Magnetic properties of the quasicrystal approximant ${\mathrm{Au}}_{65}{\mathrm{Ga}}_{21}{\mathrm{Tb}}_{14}$

The magnetic properties of the quasicrystal approximant ${\mathrm{Au}}_{65}{\mathrm{Ga}}_{21}{\mathrm{Tb}}_{14}$ were investigated using magnetization and neutron diffraction experiments. The temperature dependences of the magnetic susceptibility and magnetization curve indicate dominant ferromagnetic interactions, whereas a whirling antiferromagnetic order was observed in neutron diffraction experiments. In the antiferromagnetic phase, the magnetic moments are aligned almost perpendicular to a pseudofivefold symmetry axis, which corresponds to the easy-axis direction of a Tb atom. Magnetic properties similar to those of ${\mathrm{Au}}_{72}{\mathrm{Al}}_{14}{\mathrm{Tb}}_{14}$ in spite of the substantial difference in the Au concentration suggest the robustness of the easy-axis anisotropy against the chemical environment.

Figure 1

(a) Successive shells of a Tsai-type cluster in ${\mathrm{Au}}_{65}{\mathrm{Ga}}_{21}{\mathrm{Tb}}_{14}$ obtained from single-crystal x-ray diffraction. (b) Local environment around a Tb atom. The dashed and solid lines passing through the Tb atom represent the pseudofivefold rotation axis and mirror plane, respectively. The red arrow indicates the direction of the magnetic moment in the ordered phase. Some inequivalent sites induced by disorder are merged into a single site for clarity. (c) Antiferromagnetic order in ${\mathrm{Au}}_{65}{\mathrm{Ga}}_{21}{\mathrm{Tb}}_{14}$. The whirling arrangement is formed around the [111] direction. (d) Magnetic structure expected under a magnetic field. Half of the magnetic moments denoted by dashed circles are oriented in directions opposite to those illustrated in (c). The figures were obtained by using vesta software [26].

Figure 2

(a) Temperature dependence of the magnetic susceptibility and inverse susceptibility. (b) Magnetic susceptibility below 30 K measured using zero-field-cooling and field-cooling protocols. (c) Temperature dependence of the 210 magnetic reflection intensity at $20.7^{\circ }$ . The inset shows the temperature dependence near $T_{\mathrm{N}}$. The dashed curve represents a fit to the power-law function (see the text for details). (d) Magnetization curves at 2, 10, and 15 K. The black solid curve represents the simulated curve of a single cluster with the ferromagnetic interactions $J_1=0.02$ K and $J_2=0.13$ K. The inset shows the enlarged view at a near-zero field.

Figure 3

Powder neutron diffraction patterns measured at (a) 4 K and (b) 20 K. The observed intensities, calculated intensities, and their differences are represented by red dots and black and blue curves, respectively. The positions of the nuclear and magnetic reflections are indicated by black and red solid lines, respectively.

Figure 4

Schematic view of energy levels and eigenfunctions $|J,J_z\rangle$ of a rare-earth atom under the model Hamiltonian (A1) with easy-axis anisotropy ($D>0$).

Figure 5

Temperature dependences of inverse magnetic susceptibility. The inverse of parallel (red), perpendicular (blue), and averaged (black) susceptibility multiplied by a normalization factor is plotted as a function of temperature. The green dashed line indicates the Curie rule expected for free ${\mathrm{Tb}}^{3+}$ ions. The inset shows the deviation of the inverse susceptibility against the Curie rule.

Figure 6

Direction of local principal axes of Tb1–Tb12 atoms. The directions of the $z$ axes are highlighted in red.