  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 originate 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.
