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# Valence bond glass on an fcc lattice in the double perovskite Ba$_{2}$YMoO$_{6}$. 

M. A. de Vries, 1, 2,$_{∗}$ A. C. Mclaughlin, 3 and J.-W. G. Bos 4, 5 

$^{1}$School of Physics and Astronomy, E. C. Stoner Laboratory, University of Leeds, Leeds. LS2 9JT, UK 

$^{2}$School of Physics & Astronomy, University of St-Andrews, the North Haugh, KY16 9SS, UK 

$^{3}$Department of Chemistry, University of Aberdeen, Meston Walk, Aberdeen AB24 3UE, UK 

$^{4}$School of Chemistry, University of Edinburgh, King’s Buildings, Mayfield Road, Edinburgh EH9 3JZ, UK 

$^{5}$Department of Chemistry - EPS, Heriot-Watt University, Edinburgh, EH14 4AS, UK 

(Dated: October 29, 2018) 

We report on the unconventional magnetism in the cubic B-site ordered double perovskite Ba 2 YMoO 6 , using AC and DC magnetic susceptibility, heat capacity and µ SR. No magnetic order is observed down to 2 K while the Weiss temperature is ∼ − 160 K. This is ascribed to the geo- metric frustration in the lattice of edge-sharing tetrahedra with orbitally degenerate Mo 5+ s = 1 / 2 spins. Our experimental results point to a gradual freezing of the spins into a disordered pattern of spin-singlets, quenching the orbital degeneracy while leaving the global cubic symmetry unaffected, and providing a rare example of a valence bond glass. 

Magnetic insulators with lattices in which antiferro- magnetic (AF) bonds are geometrically frustrated have been studied widely in the pursuit of exotic quantum ground states such as spin liquid [1, 2]. Such non-classical ground states have mainly been sought in low dimen- sional structures such as the triangular lattice system κ -(BEDT-TTF)$_{2}$Cu$_{2}$(CN)$_{3}$ [3] and the kagome antifer- romagnet herbertsmithite [4]. Materials with a geomet- rically frustrated face centred cubic (fcc) lattice have in this respect received much less attention. The 12 near- neighbour magnetic bonds J$_{1}$ between the [000] and [ 1 2 1 $_{2}$0] spins on the fcc lattice form a network of edge-sharing tetrahedra (Fig. 1). When these bonds are AF ( J$_{1}$ > 0) the magnetism is geometrically frustrated, giving rise to a large (but not macroscopically large [5] as for the kagome lattice) ground-state manifold of spin configura- tions unrelated by symmetry. Further neighbour inter- actions ( J$_{2}$ ) along the 6 [100] vectors lift this degeneracy only partially; J$_{2}$ < 0 (along the 6 [100] vectors) leads to type I order, weak AF exchange (0 < J$_{2}$ < 2 J$_{1}$ ) to type III order and stronger AF exchange J$_{2}$ > 2 J$_{1}$ to type II order. Thermal/quantum fluctuations and quenched dis- order have been shown to result in a bias for respectively collinear and anti collinear states within these degenerate ground state manifolds [6–8], an entropic selection effect termed “order from disorder” [9]. This is in agreement with experiments on well-known compounds of rock-salt structure such as MnO [10, 11], Cd$_{1}$$_{−}$$_{x}$Mn$_{x}$Te [12], NiO, MnSe [10]. Classical type I, II or III order has also been confirmed for s = 1 / 2 [13–15] although less is known about the physics at the boundaries between the classi- cal phases. In this Letter we describe the unconventional magnetism in the compound Ba$_{2}$YMoO$_{6}$, providing ex- perimental evidence that an exotic valence bond glass (VBG) [16, 17] state can stabilize at the boundary be- tween the known classical phases on the fcc lattice. Such a disordered state has been predicted to be possible even 

PACS numbers: 75.10.Jm, 76.75.+i, 75.40.Cx 

in the absence of structural disorder, as an example of a non-equilibrium quantum ground state [16]. 

The B-site ordered double perovskites are of general stoichiometry A$_{2}$BB $^{′}$O$_{6}$ where the A site typically hosts alkaline-earths and lanthanides and the B sites can host 3 d , 4 d and 5 d transition metal (TM) ions. Depending on the combination of B and B ′ site ions, electronic phases from strongly correlated metals via half-metals [18] and semiconductors [19, 20] to Mott insulating can be real- ized. Mott insulating 4 d and 5 d TM compounds are rare. The occurrence of this insulating phase in the double per- ovskites is due to the large distance between the TM ions, of the order of 5 to 6 ˚ A. Examples of Mott insulators are Ba$_{2}$LaRuO$_{6}$ and Ca$_{2}$LaRuO$_{6}$ [21], respectively type III and type I antiferromagnets. Sr$_{2}$CaReO$_{6}$ [22] and Sr$_{2}$MgReO [23] (the Re 6+ has s = 1 / 2) have spin-glass ground states, consistent with a negligible J$_{2}$ along the pathway Re-O- B $^{′}$-O-Re. There is a large group of Mo 5+ compounds Ba$_{2}$ Ln MoO$_{6}$ with Ln = Nd, Sm, Eu, Gd, Dy, Er, Yb and Y [24]. The Mo 5+ has a singly occupied 4 d t$_{2}$$_{g}$ level with s = 1 / 2. Due to the strong spin-orbit coupling in 4 d TM ions in a cubic crystal field this is expected to lead to a j = 3 / 2 triplet [25, 26]. Only the larger lan- thanide compounds ( Ln = Nd, Sm and Eu) have N´eel order (Type I, implying J$_{2}$ < 0) coinciding with a weak 

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