Low temperature magnetic properties of geometrically frustrated Gd₂Sn₂O₇and Gd₂Ti₂O₇

Abstract

We attempt to solve the magnetic structure of the gadolinium analogue of 'spin-ice', using a mixture of experimental and theoretical assumptions. The eventual predictions are essentially consistent with both the Mössbauer and neutron measurements but are unrelated to previous proposals. We find two possible distinct states, one of which is coplanar and the other is fully three-dimensional. We predict that close to the initial transition the preferred state is coplanar but that at the lowest temperature the ground-state becomes fully three-dimensional. Unfortunately the energetics are consequently complicated. There is a dominant nearest-neighbour Heisenberg interaction but then a compromise solution for lifting the final degeneracy resulting from a competition between longer-range Heisenberg interactions and direct dipolar interactions on similar energy scales.

Evidence for Gapped Spin-Wave Excitations in the FrustratedGd2Sn2O7Pyrochlore Antiferromagnet from Low-Temperature Specific Heat Measurements

“…Our measurements, however, extend to considerably lower temperature (∼ 115 mK) allowing us to test the proposal of gapped magnon excitations [19]. We observe below ∼ 350 mK a deviation from the T 2 behavior describing the data between 350 mK and 800 mK as previously reported [5]. The specific heat decreases also faster than the T 3 power-law expected for conventional gapless antiferromagnetic magnons.…”

“…Previous C m measurements on this material between 350 mK and 800 mK (see Fig. 1) were found to be parametrized by a C m (T ) ∼ T 2 law [5]. Such a temperature dependence of C m is unusual since conventional antiferromagnetic magnon excitations without a gap lead to C m (T ) ∼ T 3 or, with an anisotropy energy gap ∆, to C m (T ) ∼ exp(−∆/T ).…”

“…In contrast, a recent theoretical work [19] argues that the lowest temperature ∼ 350 mK considered in Ref. [5] for GSO corresponds to the upper temperature limit above which multi-magnon excitations start to proliferate, obscuring the genuine single-magnon/lowtemperature regime. In particular, calculations using the microscopic spin Hamiltonian [10,18,19] that describes the experimentally observed ground state of GSO [10] predict that C m should begin to drop away exponentially exactly at or just below 350 mK as gapped magnetic excitations become quenched at lower temperature [19].…”

“…As such, these materials display a wide variety of interesting and unusual behaviors. Examples of observed phenomenology include spin ice [1], spin glass [2,3], and spin liquid [4] behaviors as well as long-range magnetic order [5,6,7,8,9,10,11] and perhaps some novel type of hidden order [12]. A common trend observed in all of these systems is an apparent persistence of spin dynamics down to the lowest temperatures as revealed by muon spin relaxation (µSR) [3,4,7,8,9,11,12] Perhaps what is most perplexing, is that PSDs have been found in pyrochlores, such as Gd 2 Ti 2 O 7 (GTO) [9,11] and Gd 2 Sn 2 O 7 (GSO) [7,8,13], which, according to neutron scattering experiments [6,10], display long-range magnetic order below a critical temperature T c = 0.74 K for GTO [6] and T c = 1.0 K for GSO [10].…”

“…Thus Gd 2 Sn 2 O 7 is particularly well suited to the standard protocol of, after having identified the ground state, computing the secondquantized (magnon) low-lying spin excitations around that state [19,24]. The nearest neighbor exchange interaction is estimated from the Curie-Weiss constant θ CW = −8.6 K by J 1 = 3θ CW /zS(S + 1) = −0.273 K [5] where z = 6 is the number of nearest neighbors. The strength of the dipolar interaction is derived from the size of the magnetic moments and the geometry of the lattice [10,18,19,24].…”