Experimental Evidence for field induced emergent clock anisotropies in the XY pyrochlore Er$_2$Ti$_2$O$_7$

The XY pyrochlore Er$_2$Ti$_2$O$_7$, with its $\psi_2$ magnetic ground state, has garnered much attention due to the possibility that its ground state selection could originate from an order-by-disorder mechanism[1,2]. However, recently, theoretical work has exploited the fact that the symmetry breaking in this system is a rare case of high discrete symmetry (Z$_6$) [3]. This work studied the effect of a magnetic field on the Z$_6$ symmetry breaking and predicted rich and controllable magnetothermodynamic properties. Indeed, the authors predict numerous domains transitions in the low field regime that strongly depends on the field direction. In this talk, I will present neutron scattering data on Er$_2$Ti$_2$O$_7$ with a magnetic field applied along different high symmetry direction. Our experimental study has provided the first experimental evidence for this rich Z$_6$ domain phase behaviour. Lastly, I will address how our results could shed light on the putative ground state selection mechanism in Er$_2$Ti$_2$O$_7$. [1]L. Savary et al., Phys. Rev. Lett.,109,167201 (2012) [2]M. E. Zhitomirsky et al., Phys. Rev. Lett.,109,077204 (2012) [3]V. S. Maryasin et al., Phys. Rev. B., 93,100406(R) (2016)