Neutron diffraction and x-ray resonant exchange-scattering studies of the zero-field magnetic structures of ${\mathrm{TbNi}}_2{\mathrm{Ge}}_2$

The zero-field magnetic structures of the rare-earth intermetallic compound ${\mathrm{TbNi}}_2{\mathrm{Ge}}_2$ have been determined using conventional magnetic neutron diffraction and high-resolution x-ray resonant exchange scattering techniques. There are two distinct magnetic phase transitions in this material: one is from the high-temperature paramagnetic state to a long period antiferromagnetic phase at the Néel temperature ${(T}_N=16.8\mathrm{}\hspace{0.5em}\mathrm{K}),$ and the other is at a lower temperature ${(T}_t=9.3\mathrm{}\hspace{0.5em}\mathrm{K}),$ where the system locks into a commensurate phase. The structure above $T_t$ is described by a longitudinal, amplitude modulated, sinusoidal wave with propagation vector ${\mathit{\tau }}_1\approx (000.758\mathrm{}\pm 0.002)$ in reciprocal-lattice units (r.l.u.). As the temperature is lowered below $T_t,$ ${\mathit{\tau }}_1$ locks at $\left(0\mathrm{}\hspace{0.5em}0\hspace{0.5em}\frac{3}{4}\right)$ and additional magnetic Bragg reflections corresponding to ${\mathit{\tau }}_2=\left(\frac{1}{2}\hspace{0.5em}\frac{1}{2}\hspace{0.5em}0\right)$ and ${\mathit{\tau }}_3=\left(\frac{1}{2}\hspace{0.5em}\frac{1}{2}\hspace{0.5em}\frac{1}{2}\right)$ develop. A weak modulation ${\mathit{\tau }}_1^{\prime }=\left(0\mathrm{}\hspace{0.5em}0\hspace{0.5em}\frac{1}{4}\right),$ related to ${\mathit{\tau }}_1$ also appears indicating a squaring-up of the low-temperature structure. In this equal moment structure all Tb moments have the saturation value of ${\mu }_s=9.0\mathrm{}\pm 0.2{\mu }_{\mathrm{B}}.$ Both the phases are uniaxial with Tb moments parallel to the $\mathbf{c}^$ axis of the tetragonal unit cell.