Unveiling exotic magnetic phase diagram of a non-Heisenberg quasicrystal approximant

A magnetic phase diagram of the non-Heisenberg Tsai-type 1/1 Au-Ga-Tb approximant crystal (AC) has been established across a wide electron-per-atom (e/a) range via magnetization and powder neutron diffraction measurements. The diagram revealed exotic ferromagnetic (FM) and antiferromagnetic (AFM) orders that orig-inate from the unique local spin icosahedron common to icosahedral quasicrystals (iQCs) and ACs; The noncoplanar whirling AFM order is stabilized as the ground state at the e/a of 1.72 or less whereas a noncoplanar whirling FM order was found at the larger e/a of 1.80, with magnetic moments tangential to the Tb icosahedron in both cases. Moreover, the FM/AFM phase selection rule was unveiled in terms of the nearest neighbour (J1) and next nearest neighbour (J2) interactions by numerical calculations on a non-Heisenberg single icosahedron. The present findings will pave the way for understanding the intriguing magnetic orders of not only non-Heisenberg FM/AFM ACs but also non-Heisenberg FM/AFM iQCs, the latter of which are yet to be discovered.