Magnetic Structures of RNiSi3 (R = Gd, Tb and Ho)

The competing or cooperative character between different degrees of freedom drives different ground states in strongly correlated systems. Even simple systems, such as pure rare earth compounds, present multiple phase transitions with complex magnetic structures in some of them, resulting from a strong interplay between magnetic dipolar interaction and temperature dependence of crystal field parameters [1]. Therefore, it is anticipated that some rare-earth-based compounds also have rich magnetic phase diagrams. One example is the series of intermetallic compounds $R$NiSi$_{3}$ ($R$ = rare earth), which shows a change of the antiferromagnetic axis between the lighter elements Gd and Tb and the heavier Yb. In between, for HoNiSi$_{3}$, the situation is more complicated since this compound show two well-defined $\lambda$-shape anomalies at T$_{N1}$ = 6.3 K and T$_{N2}$ = 10.4 K. Additionally, different components of the total magnetic moment order at different temperatures. The $\vec{a}$ component orders at T$_{N2}$, and after further cooling above T$_{N1}$, the $\vec{c}$ component orders [2-4]. Thus, to better grasp this change, the magnetic structure of GdNiSi$_{3}$, TbNiSi$_{3}$, and HoNiSi$_{3}$ single crystals at zero fields were determined employing resonant X-ray magnetic diffraction experiments. For them, the primitive magnetic unit cell matches the chemical cell below their Néel temperatures. In the case of Gd- and Tb-based compounds, the magnetic structure is the same for both (magnetic space group $Cmmm′$) and can be described by a one-dimensional irreducible representation of the $Cmmm$ space group. It features ferromagnetic $ac$ planes stacked in an antiferromagnetic + − + − pattern along with the $\vec{b}$ direction, with the rare-earth magnetic moments pointing toward the $\vec{a}$ direction [5]. For HoNiSi$_{3}$, our results show that at temperatures between T$_{N1}$ and T$_{N2}$ (phase II), the ordered magnetic moment points along the $\vec{a}$ axis, while below T$_{N1}$ (phase I), the ordered magnetic moments have components both along with $\vec{a}$ and $\vec{c}$. Remarkably, while at phase II the possible magnetic structure is the same as found in GdNiSi$_{3}$ and TbNiSi$_{3}$, at phase I two irreducible representations are needed to account for the total magnetic moment direction. In this phase, the magnetic structure is consistent with $C2’/m$ magnetic structure. Lastly, those magnetic structures contrast with the + − − + stacking and moment direction along the $\vec{b}$ axis previously reported for YbNiSi$_{3}$ [6]. This indicates a sign reversal of the coupling constant between second-neighbor $R$ planes as $R$ is varied from Gd, Tb, and Ho to Yb. This behavior suggests a competition between distinct magnetic stacking patterns with similar exchange energies tuned by the size of $R$.