetic structure of HoAgGe at 4 K. (F) Clockwise and counterclockwise hexagons of spins in the magnetic structure of HoAgGe at 4 K, which is exactly the expected √3 × √3 ground state of kagome spin ice. (G) Refined magnetic structure of HoAgGe at H = 1.5 T and T = 4 K. The refinement was done in the 3 × √3 light-green rectangle. The six inequivalent Ho sites are labeled by numbers 1 to 6 for simplicity. (H) Refined magnetic structure of HoAgGe at H = 2.5 T and T = 1.8 K. (I) Refined magnetic structure of HoAgGe at H = 4 T and T = 1.8 K, with the two inequivalent Ho sites labeled by 1 and 2. The field direction is marked by the red arrow for (G) to (I).