Antiferromagnetic ordering and chiral crystal structure transformation in ${\mathrm{Nd}}_3{\mathrm{Rh}}_4{\mathrm{Sn}}_{13}$

The detailed electronic superlattice structure of the Remeika phase compound ${\mathrm{Nd}}_3{\mathrm{Rh}}_4{\mathrm{Sn}}_{13}$ was investigated. The material undergoes a structural phase transition at $T_{\mathrm{D}}\simeq 338$ K between the high temperature phase ($Pm\overline{3}n$) and the low temperature chiral structure phase ($I{2}_{1}3$), which is the same symmetry change as that of the La- and Ce-based Remeika phase compounds. The inequivalent Nd-ion sites in the chiral phase are occupied by different crystalline electronic field splitting schemes of the $4f^3$ electronic configuration with the total angular moment $J=9/2$, which results in two-sublattice antiferromagnetic ordering below $T_{\mathrm{N}}=1.65$ K. The one-dimensional Nd-ion chains in which the magnetic moments are alternately arranged are connected via the second-neighbor triangular lattice in the chiral phase, which suggests a magnetic frustration effect.

Figure 1

(a) Inset figure shows scan profiles at $\mathit{Q}=(6.5,0.5,0)$ of ${\mathrm{Nd}}_3{\mathrm{Rh}}_4{\mathrm{Sn}}_{13}$ at selected temperatures obtained on the two-dimensional detector of BL-4C. The main panel shows the temperature dependence of integrated intensity at $\mathit{Q}=(6.5,0.5,0)$, which is normalized by that of the fundamental reflection at $\mathit{Q}=(8,0,0)$. The solid line indicates a fitting result based on a critical behavior expressed as ${(1-T/T_{\mathrm{D}})}^{2\beta }$ with $\beta =0.484\left(4\right)$ and $T_{\mathrm{D}}=338\left(1\right)$ K. (b) Scan profiles at $\mathit{Q}=(9,0,0)$ of ${\mathrm{Nd}}_3{\mathrm{Rh}}_4{\mathrm{Sn}}_{13}$ at selected temperatures obtained on the two-dimensional detector of BL-4C.

Figure 2

(a) Inverse of $M/H$ data of ${\mathrm{Nd}}_3{\mathrm{Rh}}_4{\mathrm{Sn}}_{13}$ at $B=0.1\mathrm{T}$. The solid line indicates a fitted result based on the Curie-Weiss law. (b) The blue triangles with the right ordinate indicate low-temperature $M/H$ data, and the red squares with the left ordinate indicate ND intensity of (1 1 0) [36].

Figure 3

The black circles indicate magnetic scattering functions $S\left(E\right)$ of ${\mathrm{Nd}}_3{\mathrm{Rh}}_4{\mathrm{Sn}}_{13}$ measured at 8 K (a) and 100 K (b), which were evaluated from intensity integration in the range of $Q=1.0$–$2.0{\AA }^{-1}$. The red solid lines are fitted results based on the two inequivalent CEF scheme models (the blue dotted lines for Nd1 and the green broken lines for Nd2).

Figure 4

The red circles and the green lines in the left inset indicate powder ND data of ${\mathrm{Nd}}_3{\mathrm{Rh}}_4{\mathrm{Sn}}_{13}$ at 0.64 and 2.0 K, respectively. The blue solid lines indicate the calculated results of the Rietveld analysis for the AFM structure. The green vertical bars indicate the peak positions for the nuclear and magnetic scattering.

Figure 5

Temperature dependencies of integrated intensities of ND from ${\mathrm{Nd}}_3{\mathrm{Rh}}_4{\mathrm{Sn}}_{13}\mathrm{at}$ (a) $\left(110\right)$ and $\left(223\right)$, (b) $\left(133\right), (15/25/2)$, and $(5/215/2)$, and (c) $\left(313\right), (3/23-3/2)$, and $(3/23/23)$.

Figure 6

Two enantiomers of $I{2}_{1}3$ chiral cubic structures of ${\mathrm{Nd}}_3{\mathrm{Rh}}_4{\mathrm{Sn}}_{13}$, which were determined from the BL-8A data. The large blue atoms and green atoms correspond to two inequivalent Wyckoff sites of Nd ions. The small red circles and grey circles indicate the Rh and Sn atoms, respectively. Atomic coordinates are listed in Table S.3 of the Supplemental Material [44]. The views were drawn using vesta [45].

Figure 7

Magnetic structure of ${\mathrm{Nd}}_3{\mathrm{Rh}}_4{\mathrm{Sn}}_{13}$ at 0.64 K, as determined from the HERMES data. The blue and green circles correspond to two inequivalent Nd-ion sites, and the arrows indicate the ordered magnetic moments. The upper panel shows bars bonding the nearest neighbor Nd ions along the principal cubic axes, and the lower panel shows triangular bonds between the second neighbors of each Nd-ion site.