Ferromagnetic 2/1 quasicrystal approximants

The existence of various magnetic orders has recently been established in the Tsai-type 1/1 approximant Au-Al-Gd by variation of the electron-per-atom (e/a) ratio [Ishikawa et al. Phys. Rev. B 98, 220403(R) (2018)]. Here, we report ferromagnetic (FM) 2/1 quasicrystal approximants and show that the magnetic order of higher-order approximants can be tailored starting from known magnetic 1/1 approximants. The (Au,Cu)-(Al,In)-$R\left(R=\mathrm{Gd},\mathrm{Tb}\right)2$/1 approximants are synthesized by the simultaneous substitution of isovalent elements Cu and In for Au and Al, respectively, to the FM Au-Al-$R\left(R=\mathrm{Gd},\mathrm{Tb}\right)1$/1 approximants with $e/a=1.74$. Both the (Au,Cu)-(Al,In)-$R\left(R=\mathrm{Gd},\mathrm{Tb}\right)2$/1 approximants exhibit a FM transition at significantly high Curie temperatures of $T_{\mathrm{C}}=30.0$ and 15.3 K, respectively. Therefore, this method of isovalent substitution will also enable the realization of a variety of magnetic orders for the 2/1 approximant by variation of the e/a ratio. Such isovalent substitution may also stabilize magnetic quasicrystals for a given e/a ratio, which would lead to the realization of the long-range magnetic order in quasicrystals.

Figure 1

$\text{Cu}K$α powder XRD patterns for (a) $\mathrm{A}{\mathrm{u}}_{54}\mathrm{C}{\mathrm{u}}_9\mathrm{A}{\mathrm{l}}_{9.5}\mathrm{I}{\mathrm{n}}_{13.5}\mathrm{G}{\mathrm{d}}_{14},\mathrm{A}{\mathrm{u}}_{64}\mathrm{A}{\mathrm{l}}_9\mathrm{I}{\mathrm{n}}_{13}\mathrm{G}{\mathrm{d}}_{14},\mathrm{A}{\mathrm{u}}_{59}\mathrm{C}{\mathrm{u}}_5\mathrm{A}{\mathrm{l}}_{22}\mathrm{G}{\mathrm{d}}_{14}$, and (b) $\mathrm{A}{\mathrm{u}}_{56}\mathrm{C}{\mathrm{u}}_7\mathrm{A}{\mathrm{l}}_{10}\mathrm{I}{\mathrm{n}}_{13}\mathrm{T}{\mathrm{b}}_{14}$, together with the results of Le Bail fitting. $I_{\mathrm{obs}}$ (red cross) and $I_{\mathrm{cal}}$ (blue solid line) represent measured and calculated intensities, respectively. The purple and green vertical bars represent the Bragg peak positions for the space group $Im\overline{3}$ and $Pa\overline{3}$, respectively. The 2/1 approximants are obtained by simultaneous substitution of Cu and In for Au and Al, respectively, to the Au-Al-$R\left(R=\mathrm{Gd},\mathrm{Tb}\right)1$/1 approximant.

Figure 2

Reciprocal-space sections perpendicular to (a) twofold, (b) threefold, and (c) pseudo-fivefold [3 5 0] directions for 2/$1\mathrm{A}{\mathrm{u}}_{56}\mathrm{C}{\mathrm{u}}_7\mathrm{A}{\mathrm{l}}_{10}\mathrm{I}{\mathrm{n}}_{13}\mathrm{T}{\mathrm{b}}_{14}$, reconstructed from single-crystal XRD intensity data.

Figure 3

Temperature dependence of inverse magnetic susceptibility ${\chi }^{-1}$, for 2/$1\mathrm{A}{\mathrm{u}}_{54}\mathrm{C}{\mathrm{u}}_9\mathrm{A}{\mathrm{l}}_{9.5}\mathrm{I}{\mathrm{n}}_{13.5}\mathrm{G}{\mathrm{d}}_{14}$ and 2/$1\mathrm{A}{\mathrm{u}}_{56}\mathrm{C}{\mathrm{u}}_7\mathrm{A}{\mathrm{l}}_{10}\mathrm{I}{\mathrm{n}}_{13}\mathrm{T}{\mathrm{b}}_{14}$.

Figure 4

(Inset) Temperature dependences of ZFC and FC magnetization $M$ for (a) 2/$1\mathrm{A}{\mathrm{u}}_{54}\mathrm{C}{\mathrm{u}}_9\mathrm{A}{\mathrm{l}}_{9.5}\mathrm{I}{\mathrm{n}}_{13.5}\mathrm{G}{\mathrm{d}}_{14}$ and (b) 2/$1\mathrm{A}{\mathrm{u}}_{56}\mathrm{C}{\mathrm{u}}_7\mathrm{A}{\mathrm{l}}_{10}\mathrm{I}{\mathrm{n}}_{13}\mathrm{T}{\mathrm{b}}_{14}$ in a low-temperature region below 50 K. Both the ZFC and FC curves increase sharply at $T_{\mathrm{C}}=30.0\mathrm{K}$ and $T_{\mathrm{C}}=15.3\mathrm{K}$. $M$ for (a) 2/$1\mathrm{A}{\mathrm{u}}_{54}\mathrm{C}{\mathrm{u}}_9\mathrm{A}{\mathrm{l}}_{9.5}\mathrm{I}{\mathrm{n}}_{13.5}\mathrm{G}{\mathrm{d}}_{14}$ and (b) 2/$1\mathrm{A}{\mathrm{u}}_{56}\mathrm{C}{\mathrm{u}}_7\mathrm{A}{\mathrm{l}}_{10}\mathrm{I}{\mathrm{n}}_{13}\mathrm{T}{\mathrm{b}}_{14}$ as a function of the magnetic field up to 7 T at 2 K.

Figure 5

Temperature dependence of the specific heat $C$ for (a) 2/$1\mathrm{A}{\mathrm{u}}_{54}\mathrm{C}{\mathrm{u}}_9\mathrm{A}{\mathrm{l}}_{9.5}\mathrm{I}{\mathrm{n}}_{13.5}\mathrm{G}{\mathrm{d}}_{14}$ and (b) 2/$1\mathrm{A}{\mathrm{u}}_{56}\mathrm{C}{\mathrm{u}}_7\mathrm{A}{\mathrm{l}}_{10}\mathrm{I}{\mathrm{n}}_{13}\mathrm{T}{\mathrm{b}}_{14}$. A lambda-shape anomaly due to the FM transition is observed for both compounds as denoted by the vertical bars.

Figure 6

Paramagnetic Curie temperature ${\mathrm{\Theta }}_{\mathrm{p}}$ normalized by the de Gennes factor, plotted as a function of the electron-per-atom (e/a) ratio for the Gd- and Tb-bearing Tsai-type 1/1 approximants and quasicrystals in Au- and Cd-based systems reported in the literature. The light yellow region approximately represents the region of FM phases. The ${\mathrm{\Theta }}_{\mathrm{p}}/\mathrm{dG}$ values of both the Au-Cu-Al-In-Gd and Au-Cu-Al-In-Tb FM 2/1 approximants are plotted and both ${\mathrm{\Theta }}_{\mathrm{p}}/\mathrm{dG}$ values are close to the values of 1/1 approximant at the same e/a ratios.