Order-by-disorder in theXYpyrochlore antiferromagnet

Abstract

We investigate the properties of the XY pyrochlore antiferromagnet with infinite local 111 planar anisotropy. We identify the ground states and show that the configurational ground state entropy is subextensive. By computing the free energy due to harmonic fluctuations and by carrying out Monte Carlo simulations, we find that the model exhibits thermal order-by-disorder leading to low-temperature long-range order consisting of discrete magnetic domains. In doing so, we set aside doubts that order-by-disorder survives in the thermodynamic limit in this model. We compute the spin wave spectrum and show that thermal and quantum fluctuations select the same magnetic structure. With a previously unreported finite-size scaling analysis of Monte Carlo data, we confirm that the transition is first order for the XY model. Using Monte Carlo simulations, we find that the state selected by thermal fluctuations in this XY pyrochlore antiferromagnet can survive the addition of sufficiently weak nearest-neighbor pseudo-dipolar interactions or long-range dipolar interactions to the spin Hamiltonian. Quite interestingly, the resulting state selected by thermal order-by-disorder is metastable below some temperature. We discuss our results in relation to the Er 2 Ti 2 O 7 and Er 2 Sn 2 O 7 pyrochlore antiferromagnets.

Spin freezing in the disordered pyrochlore magnet NaCaCo2F7 : NMR studies and Monte Carlo simulations

“…The two states form a basis of the E irreducible representation of the tetrahedral point group and can be continuously turned into each other by simultaneous rotation of four sublattices. The degeneracy between ψ 2 and ψ 3 persists even with an extra biquadratic exchange, however, both quantum and thermal fluctuations choose the noncoplanar ψ 2 state, [12][13][14][38][39][40] an instance of the phenomenon known as order by disorder. [41] An experimental example is provided by Er 2 Ti 2 O 7 .…”

Order from structural disorder in theXYpyrochlore antiferromagnetEr2Ti2O7

“…The two states form a basis of the E irreducible representation of the tetrahedral point group and can be continuously turned into each other by simultaneous rotation of four sublattices. Such degeneracy persists even with an extra biquadratic exchange, but the harmonic spin-wave calculations indicate that fluctuations choose the noncoplanar m 3z 2 −r 2 state [7,8,[23][24][25][26]. Therefore, it is instructive to study the role of structural disorder, in particular, nonmagnetic vacancies, on degeneracy lifting for the XY pyrochlore antiferromagnet.…”

Antiferromagnetic order in the pyrochloresR2Ge2O7 (R=Er,Dun1, Li2, Freitas3 et al. 2015Phys. Rev. B

“…Recently, both experimental and theoretical studies suggest that the quantum spin fluctuations lift the U(1) degeneracy with a small gap opening in the spin-wave spectrum and select an antiferromagnetic (AFM) ordering state (ψ 2 ) as the ground state for Er 2 Ti 2 O 7 . This is the so called "order by disorder" (ObD) mechanism [14][15][16][17][18], in which the ground state is selected through entropic effects. Meanwhile, an alternative CEF-induced energetic selection mechanism is proposed that will likewise result in the ψ 2 state with similar value of the gap [19,20].…”