1/3 plateau and 3/5 discontinuity in the magnetization and the magnetic phase diagram of hexagonal GdInO3

We report the high-pressure optical floating-zone growth of ${\mathrm{GdInO}}₃$ single crystals and show its magnetic phase diagram down to the millikelvin regime as determined by magnetization measurements. The centered-honeycomb lattice structure shows considerable magnetic frustration ($|\mathrm{\ensuremath{\Theta}}|/{T}_{\mathrm{N}}\ensuremath{\simeq}5$) and develops long-range magnetic order below ${T}_{\mathrm{N}}=2.1$ K from a short-range-ordered paramagnetic phase. Concomitantly, a small net magnetic moment evolves at ${T}_{\mathrm{N}}$ which points along the crystallographic $c$ direction. Upon cooling, the net moment reorients at ${T}^**\ensuremath{\simeq}1.7$ K and ${T}^*\ensuremath{\simeq}1$ K. A broad 1/3 plateau indicative of the up-up-down ($uud$) spin configuration appears for magnetic fields $B\ensuremath{\parallel}c$ but is absent for $B\ensuremath{\parallel}ab$, thereby suggesting easy-axis anisotropy. At $T=0.4$ K, a jump in magnetization at $\ensuremath{\simeq}$3/5 of the saturation magnetization signals a discontinuous transition to a high field phase and we find evidence for a possible tricritical point. Small energy and field scales in the accessible regimes render ${\mathrm{GdInO}}₃$ a well-suited example to study the phase diagram of a semiclassical frustrated hexagonal lattice in the presence of weak easy-axis anisotropy of mainly dipolar origin.