Absence of magnetic ordering and field-induced phase diagram in the gadolinium aluminum garnet

Abstract

The robustness of spin liquids with respect to small perturbations, and the way magnetic frustration can be lifted by slight changes in the balance between competing magnetic interactions, remains a rich and open issue. We address this question through the study of the gadolinium aluminum garnet Gd 3 Al 5 O 12 , a related compound to the extensively studied Gd 3 Ga 5 O 12 . We report on its magnetic properties at very low temperatures. We show that despite a freezing at about 300 mK, no magnetic transition is observed, suggesting the presence of a spin-liquid state down to the lowest temperatures, similarly to Gd 3 Ga 5 O 12 , in spite of a larger ratio between exchange and dipolar interactions. Finally, the phase diagram as a function of field and temperature is strongly reminiscent of the one reported in Gd 3 Ga 5 O 12 . This study reveals the robust nature of the spin-liquid phase for Gd ions on the garnet lattice, in stark contrast to Gd ions on the pyrochlore lattice for which a slight perturbation drives the compound into a range of magnetically ordered states. DOI: 10.1103/PhysRevB.96.220413 In the last few decades, great interest has been devoted to the study of frustrated systems. In particular, in geometrically frustrated magnetic systems, a competition between exchange energies is induced by the geometry of the lattice. It prevents conventional magnetic ordering, resulting in exotic correlations and ground states that can remain disordered down to zero temperature [1]. Additional perturbations such as exchange interactions beyond the nearest-neighbor exchange, dipolar interactions, quantum fluctuations, or disorder can then play a crucial role and select a unique ground state in the system. The characterization of the robustness of the frustrated ground states with respect to these perturbations is thus an important question.Among the lattices that are prone to exhibit magnetic frustration, an interesting example is the hyperkagome structure, a three-dimensional lattice of corner-sharing triangles. Few realizations of such a structure have been discovered. The main examples are the garnets of formula X 3 A 2 B 3 O 12 (with X a magnetic element, and A,B nonmagnetic elements), the iridate compound Na 4 Ir 3 O 8 [2][3][4], and more recently PbCuTe 2 O 6 [5]. While the last two compounds are studied for their properties related to quantum effects, many studies on the frustration in magnetic garnets have focused on the gadolinium gallium garnet GGG (formula Gd 3 Ga 5 O 12 ), considered as an archetypal system to study the classical Heisenberg model with antiferromagnetic interactions on the hyperkagome lattice. The interesting physics in this compound is derived directly from the peculiar structure, Gd ions positioned on two interpenetrating hyperkagome lattices (see Fig. 1), and the effect of the long-range dipolar interactions on the ground state.Experimentally, GGG presents no evidence of conventional long-range ordering down to 25 mK [6]. Short-range correla-* elsa.lhotel@neel.cnrs.fr † Present addr...

Spin dynamics of the director state in frustrated hyperkagome systems

“…Both compounds show an increase in g max below 1.5 K, as the director state emerges; g max increases rapidly with decreasing temperatures and peaks at ∼400 and 175 mK for GAG and GGG, respectively. Below this temperature, which coincides roughly with the onset of the spin freezing [17][18][19], g max appears to remain constant. The director-director correlations at the lowest temperatures are stronger in GGG than in GAG, as seen by the fact that g max (GGG) ≈ 3g max (GAG).…”

“…We have carried out several experiments on powdered samples of GAG and GGG, previously used in Ref. [19] and Refs. [9,21,22], respectively.…”

“…For the GGG powder, we have insufficient data to determine K. For GAG, we obtain K GAG = 0.03 − 0.04, which falls in the range of insulating spin glasses, if a bit smaller [46]. Nevertheless, the broad shape of the χ features in GAG and of the ZFC-FC magnetization [19] seems to preclude a conventional spin-glass transition. In particular, we could not accurately determine the freezing temperature T g which would have allowed us to perform dynamical scaling and estimate possible critical exponents.…”

“…In comparison to GGG, GAG has a larger near-neighbor exchange constant of J 1 = 186 mK [19], and the magnitude of the Curie-Weiss constant is larger as well, θ CW ∼ −3.9(3) K. The further-neighbor exchange constants are presently unknown for GAG. The (H, T ) phase diagram determined for GAG [19] is similar to that of GGG [17,21] with phase boundaries normalized to the magnitude of J 1 . A spin freezing in GAG happens below T GAG f ∼ 300 mK.…”

“…Neutron scattering revealed the onset of short-range correlations for T < 4 K with the director correlations developing for T 1.5 K [6,16]. Below T GGG f = 175 mK, the spins freeze partially [17][18][19]. The freezing is a result of the interplay between the next-nearest exchange interaction, −12 mK J 2 4 mK, the intersublattice exchange interaction, −3 mK < J 3 < 12 mK, and the long-range dipole interaction, D [20].…”