Spin Hamiltonian, Competing Small Energy Scales, and Incommensurate Long-Range Order in the Highly FrustratedGd3Ga5O12Garnet Antiferromagnet

Abstract

Despite the availability of a spin Hamiltonian for the Gd3Ga5O12 garnet (GGG) for over twenty five years, there has so far been little theoretical insight regarding the many unusual low temperature properties of GGG. Here we investigate GGG in zero magnetic field using mean-field theory. We reproduce the spin liquid-like correlations and, most importantly, explain the positions of the sharp peaks seen in powder neutron diffraction experiments. We show that it is crucial to treat accurately the long-range nature of the magnetic dipolar interactions to allow for a determination of the small exchange energy scales involved in the selection of the experimental ordering wave vector. Our results show that the incommensurate order in GGG is classical in nature, intrinsic to the microscopic spin Hamiltonian and not caused by weak disorder.The diversity of empirical data collected over the past fifteen years has demonstrated that geometrically frustrated triangular and tetrahedral arrangements of antiferromagnetically coupled spins are highly partial towards the realization of exotic correlated phases in magnetic materials [1,2,3]. The reason for the rich and typically material specific properties of frustrated magnets is understood. It stems from their sensitivity to perturbations beyond the frustrating nearest-neighbor antiferromagnetic (AFM) exchange which, on its own, leads to a macroscopic number of exactly degenerate and competing, hence fragile, classical ground states. In this paper we show, through a careful theoretical analysis of neutron scattering experiments, that the extensively studied Gd 3 Ga 5 O 12 garnet (GGG) is precisely such a system, though evidence for this fact emerges from a perspective on the problem that has heretofore escaped scrutiny.GGG displays a gamut of complex and interesting low temperature magnetic phenomena. In zero magnetic field, the behavior of GGG is uniquely rich. The nonlinear magnetic susceptibility χ 3 peaks at T g ∼ 180 mK [4], indicating a spin glass transition [5]. However, muon spin relaxation [6,7] and Mössbauer spectroscopy [8] find persistent spin dynamics down to T ≪ T g . Meanwhile, powder neutron scattering data [9,10] indicate that GGG is on the verge of developing true incommensurate longrange magnetic order with a correlation length (ξ ≈ 100 A) extending over 8 cubic unit cells below 140 mK.A Hamiltonian H describing GGG, that we shall explicitly define below, has long been available [11]. It assumes classical Gd 3+ spins, is parameterized as a sum of empirical exchange contributions up to third nearestneighbors as well as a magnetic dipolar contribution, and ignores potentially important quantum fluctuations or disorder inherent to GGG [4]. Previous numerical studies based on H have been unable to provide a quantitative explanation for the bulk [4] and dynamical [6,7,8] properties of GGG or the incommensurate spin-spin correlations that develop below 200 mK [9,10]. This could be interpreted as evidence that exotic mechanisms involving either quantum fluctuations ...

spinvert: a program for refinement of paramagnetic diffuse scattering data

“…In fact, the key point here may not relate directly to RMC at all: it is simply that the magnetic powder diffraction data-together with knowledge of the the crystal structure-contain a great deal of information. It seems very likely that other techniques could be developed to access this information effectively; for example, it is possible to fit interaction parameters directly to powder data within a mean-field theory model (see, e.g., [45,46]). …”

Juxtaposition of spin freezing and long range order in a series of geometrically frustrated antiferromagnetic gadolinium garnets

“…Further neighbor interactions may be important, as seems to be the case in GGG, 27,28 but for the other compounds (GTLG and GAG) studied here, these interactions have not yet been determined. There also may be some small single-ion anisotropy present in these materials.…”

“…27,31 The dipolar interaction, on the other hand, is purely defined by the size of the moments and the distance between the magnetic ions. Since the lattice parameters of these compounds are very similar and we have the same magnetic species in each material, the dipolar interactions are also very similar in magnitude.…”

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

“…This is highly unusual since conventional wisdom suggests that collective magnon-like excitations, hence spin dynamics, should freeze out in the limit of zero temperature. Similarly, the Gd 3 Ga 5 O 12 antiferromagnetic garnet (GGG), which displays rather extended magnetic correlations below 140 mK [14] that are now theoretically rationalized [15], also exhibits PSDs below 100 mK [16]. It is tempting to speculate that the unusual low-energy excitations giving rise to PSDs may result from a remnant of the high frustration that these systems possess and the lack of long-range order that would occur were it not for perturbatively small exchange interactions beyond nearest-neighbor [17], dipolar interactions [18,19] or single-ion anisotropy [20].…”