Identification of two distinct antiferromagnetic phases in the Au-Al-Gd quasicrystal approximant

The structural and physical properties of two single-grain Au-Al-Gd 1/1 approximant crystals (ACs) with analyzed compositions $\mathrm{A}{\mathrm{u}}_{73.67}\mathrm{A}{\mathrm{l}}_{12.24}\mathrm{G}{\mathrm{d}}_{14.09}$ and $\mathrm{A}{\mathrm{u}}_{74.67}\mathrm{A}{\mathrm{l}}_{11.35}\mathrm{G}{\mathrm{d}}_{13.98}$ were thoroughly investigated. The two variants are isostructural (cubic, space group: $Im\overline{3}$), undergoing sharp antiferromagnetic (AFM) transitions at ${T}_{\mathrm{N}}=9.6$ K and ${T}_{\mathrm{N}}=8.3$ K, respectively. Specific-heat measurements in both samples evidenced sharp jump at ${T}_{\mathrm{N}}$, associated with the AFM transition, accompanied by broad Schottky-type anomalies at lower temperatures. Strikingly, the two 1/1 ACs exhibited markedly different responses to applied magnetic fields: one displayed a pronounced metamagnetic anomaly while the other did not. In this regard, variational calculations with adiabatic transformation of the magnetic field in realistic structural models identified the existence of two possible AFM phases: the cuboc phase with a metamagnetic anomaly and the cluster N\'eel phase without it, thereby clearly revealing the possible magnetic structures of the present AFM variants. These findings have led to the establishment of a comprehensive magnetic-phase diagram for Heisenberg-type 1/1 ACs. This work not only advances our understanding of magnetic-phase transitions in these complex systems but also suggests the existence of a broader spectrum of unexplored magnetic states in Tsai-type materials.