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

Abstract

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 and, 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 the first 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 two-fold, three-fold and possibly six-fold 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.

Frustrated Quantum Rare-Earth Pyrochlores

“…Due to the small energy scales, the competition between the order-by-disorder selection and the selection by the applied field occurs at small magnetic fields, of order 0.5 T. This selection is highly direction dependent, with qualitatively different behavior for ψ 2 and ψ 3 ordering. Experimentally, most of these transitions have been observed in Er 2 Ti 2 O 7 , and are qualitatively consistent with theoretical expectations [65,66]. Given the inherent tunability of an applied field, coupled with the diverse set of behaviors predicted, the exploration of this low-field behavior serves as an instructive setting for addressing quantitative questions about order-by-disorder in Er 2 Ti 2 O 7 .…”

“…The effect of a magnetic field on Er 2 Ti 2 O 7 has a number of interesting regimes, such as quantum criticality in a [110] field [61], as well as rich physics at low-fields where aspects of the order-by-disorder come into play. This low-field behavior has been explored in detail in recent theoretical [65] and experimental [64,66] studies. Due to the small energy scales, the competition between the order-by-disorder selection and the selection by the applied field occurs at small magnetic fields, of order 0.5 T. This selection is highly direction dependent, with qualitatively different behavior for ψ 2 and ψ 3 ordering.…”

Crystal-field Hamiltonian and anisotropy in KErSe2 and CsErSe2

“…This is also similar to Er 3+ pyrochlores Er 2 B 2 O 7 (B = Ge, Ti, Pt, and Sn) which likewise have easy-plane magnetic anisotropies from a D 3 CEF environment [43]. In the pyrochlore Er 2 Ti 2 O 7 , this easyplane anisotropy leads to a degenerate ground state with emergent "clock anisotropies" in its magnetic ground state [44][45][46]. Given the similar XY CEF Hamiltonians, similar such behaviors could be found in the 2D triangular lattice Er 3+ delafossites.…”

Experimental Insights into Ground-State Selection of Quantum XY Pyrochlores

“…The effect of a magnetic field on the powder diffraction pattern of Er2Ge2O7 has been argued to indicate a pure ψ3 state (66). However, the domain selection arguments upon which this determination is based have been found to be incorrect (103)(104)(105). Thus, while it is possible that Er2Ge2O7 has a ψ3 ground state, it remains to be definitively shown.…”