X-ray resonance Exchange scattering study of Field induced meta-magnetic phases in TbNi$_2$Ge$_2$

Rare-earth inter-metallic compound, TbNi$_2$Ge$_2$ is an interesting material for its uniaxial anisotropy and the presence of a number of meta-magnetic phases (MP), which we have investigated using x-ray resonant exchange scattering techniques. Two distinct field induced MPs have been revealed at 5 K for fields below 3 T applied along the c axis. In zero field, the magnetic structure is characterized primarily by commensurate q$_1$=(0,0,0.75), q$_2$=(0.5,0.5,0) and q$_3$=(0.5,0.5,0.5) wave vectors, implying a complex sequence of FM and AFM planes. With increasing magnetic field, a weak (0,0,1) peak starts to evolve reaching a maximum in the first MP (1.2 T $<$ H $<$ 1.6 T) and sharply disappears on entering the second MP (H $>$ 1.6 T). In the second MP, q$_1$ becomes incommensurate, (0,0,0.766), q$_2$ gets strongly suppressed, and q$_3$ peak splits into combination harmonics of q$_1$ and q$_2$. The persistence of AF peaks imply that AF planes are quite robust to spin-flip transitions and MP phases are intricate in nature due to several competing interactions in this compound.