Discovery of antiferromagnetic chiral helical ordered state in trigonal ${\mathrm{GdNi}}_3{\mathrm{Ga}}_9$

We have performed magnetic susceptibility, magnetization, and specific heat measurements on a chiral magnet ${\mathrm{GdNi}}_3{\mathrm{Ga}}_9$, belonging to the trigonal space group $R32$ (No. 155). A magnetic phase transition takes place at $T_{\mathrm{N}}=19.5$ K. By applying a magnetic field along the $a$ axis at 2 K, the magnetization curve exhibits two jumps at $\sim 3$ kOe and = 45 kOe. To determine the magnetic structure, we performed a resonant x-ray diffraction experiment by utilizing a circularly polarized beam. It is shown that a long-period antiferromagnetic (AFM) helical order is realized at zero field. The Gd spins in the honeycomb layer are coupled in an antiferromagnetic manner in the $c$ plane and rotate with a propagation vector $\mathit{q}=(0,0,1.485)$. The period of the helix is 66.7 unit cells $(\sim 180$ nm). In magnetic fields above 3 kOe applied perpendicular to the helical $c$ axis, the AFM helical order changes to an AFM order with $\mathit{q}=(0,0,1.5)$.

Figure 1

(a) The unit cell of ${\mathrm{GdNi}}_3{\mathrm{Ga}}_9$. Ga(5), which is located in the Gd honeycomb layer, is colored green. (b) Gd honeycomb layer $\left(z\sim 1/6\right)$. This figure contains nine unit cells. Gd forms a honeycomb network. Ga(5) forms a small triangle at the center of this network. (c) Spiral in the crystal structure of ${\mathrm{GdNi}}_3{\mathrm{Ga}}_9$. The figure shows the $c$-axis spiral of Ga(5). Although hard to see because the changes are so small, atoms in general positions, such as Ni and Ga(6), are also arranged in spirals in addition to Ga(5). In this figure, Ga(1)–Ga(4) was eliminated for simplicity. vesta was used to draw the figure [4].

Figure 2

Scattering configuration of the RXD experiments with a phase retarder system inserted in the incident x ray.

Figure 3

(a) Temperature dependences of magnetic susceptibility obtained in the magnetic fields of 0.05, 1, 10, and 50 kOe along the $a$ axis, together with that obtained in $H\parallel c$ at 1 kOe. (b) Magnetization curves were measured at 2, 4, 6, 10, and 15 K with increasing the magnetic field. (c) Enlarged view of the low magnetic field region of Fig. 3.

Figure 4

$H\text{−}T$ phase diagram of ${\mathrm{GdNi}}_3{\mathrm{Ga}}_9$ in $H\parallel a$. The dots in this figure are obtained by magnetization measurements. The $\alpha$ phase is the AFM helical phase.

Figure 5

Temperature dependence of specific heat divided by temperature $C_{\mathrm{mag}}/T$, together with the entropy $S_{\mathrm{mag}}$.

Figure 6

X-ray energy $E$ dependence of the $(1,0,20.48)$ reflection around $E=7.246$ keV, together with the background (black curve) obtained with $\theta$ shifted slightly from $(1,0,20.48)$.

Figure 7

Temperature dependence of the $(-1,0,L)$ peak profile at zero magnetic field in the AFM helical $\alpha$ phase.

Figure 8

Temperature variation of the $(-1,0,17+q)$ peak intensity shown in Fig. 7.

Figure 9

$\mathrm{\Delta }{\theta }_{\mathrm{PR}}$ scans, which show the intensity relations for the RCP and LCP incident x rays at (a) $(-1,0,17+q)$ and $(-1,0,20-q)$, and (b) $(1,0,19+q)$ and $(1,0,22-q)$ reflection peaks.

Figure 10

Schematic view of the AFM helical and commensurate AFM structures in the $\alpha$ and $\beta$ phases of ${\mathrm{GdNi}}_3{\mathrm{Ga}}_9$, respectively. In this figure, the twist angle is emphasized about ten times. vesta was used to draw the figure [4].

Figure 11

Magnetic field dependence of the $(-1,0,L)$ peak profile at the lowest temperature 3 K.

Figure 12

$\mathrm{\Delta }{\theta }_{\mathrm{PR}}$ scan at $(-1,0,18.5)$, where $\mathit{q}=(0,0,1.5)$, in the $\beta$ phase.