Figure 1

(a) Building blocks of icosahedral quasiperiodic order. From left to right: rhombic triacontahedron (RTH), acute rhombohedron (AR), and obtuse rhombohedron (OR). (b) The two linkages rules that connect Tsai clusters and (c) the stray ARs separate from the Tsai clusters network, with two R inequivalent positions. The red spheres located in the RTH and stray AR represent the rare-earth positions.

Figure 2

Powder XRD pattern of the $i$-Tb-Cd QC; peaks from residual Cd flux are indicated with arrows.

Figure 3

(a) Zero-field cooled and field cooled magnetization curves of the $i$-Tb-Cd QC. (b) The dc magnetic susceptibility of the $i$-Tb-Cd QC recorded in a larger magnetic field. The inset shows the inverse susceptibility plotted as 1/($\chi \text{−}{\chi }_0$) vs T

(${\chi }_0=1.1\times {10}^{-7}$ mol/m3), and linear fit.

Figure 4

(a) The results of memory experiments performed with $t_{\mathrm{halt}}=1000$ s at different temperatures $T_{\mathrm{halt}}$ in the range 2.5 K–7 K are shown in Fig. S4(a) in the SM (as M-T curves) and here as difference plots $\mathrm{\Delta }M$(T), obtained by subtracting the reference curve from each curve recorded after a halt. (b) Sketch of the change in temperature and applied magnetic field with time in the memory experiments: The ZFC magnetization is recorded on reheating after rapid and direct cooling down to the lowest temperature (“reference,” black curve) or after including halts (red and blue curves, illustrating halts of different durations). Another reference curve recorded after a slower cooling (0.2K/min) down to the lowest temperature is also depicted (green curve). (c), (d) The $\mathrm{\Delta }M$(T), plots for different halt times $t_{\mathrm{halt}}=1000$, 3600 s performed at $T_{\mathrm{halt}}$ = (c) 3.5 K and (d) 6 K. The difference plot of a curve collected without halt, yet employing a slow cooling rate of (0.2 K/min) is added in (d) for comparison, with same color scheme as the sketch in (b).