Magnetic structure and magnetoelastic coupling of ${\mathrm{GdNiSi}}_3$ and ${\mathrm{TbNiSi}}_3$

The series of intermetallic compounds $R{\mathrm{NiSi}}_3 (R=\text{rare} \text{earth})$ shows interesting magnetic properties evolving with $R$ and metamagnetic transitions under applied magnetic field for some of the compounds. The microscopic magnetic structures must be determined to rationalize such rich behavior. Here, resonant x-ray magnetic diffraction experiments are performed on single crystals of ${\mathrm{GdNiSi}}_3$ and ${\mathrm{TbNiSi}}_3$ at zero field. The primitive magnetic unit cell matches the chemical cell below the Néel temperatures $T_N=22.2$ and 33.2 K, respectively. The magnetic structure is determined to be the same for both compounds (magnetic space group $Cmm{m}^{\prime }$). It features ferromagnetic $ac$ planes that are stacked in an antiferromagnetic $+-+-$ pattern, with the rare-earth magnetic moments pointing along the $\vec{a}$ direction, which contrasts with the $+--+$ stacking and moment direction along the $\vec{b}$ axis previously reported for ${\mathrm{YbNiSi}}_3$. This indicates a sign reversal of the coupling constant between second-neighbor $R$ planes as $R$ is varied from Gd and Tb to Yb. The long $b$ lattice parameter of ${\mathrm{GdNiSi}}_3$ and ${\mathrm{TbNiSi}}_3$ shows a magnetoelastic expansion upon cooling below $T_N$, pointing to the conclusion that the $+-+-$ stacking is stabilized under lattice expansion. A competition between distinct magnetic stacking patterns with similar exchange energies tuned by the size of $R$ sets the stage for the magnetic ground state instability observed along this series.

Figure 1

Crystal and magnetic structures of ${\mathrm{YbNiSi}}_3$ [14] (left), ${\mathrm{GdNiSi}}_3$, and ${\mathrm{TbNiSi}}_3$ (this work, right).

Figure 2

(a) Temperature dependence of the integrated intensity of the 0 16 0 Bragg reflection of ${\mathrm{GdNiSi}}_3$ at $\sigma {\pi }^{\prime }$ and $\sigma {\sigma }^{\prime }$ polarizations, with x-ray energy either on resonance at the Gd $L_{II}$ edge ($E=7.924$ keV) or off resonance ($E=7.885$ keV). (b) Similar to (a) for the 1 17 0 reflection (on resonance only).

Figure 3

Temperature dependence of the integrated intensity of the 0 14 1 Bragg reflection of ${\mathrm{TbNiSi}}_3$ at $\sigma {\pi }^{\prime }$ and $\sigma {\sigma }^{\prime }$ polarizations, with x-ray energy on resonance at the Tb $L_{II}$ edge ($E=7.516$ keV).

Figure 4

Temperature-dependence of $a$, $b$, $c$ orthorhombic lattice parameters and unit-cell volume $V$ for ${\mathrm{GdNiSi}}_3$ (a)–(d), respectively.

Figure 5

Temperature-dependence of $a$, $b$, $c$ orthorhombic lattice parameters and unit-cell volume $V$ for ${\mathrm{TbNiSi}}_3$ (a)–(d), respectively.