Competing interactions in Dy and Tb garnets

The last decades in solid state research have seen the rise of rich and novel physics, beyond the Néel paradigm and transcending conventional descriptions based on Landau theory. Frustrated magnetism has contributed to these developments in major ways, through new concepts like the “Coulomb phase”, a highly degenerate state of matter brought to light by the discovery of spin ice in rare-earth pyrochlore networks. Amongst other geometrical-ly frustrated architectures candidates for frustrated magnetism physics, is the hyperkagome network. It consists in a twisted spatial arrangement of corner-sharing triangles and is found in rare-earth (R) garnets as R3Al5O12 or R3Ga5O12. Gd3Ga5O12 and Yb3Ga5O12 are among the most studied members of this family and it has been pro-posed that frustration is responsible for the emergence of a collective spin formed by a 10-ion loop which may exhibit long or short range order [1,2]. These two compounds also show a modest crystal field anisotropy, which is at variance with most other rare earth garnets. Indeed, a very strong Ising-like crystal field anisotropy character-izes the latter, and forces the spins to align along the cubic axes of the structure. Combined with dipolar interac-tions, this situation leads to classical long range (multi-axis) magnetic ordering, pointing to the less prominent role of frustration than in the isotropic case [3]. Using a combination of neutron scattering techniques, including polar-ized neutron powder diffraction, we illustrate this issue by studying the evolution of the magnetic properties of Dy3Al5O12 and Dy3Ga5O12. A dramatic change is observed, from an Ising-like anisotropy in Dy3Al5O12, to a quasi-planar one in Dy3Ga5O12. Concomitantly, the Néel temperature is considerably reduced from 2 K down to 0.3 K in Dy3Ga5O12. According to a point charge modeling, this change in the anisotropy is due to small variations of the oxygen positions surrounding Dy3+ ions. To widen the scope of these experimental results, we performed mean-field calculations to generate the magnetic phase diagram of an effective anisotropic pseudospin S = 1/2, charac-terized by general gxx, gyy, and gzz Landé factors. A very rich magnetic phase diagram, encompassing complex phases, likely disordered, is evidenced when magnetic anisotropy departs from the strong Ising case. We also studied Tb3Ga5O12, which is based on a non-Kramers ion [4]. In this case, the low symmetry at the rare earth site yields a two singlets crystal field ground state, separated by a small gap . We show that the mode at  becomes a band because of the magnetic couplings and should be then considered as a collective excitonic mode, rather than a simple crystal field line. Upon decreasing temperature, this exciton softens progressively and condenses at the Néel temperature. The two singlets recombine in magnetic states characterized by a strong Ising anisotropy, hence driving the formation of a conventional magnetic state. Interestingly, as in Tb-pyrochlores, the same type of mag-neto-elastic coupling is at work in Tb3Ga5O12, as suggested by intriguing phenomena such as the phonon hall or acoustic Faraday effects. Here, we provide direct microscopic evidence for this magneto-elastic, showing that Tb3Ga5O12 hosts hybrid phonon/exciton modes, in close analogy with the situation in Tb2Ti2O7 [5].

[1] J. A. M. Paddison et al, Science, 350, 179–181, 2015
[2] Lise Orduk Sandberg, et al, “Emergent magnetic behaviour in the frustrated Yb3Ga5O12 garnet”, 2021
[3] I. A. Kibalin et al, Phys. Rev. Research, 2, 033509, 2020
[4] S. Petit, et al, Phys. Rev. Research, 3, 013030, 2021
[5] T. Fennell, et al, Phys Rev Lett, 112, 017203, 2014.