Order by Disorder Spin Wave Gap in theXYPyrochlore MagnetEr2Ti2O<

Abstract

The recent determination of a robust spin Hamiltonian for the antiferromagnetic XY pyrochlore Er2Ti2O7 reveals a most convincing case of the "Order-by-Quantum-Disorder" mechanism for ground state selection. This mechanism relies on quantum fluctuations to remove an accidental symmetry of the magnetic ground state, and selects a particular ordered spin structure below TN=1.2 K. The removal of the continuous degeneracy results in an energy gap in the spectrum of spin wave excitations, long wavelength pseudo-Goldstone modes. We have measured the Order-by-Quantum-Disorder spin wave gap at a zone center in Er2Ti2O7, using low incident energy neutrons and the time-of-flight inelastic scattering method. We report a gap of Δ=0.053±0.006 meV, which is consistent with upper bounds placed on it from heat capacity measurements and roughly consistent with the theoretical estimate of ∼0.02 meV, further validating the spin Hamiltonian that led to that prediction. The gap is observed to vary with the square of the order parameter, and goes to zero for T∼TN.

Spin dynamics in highly frustrated pyrochlore magnets

“…The present data also confirm the opening of a spin gap at zone centers: Fig. 1c], a value which compares very well with previous estimates [29][30][31].…”

“…In zero field, theory predicts for these parameters a quantum ObD selection of the ψ 2 state [7][8][9][10][11]. The ObD mechanism also predicts the opening of a spin gap, yet smaller that experimental findings [29][30][31]. In a recent work, the impact of the projection onto the spin 1/2 subspace was examined to see if ObD is also at play when using the full CEF Hamiltonian of Eq.…”

Order from structural disorder in theXYpyrochlore antiferromagnetEr2Ti2O7

“…As a matter of fact, such a highly symmetric frustrated spin model is realized in the anisotropic XY pyrochlore Er 2 Ti 2 O 7 [16][17][18][19][20][21][22]. This pyrochlore material orders at T N ≃ 1.2 K into a noncoplanar k = 0 antiferromagnetic structure called the ψ 2 state [16,17].…”

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].…”