Fig. 1. Crystal structure and electrical and magnetic properties of YMn₆Sn₆.

(A) Sketch of the crystal structure of YMn₆Sn₆. (B) Top view of the structure shown in (A). Within a unit cell shown by the grey solid lines, there are two kagome planes with the formula Mn₃Sn that are separated by Sn₃ and YSn₂ layers. The symbols J_i are the exchange constants between different Mn layers. (C) Electrical resistivity of YMn₆Sn₆ as a function of temperature with the electric current applied in the ab plane. Inset shows the temperature derivative of the electrical resistivity in the vicinity of T_N, which shows a jump at 333 K below which an incommensurate spiral state develops. The residual resistivity ratio (RRR = ρ_400K/ρ_2K) is 42 indicating a good sample quality. (D) Magnetic susceptibility (M/H) of YMn₆Sn₆ as a function of temperature. (E) Incommensurate magnetic structure of YMn₆Sn₆ in the absence of external magnetic field. Arrows represent the direction of FM spins within a kagome plane. There are small constant angles α between the FM-coupled spins across the Sn₃ layer, and β between the AF ones across the Sn₂Y, which result in a spiral spin arrangement, where every other Mn layer forms a spiral with the pitch defined by α + β ≈ 90° and the two spirals rotated by α with respect to each other. The incommensurate spirals repeat after about four crystallographic unit cells or about nine Mn layers that are indicated by the numbers 1 to 9.