Fig. 1
From: A series of magnon crystals appearing under ultrahigh magnetic fields in a kagomé antiferromagnet
Calculated magnetization process for the spin-1/2 KAFM with the nearest-neighbor interaction J. The tensor network method with the projected entangled pair state (PEPS) is used. The vertical and horizontal axes represent magnetization M divided by saturated magnetization Ms and magnetic field B divided by J, respectively. The top left inset shows a schematic drawing of hexagonal magnons that are depicted by doughnuts containing six entangled spins. The other intervening spins point upward in the direction of magnetic field. The magnon crystal forms a superlattice with a √3 × √3 unit cell. The bottom right inset shows hexagonal magnons expected to appear at the 1/3, 5/9, and 7/9 plateaus. In the upper part, the magnons are defined by the total spin Sz = 0, 1, and 2 for the six spins on the hexagon, respectively, while in the lower part based on the magnon picture, the number of magnons correspond to 3 (hexagon + double circle), 2 (single circle), and 1 (only hexagon), respectively. Using the bracket notation, the one-magnon state with Sz = 2 is expressed as \({\sum }_{i = 1}^6 \left( { - 1} \right)^iS_i^ - |0 > \), where the sum is obtained inside the hexagon, and \(|0 > \) denotes the saturated state
