Intertwined Magnetic Dipolar and Electric Quadrupolar Correlations in the Pyrochlore Tb$_2$Ge$_2$O$_7$

Abstract

We present a comprehensive experimental and theoretical study of the pyrochlore Tb 2 Ge 2 O 7 , an exemplary realization of a material whose properties are dominated by competition between magnetic dipolar and electric quadrupolar correlations. The dipolar and quadrupolar correlations evolve over three distinct regimes that we characterize via heat capacity, elastic and inelastic neutron scattering. In the first regime, above T * = 1.1 K, significant quadrupolar correlations lead to an intense inelastic mode that cannot be accounted for within a scenario with solely magnetic dipole-dipole correlations. The onset of extended dipole correlations occurs in the intermediate regime, between T * = 1.1 K and T c = 0.25 K, with the formation of a collective paramagnetic state characterized by extended ferromagnetic canted spin ice domains. Here, long-range order is impeded not only by the usual frustration operating in classical spin ice systems, but also by a competition between dipolar and quadrupolar correlations. Finally, in the lowest temperature regime, below T c = 0.25 K, there is an abrupt and significant increase in the dipole ordered moment. The majority of the ordered moment remains tied up in the ferromagnetic spin ice-like state, but an additional k = (0, 0, 1) antiferromagnetic order parameter also develops. Simultaneously, the spectral weight of the inelastic mode, which is a proxy for the quadrupolar correlations, is observed to drop, indicating that dipole order ultimately wins out. Tb 2 Ge 2 O 7 is therefore a remarkable platform to study intertwined dipolar and quadrupolar correlations in a magnetically frustrated system and provides important insights into the physics of the whole family of terbium pyrochlores.

Elastic study of electric quadrupolar correlation in the paramagnetic state of a frustrated quantum magnet $\rm Tb_{2+\it δ}Ti_{2-\it δ}O_7$

“…Inelastic neutron scattering experiments showed that the first excited CEF mode becomes dispersive below about 20 K, suggesting CEF levels among adjacent Tb 3+ ions are interacted [29,36]. Moreover, in a sister compound Tb 2 Ge 2 O 7 , recent comprehensive study showed that significant correlations between quadrupolar moments of Tb 3+ ions are present above 1.1 K [37]. All these suggests that the onset of quadrupolar correlation is much higher than the longrange quadrupolar ordering temperature.…”

Traversing the pyrochlore stability diagram; microwave-assisted synthesis and discovery of mixed B-site Ln$_2$InSbO$_7$ family

“…In contrast to the other lanthanide ions presented so far, the non-Kramers doublet of the J=6 free-ion ground state manifold of Tb 3+ is separated from its first excited doublet by only ∼1.4 meV [2,64,176,[312][313][314]. Corresponding to a gap roughly an order of magnitude smaller than Yb 3+ , the application of the pseudospin-1/2 model is not necessarily straightforward, necessitating the incorporation of more subtle effects, possibly even on equal footing with ĤCEF [315][316][317]. Such subtle effects include virtual crystal field transitions, secondary corrections that introduce anistropic exchange and may potentially stabilize a quantum spin ice ground state in the cooperative paramagnet Tb 2 Ti 2 O 7 [176,268,315,316,[318][319][320].…”

Frustrated Magnetism in Fluoride and Chalcogenide Pyrochlore Lattice Materials

“…More recently, direct measurement of the CEF levels in MgHo 2 Se 4 via inelastic neutron scattering reveals a non-Kramers doublet ground state, in close proximity to an excited doublet and singlet below 1 meV, and yet another singlet below 3 meV [50]. The complicated CEF scheme with many low lying levels bares some resemblance to the terbium oxide pyrochlores, whose ground states are formed by two closely spaced doublets and the competing energy scales of single ion effects and the ion-ion interactions leads to rich and complex physics that has eluded description by a microscopic theory [72][73][74][75]. In the holmium spinels the lowest lying excited CEF levels are even more numerous and closely spaced than the 1.5 meV level in the terbium pyrochlores, and thus we can expect similarly rich physics.…”