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If magnetic frustration is most commonly known for undermining long-range order, as famously illustrated by spin liquids, the ability of matter to develop new collective mechanisms in order to fight frustration is no less fascinating, providing an avenue for the exploration and discovery of unconventional properties of matter. Here we study an ideal minimal model of such mechanisms which, incidentally, pertains to the perplexing quantum spin ice candidate Yb2Ti2O7. Specifically, we explain how thermal and quantum fluctuations, optimized by order-by-disorder selection, conspire to expand the stability region of an accidentally degenerate continuous symmetry U(1) manifold against the classical splayed ferromagnetic ground state that is displayed by the sister compound Yb2Sn2O7. The resulting competition gives rise to multiple phase transitions, in striking similitude with recent experiments on Yb2Ti2O7 [Lhotel et al., Phys. Rev. B 89 224419 (2014)]. Considering the effective Hamiltonian determined for Yb2Ti2O7, we provide, by combining a gamut of numerical techniques, compelling evidence that such multiphase competition is the long-sought missing key to understanding the intrinsic properties of this material. As a corollary, our work offers a pertinent illustration of the influence of chemical pressure in rare-earth pyrochlores.
We document the coexistence of ferro- and anti-ferromagnetism in pyrochlore $rm Yb_2Ti_2O_7$ using three neutron scattering techniques on stoichiometric crystals: elastic neutron scattering shows a canted ferromagnetic ground state, neutron scatterin
Motivated by recent neutron scattering experiments, we derive and study an effective pseudo-dipolar spin-1/2 model for the XY pyrochlore antiferromagnet Er2Ti2O7. While a bond-dependent in-plane exchange anisotropy removes any continuous symmetry, it
Several rare earth magnetic pyrochlore materials are well modeled by a spin-1/2 quantum Hamiltonian with anisotropic exchange parameters Js. For the Er2Ti2O7 material, the Js were recently determined from high-field inelastic neutron scattering measu
In frustrated magnetic systems with competing interactions fluctuations can lift the residual accidental degeneracy. We argue that the state selection may have different outcomes for quantum and thermal order by disorder. As an example, we consider t
We examine the Si(111) multi-valley quantum Hall system and show that it exhibits an exceptionally rich interplay of broken symmetries and quantum Hall ordering already near integer fillings $ u$ in the range $ u=0-6$. This six-valley system has a la