Robust spin-ice freezing in magnetically frustrated Ho$_{2}$Ge$_{x}$Ti$_{2−x}$O$_{7}$ pyrochlore

Structural analysis of spin frustrated Ho$_2$GexTi$_{2−x}$O$_7$ (x = 0, 0.1, 0.15 & 0.25) pyrochlore oxides has been performed using high resolution x-ray diffraction pattern and low temperature synchrotron x-ray diffraction pattern. The effect of positive chemical pressure on the spin dynamics ofHo$_2$GexTi$_{2−x}$O$_7$ has been analysed through the study of static (M–T and M–H; magnetisation against temperature & magnetisation against magnetic field) and dynamical (ac susceptibility) magnetic measurements. In lower temperature regime (~2 K), such systems are predominantly governed by competing exchange (J$_{nn}$) and dipolar (D$_{nn}$) magnetic interactions. Magnetic measurements indicate that the application of increased chemical pressure in Ho$_2$Ti$_2$O$_7$ matrix propels the system towards diminished ferromagnetic interaction. Dipolar coupling constant remains almost unchanged but Curie–Weiss temperature $(θ_{cw})$ reduces to −0.04 K from 0.33 K (for an applied magnetic field; H = 100 Oe) with increasing x in Ho$_2$GexTi$_{2−x}$O$_7$. Positive chemical pressure establishes the dominance of Ho–Ho antiferromagnetic interaction J$_{nn}$ over dipolar interaction D$_{nn}$. Spin relaxation feature corresponding to thermally activated single ion freezing (T$_s$~15 K) is shifted towards lower temperature. This chemical pressure-driven T$_s$ shift is ascribed to the alteration in crystal field effect, which reduces the activation energy for singe ion spin freezing. The reduction in the activation energy indicates crystal field-phonon coupling in Ho$_2$GexTi$_{2−x}$O$_7$ system. The robustness in spin ice freezing (second spin relaxation feature in ac susceptibility curve) remains unaffected with increasingly chemical pressure. This spin freezing ('2 in-2 out' spin arrangement in tetrahedra) is related to quantum tunneling phenomenon, at T$_{ice}$ ~ 2 K. It indicates that majority of spins still follow the 'ice rule' in Ho$_2$GexTi$_{2−x}$O$_7$ even after the application of chemical pressure