Experimental evidence for field-induced emergent clock anisotropies in the XY pyrochlore Er2Ti2O7

The XY pyrochlore antiferromagnet Er2Ti2O7 exhibits a rare case of Z6 discrete symmetry breaking in its ψ2 magnetic ground state. Despite being well-studied theoretically, systems with high discrete symmetry breakings are uncommon in nature. Thus, Er2Ti2O7 provides an experimental playground for the study of broken Zn symmetry, for n>2. A recent theoretical work examined the effect of a magnetic field on a pyrochlore lattice with broken Z6 symmetry and applied it to Er2Ti2O7. This study predicted multiple domain transitions depending on the crystallographic orientation of the magnetic field, inducing rich and controllable magnetothermodynamic behavior. In this work, we present neutron scattering measurements on Er2Ti2O7 with a magnetic field applied along the [001] and [111] directions and provide experimental observation of these exotic domain transitions. In a [001] field, we observe a ψ2 to ψ3 transition at a critical field of 0.18±0.05 T. We are thus able to extend the concept of the spin-flop transition, which has long been observed in Ising systems, to higher discrete Zn symmetries. In a [111] field, we observe a series of domain-based phase transitions for fields of 0.15±0.03 T and 0.40±0.03 T. We show that these field-induced transitions are consistent with the emergence of twofold, threefold, and possibly sixfold Zeeman terms. Considering all the possible ψ2 and ψ3 domains, these Zeeman terms can be mapped onto an analog clock—exemplifying a literal clock anisotropy. Lastly, our quantitative analysis of the [001] domain transition in Er2Ti2O7 is consistent with order-by-disorder as the dominant ground state selection mechanism.