Orbital Dimer Model for the Spin-Glass State inY2Mo2O7

Abstract

The formation of a spin glass usually requires both structural disorder and frustrated magnetic interactions. Consequently, the origin of spin-glass behaviour in Y2Mo2O7-in which magnetic Mo 4+ ions occupy a frustrated pyrochlore lattice with minimal compositional disorder-has been a longstanding question. Here, we use neutron and X-ray pair-distribution function (PDF) analysis to develop a disorder model that resolves apparent incompatibilities between previously-reported PDF, EXAFS and NMR studies and provides a new and physical mechanism for spin-glass formation. We show that Mo 4+ ions displace according to a local "2-in/2-out" rule on each Mo4 tetrahedron, driven by orbital dimerisation of Jahn-Teller active Mo 4+ ions. Long-range orbital order is prevented by the macroscopic degeneracy of dimer coverings permitted by the pyrochlore lattice. Cooperative O 2− displacements yield a distribution of Mo-O-Mo angles, which in turn introduces disorder into magnetic interactions. Our study demonstrates experimentally how frustration of atomic displacements can assume the role of compositional disorder in driving a spin-glass transition. PACS numbers: 75.50.Lk,61.05.fm,75.10.Nr,75.25.Dk In a spin-glass transition, spins freeze into a metastable arrangement without long-range order [1]. It is generally accepted that two conditions must be satisfied for a spin-glass transition to occur: interactions between spins must be disordered and these interactions must also be frustrated [2,3]. In canonical spin glasses-e.g., dilute magnetic alloys such as Cu 1−x Mn x [4] and site-disordered crystals such as Fe 2 TiO 5 [5]-the nature of structural disorder and its coupling to magnetism is well understood. However, spin-glass behaviour is also observed in well-ordered crystals where the geometry of the magnetic lattice alone can generate frustration (see, e.g., [6][7][8]). Here, the mechanism of spin-glass formation poses an important challenge for theory [9,10]. The prototypical material that shows this anomalous behaviour is Y 2 Mo 2 O 7 -a system with apparently unremarkable levels of structural disorder, but with thermodynamic properties indistinguishable from canonical spin glasses (for a review, see [11]).The structure and dynamics of Y 2 Mo 2 O 7 have been extensively studied. The conventional nature of the spin-glass transition (freezing temperature T f = 22 K [12]) has been shown by exhaustive thermodynamic measurements, including non-linear susceptibility [12,13], specific heat [14,15], a.c. susceptibility [16], and thermo-remanent magnetization [17][18][19]. Inelastic neutron scattering [20], muon-spin rotation (µSR) [21], and neutron spin-echo studies [22,23] reveal a reduction in the spin-relaxation rate as T f is traversed. Neutron diffraction measurements show that the average structure is well-described by the ordered pyrochlore model (space group F d3m) both below and above T f [24,25]. In this structure, the average positions of magnetic Mo 4+ ions describe a network of corner-sharing tetrahedra [ Fig. 1 coo...

Local structure study of the orbital order/disorder transition inLaMnO3

“…This specific point is of relevance to the problem of disorder in the spin glass Y 2 Mo 2 O 7 , where very different real-space models again give almost-equivalent PDF fits. 9,44 Here the issue of orbital disorder is resolvable only because the temperatures involved (T < 50 K) are so much lower than those of relevance to LaMnO 3 . Looking forward, one particular challenge for the PDF community is the development of a more complete understanding of which problems are definitively solvable using PDF analysis and which are not.…”

“…This approximant approach is described fully in Ref. 9, but we proceed to summarise the key points here. The concept is to fit the low-r PDF data in terms of a small-box model derived from the known average structure by a specifically-chosen symmetry-lowering perturbation.…”

“…29 By contrast, Ahmed and Gehring reproduced the order parameter behaviour measured in resonant X-ray scattering experiments 30 using the so-called anisotropic Potts model, which describes a transition to a meaningfully-different local arrangement of JT distortions at high temperatures. 31 Motivated by the success of combined X-ray/neutron PDF measurements in characterising local orbital order in systems such as Y 2 Mo 2 O 7 , 9 we sought to establish whether a similar approach might shed new light on the nature of orbital disorder in high-temperature LaMnO 3 . The scattering contrast between X-ray and neutron measurements in principle heightens experimental sensitivity to different pairwise contributions to the PDF, and so is particularly useful in high-symmetry structures such as pyrochlores and perovskites.…”

Universal geometric frustration in pyrochlores

“…If in/out displacements have long-range order then the global symmetry drops from Fd m to F 3 m evidenced by the addition of 2 h 0 0 reflections, as seen for Pb 2 Ru 2 O 6.5 , due to a combination of lone pair effects and off-stoichiometry 10 . If in-out ordering only exists over short-length scales, it is equivalent to 2-in/2-out (2I2O) ordering, which is expected to be disordered on long-length scales due to degenerate configurations 11 . This is observed for Nb-pyrochlores due to charge disproportionation 4 , and also for Y 2 Mo 2 O 7 observed as split peaks in X-ray absorption spectroscopy 12 .…”

Spin-Orbit Dimers and Noncollinear Phases in d1 Cubic Double Perovskites

“…Our theoretical study elucidates physics behind and provides explanations of experimental data on molybdenum and osmium based compounds. The physics discussed here may also be relevant to other heavy transition metal compounds, such as molybdenum pyrochlores, in which random distribution of 'dimerized' bonds, induced by orbital degrees, have been recently revealed by pair-distribution function measurements [37]. We thank G. …”