The spin liquid state of the Tb₂Ti₂O₇pyrochlore antiferromagnet: a puzzling state of affairs

Abstract

The pyrochlore antiferromagnet Tb 2 Ti 2 O 7 has proven to be an enigma to experimentalists and theorists working on frustrated magnetic systems. The experimentally determined energy level structure suggests a local 111 Ising antiferromagnet at low temperatures, T 10 K. An appropriate model then predicts a long-range ordered Q = 0 state below approximately 2 K. However, muon spin resonance (µSR) experiments reveal a paramagnetic structure down to tens of millikelvins. The importance of fluctuations out of the ground state effective Ising doublet has been recently understood, for the measured paramagnetic correlations cannot be described without including the higher crystal field states. However, these fluctuations treated within the random phase approximation (RPA) fail to account for the lack of ordering in this system below 2 K. In this work, we briefly review the experimental evidence for the collective paramagnetic state of Tb 2 Ti 2 O 7 . The basic theoretical picture for this system is discussed, where results from classical spin models are used to motivate the investigation of quantum effects to lowest order via the RPA. Avenues for future experimental and theoretical work on Tb 2 Ti 2 O 7 are presented.

Phonon and crystal field excitations in geometrically frustrated rare earth titanates

“…Nevertheless, the experimentally observed lack of magnetic ordering down to the millikelvin range and the true magnetic ground state in Tb 2 Ti 2 O 7 still remain enigmatic. [31][32][33][34] Illustrating the diversity in magnetic behavior due to the subtle differences between the rare earth species of the titanates, the situation in both Dy 2 43 The effective ferromagnetic interaction between the spins in fact is shown to be due to the dominant ferromagnetic long-range magnetic dipole-dipole interactions. 28,44 The R 3+ ions in both Dy 2 Ti 2 O 7 and Ho 2 Ti 2 O 7 are well described by a well separated Ising doublet ͑first excited states are at ϳ266 and ϳ165 cm −1 , respectively 24 ͒ with a strong single-ion anisotropy along the local ͗111͘ directions.…”

Low-temperature specific heat and possible gap to magnetic excitations in the Heisenberg pyrochlore antiferromagnetGd2Sn2O7

“…The reason for the failure of Tb 2 Ti 2 O 7 to develop long-range magnetic order above 50 mK 22 despite a Curie-Weiss temperature, θ CW ∼ −14 K remains to this day largely unexplained 24,25,26 . Yb 2 Ti 2 O 7 is perhaps just as intriguing, with specific heat measurements revealing a sharp first order transition at T c ≈ 0.…”

Structural properties of the geometrically frustrated pyrochloreTb2Ti2OHan1, Gardner2, Booth3 2004Phys. Rev. B513320View full textAdd to dashboardCite

“…A spin-liquid state may not form if further interactions such as crystal field anisotropy, 5 , long-range exchange or dipolar interactions perturb the classical spin models. 6 However, since any amount of lattice disorder can precipitate a spin-glass phase, 7 geometrically-frustrated systems that do not magnetically order to the lowest temperatures are extremely rare. 8 This situation has inhibited experimental studies that attempt to isolate the effects of frustration.…”

“…Here, we focus on the case where the A site is occupied by a trivalent rare-earth ion with eightfold oxygen coordination, AO(2) 2 O(1) 6 , and the B site is occupied by a tetra-valent transition metal ion with sixfold oxygen co-ordination, BO(1) 6 . The A and B sites individually form infinite interpenetrating sublattices of corner-sharing tetrahedra.…”