Distinct order of Gd $4f$ and Fe $3d$ moments coexisting in $\mathrm{Gd}{\mathrm{Fe}}_4{\mathrm{Al}}_8$

Single crystals of flux-grown tetragonal $\mathrm{Gd}{\mathrm{Fe}}_4{\mathrm{Al}}_8$ were characterized by thermodynamic, transport, and x-ray resonant magnetic scattering measurements. In addition to antiferromagnetic order at $T_N\approx 155\mathrm{K}$, two low-temperature transitions at $T_1\approx 21\mathrm{K}$ and $T_2\approx 27\mathrm{K}$ were identified. The Fe moments order at $T_N$ with an incommensurate propagation vector $(\tau ,\tau ,0)$ with $\tau$ varying between 0.06 and 0.14 as a function of temperature, and maintain this order over the entire $T<T_N$ range. The Gd $4f$ moments order below $T_2$ with a ferromagnetic component mainly out of plane. Below $T_1$, the ferromagnetic components are confined to the crystallographic plane. Remarkably, at low temperatures the Fe moments maintain the same modulation as at high temperatures, but the Gd $4f$ moments apparently do not follow this modulation. The magnetic phase diagrams for fields applied in [110] and [001] direction are presented and possible magnetic structures are discussed.

Figure 1

(Color online) The crystal structure of $R{\mathrm{Fe}}_4{\mathrm{Al}}_8$. Thin lines outline the tetragonal $(I4∕mmm)$ unit cell, thick lines denote the Fe “cage” around the rare earth $R$.

Figure 2

(Color online) Zero-field resistivity $\rho$ (along [110], sample Ia) and inverse dc susceptibility ${\chi }^{-1}$ vs temperature $T$ (sample Ib).

Figure 3

(Color online) Low-temperature normalized resistance (panel a) and derivative of high-temperature resistance (panel b) vs temperature $T$ of various crystals: Ia (thick line) and II (dotted line) for $j\Vert \left[110\right]$, III (open circles) and IV (full circles) for $j\Vert \left[001\right]$.

Figure 4

(Color online) Low-field $(H\Vert \left[001\right])$ Magnetization of various crystals with Fe stoichiometry (as described in Sec. 2) determined by electron microprobe or x-ray-diffraction-structure refinement.

Figure 5

(Color online) Specific heat $C_p$ measured on sample Ib in zero field (∎) and Gd $4f$ moment contribution to the specific heat (엯), obtained by subtracting the specific heat of $\mathrm{Y}{\mathrm{Fe}}_4{\mathrm{Al}}_8$ (full line, from Ref. 21). Inset: Entropy of the Gd $4f$ moments obtained by integrating the $4f$ moment contribution to $C_p∕T$. The two lines shown were calculated using two extrapolations of the specific heat to $T=0$, indicated by dashed lines in the main panel (see text for details of the extrapolations). The dotted line in the inset indicates the full Gd $4f$ entropy.

Figure 6

(Color online) Resistivity $\rho$ vs $T$ in fields of $3.5\mathrm{T}$ applied in-plane parallel or perpendicular to the current density $j\Vert \left[110\right]$ (sample Ia). Arrows indicate the $T$ direction in which the measurements were performed. The open circle indicates the value of the $T_1$ transition in $3.5\mathrm{T}$, averaged for $T$ increasing and decreasing.

Figure 7

(Color online) (a) Resistivity $\rho$ vs $T$ (sample Ia, $j\Vert \left[110\right]$, $T$ increasing) in fields applied parallel to $j\Vert \left[110\right]$. From top to bottom 0 (thick line), 0.1, 0.2, 0.4, 0.5, 0.8, 1 (thick line), 1.5, 2, 2.5, $3.5\mathrm{T}$. (b) As in panel (a), but in fields applied parallel to [001] $(j\Vert \left[110\right])$. From top to bottom 0 (thick line), 0.1, 0.2, 0.3, 0.4, 0.5, 0.7, 0.8, 0.9, 1, 2, $5.5\mathrm{T}$.

Figure 8

(Color online) Resistivity vs $H\Vert j\Vert \left[110\right]$ at selected $T$ (sample Ia).

Figure 9

(Color online) Magnetization $M$ as a function of field $H$ at selected $T$, $H\Vert \left[110\right]$ (blue), and $H\Vert \left[001\right]$ (red), sample Ib. Thin arrows indicate the $H$ direction of the measurements, thick arrows indicate the criterion taken for the estimation of the spontaneous ferromagnetic moment.

Figure 10

(Color online) Spontaneous ferromagnetic moment $M_s$, estimated from the $M\left(H\right)$ curves in Fig. 9 vs temperature $T$, $H\Vert \left[110\right]$ (black squares), and $H\Vert \left[001\right]$ (red circles), sample Ib. The square root of the sum of the squares for both field directions is shown as open triangles.

Figure 11

(Color online) (a) Reciprocal space scans along $[h,h,0]$ at 37 and $160\mathrm{K}$ (sample Ib, Gd $L_{\mathrm{II}}$ edge). The data in the range $h=3.96$ to 4.04 have been divided by a factor of 10 000. (b) Energy scans of the intensity of the $(4-\tau ,4-\tau ,0)$ satellite reflections at 9, 37, and $130\mathrm{K}$. Note that intensities in panel (a) are not comparable to intensities in panel (b).

Figure 12

(Color online) Low-temperature phase diagrams of $\mathrm{Gd}{\mathrm{Fe}}_{3.96\left(1\right)}{\mathrm{Al}}_8$ (sample Ia/b) for $H\Vert \left[110\right]$ (a) and $H\Vert \left[001\right]$ (b). Triangles in (a) are from resistivity measurements on sample Ia, the other symbols from magnetization measurements on sample Ib (see text for details). The three magnetic phases LTP (low-temperature phase), ITP (intermediate-temperature phase), and HTP (high-temperature phase), as well as the zero-field transition temperatures $T_1$ and $T_2$ are indicated in both panels. A possible fourth magnetic phase existing in fields applied parallel to [110] (HFP) is indicated in panel (a). Underlaid is a contour plot of the magnetization $M$ (sample Ib).