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

Valence bond glass on an fcc lattice in the double perovskite BaYMoO.


We report on the unconventional magnetism in the cubic B-site ordered double perovskite BaYMoO, using AC and DC magnetic susceptibility, heat capacity and SR. No magnetic order is observed down to 2 K while the Weiss temperature is  K. This is ascribed to the geometric frustration in the lattice of edge-sharing tetrahedra with orbitally degenerate Mo 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.

75.10.Jm, 76.75.+i, 75.40.Cx

Magnetic insulators with lattices in which antiferromagnetic (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 dimensional structures such as the triangular lattice system -(BEDT-TTF)Cu(CN) (3) and the kagome antiferromagnet herbertsmithite (4). Materials with a geometrically frustrated face centred cubic (fcc) lattice have in this respect received much less attention. The 12 near-neighbour magnetic bonds between the [000] and [] spins on the fcc lattice form a network of edge-sharing tetrahedra (Fig. 1). When these bonds are AF () 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 configurations unrelated by symmetry. Further neighbour interactions () along the 6 [100] vectors lift this degeneracy only partially; (along the 6 [100] vectors) leads to type I order, weak AF exchange () to type III order and stronger AF exchange to type II order. Thermal/quantum fluctuations and quenched disorder have been shown to result in a bias for respectively collinear and anti collinear states within these degenerate ground state manifolds (6); (7); (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), CdMnTe (12), NiO, MnSe (10). Classical type I, II or III order has also been confirmed for  (13); (15); (14) although less is known about the physics at the boundaries between the classical phases. In this Letter we describe the unconventional magnetism in the compound BaYMoO, providing experimental evidence that an exotic valence bond glass (VBG) (16); (17) state can stabilize at the boundary between the known classical phases on the fcc lattice. Such a disordered state has been predicted to be possible even in the absence of structural disorder, as an example of a non-equilibrium quantum ground state (16).

Figure 1: Four MoO octahedra (shaded grey) and Y ions (large spheres) in the cubic unit cell of BaYMoO (left). The Mo ions form a lattice of edge-sharing tetrahedra (right). The cubic lattice constant is 8.389 Å.

The B-site ordered double perovskites are of general stoichiometry O where the site typically hosts alkaline-earths and lanthanides and the sites can host , and transition metal (TM) ions. Depending on the combination of and site ions, electronic phases from strongly correlated metals via half-metals (18) and semiconductors (19); (20) to Mott insulating can be realized. Mott insulating and TM compounds are rare. The occurrence of this insulating phase in the double perovskites is due to the large distance between the TM ions, of the order of 5 to 6 Å. Examples of Mott insulators are BaLaRuO and CaLaRuO (21), respectively type III and type I antiferromagnets. SrCaReO (22) and SrMgReO (23) (the Re has ) have spin-glass ground states, consistent with a negligible along the pathway Re-O--O-Re. There is a large group of Mo compounds BaMoO with  Nd, Sm, Eu, Gd, Dy, Er, Yb and Y (24). The Mo has a singly occupied level with . Due to the strong spin-orbit coupling in TM ions in a cubic crystal field this is expected to lead to a triplet (25); (26). Only the larger lanthanide compounds ( = Nd, Sm and Eu) have Néel order (Type I, implying ) coinciding with a weak Jahn-Teller distortion (24); (27); (28), while the exchange interaction is of the order of 100 K (24). The other compounds were found to be paramagnetic and with cubic symmetry at all temperatures. BaYMoO is the simplest of these compounds because the Y ion does not carry a magnetic moment. The magnetic exchange is mainly via the 90 B’-O-O-B’ bonds (21); (24), giving rise to 12 near-neighbour AF bonds for each spin, across the edges of the tetrahedra (Fig. 1).

Polycrystalline BaYMoO was prepared by the solid state reaction of stoichiometric oxides of YO, MoO and BaCO powders of at least 99.99% purity. These were ground, die-pressed into a pellet and heated under flowing 5% H/N. The final synthesis temperature was 1200-1250C with three intermediate regrinding steps to ensure phase homogeneity. It was found that a first heating step of  hr at 900C in air and thorough homogenization helps to prevent the formation of BaMoO and YO impurities. Phase purity was confirmed by laboratory X-ray powder diffraction. In a related paper (29) neutron powder diffraction results are discussed, which show that the Y/Mo site disorder is less than 1%. The diamagnetic analog, BaYNbO, was prepared at 1200C in air from YNbO and BaCO. The sample magnetisation was measured on a Quantum Design magnetic property measurement system (MPMS) in fields up to 5 T. The heat capacity was measured on a Quantum Design physical property measurement system (PPMS), using  mg of a sintered pellet. The SR experiment was carried out at MUSR at ISIS, UK.

Figure 2: (color online) The DC magnetic susceptibility (x, left axis) and (x, right axis) of BaYMoO measured in 1 T. Curie-Weiss fits in the two linear regimes in are indicated in grey (red) and the black line gives the difference between the total susceptibility and the low-temperature Curie term. The inset shows at 2.3 (+) and 5 K () and fits to the data with Brillouin functions, accounting for 7% of the Mo spins at 5K but only for 2% at 2.3 K.

The DC magnetic susceptibility measured in a 1 T field is shown in Fig. 2. A Curie-Weiss fit to the high temperature susceptibility yields a Weiss temperature of -160 K and a Curie constant of 0.25 emu mol K, small compared to the 0.38 emu mol K expected for . This difference is attributed to strong quantum fluctuations common in low-spin antiferromagnets and previously observed in double perovskites (26). Below 25 K a second linear regime is observed in , corresponding (for a 1 T field) to a % fraction of all the moments (or % if they have the full where ) and a Weiss temperature of  K indicating weak AF exchange. This fraction is too large to be ascribed directly to either structural disorder or an impurity phase in the sample. Furthermore, fits to measured at 2.3 and 5 K (inset of Fig. 2) with Brillouin functions lead to estimates of respectively 2 and 7% of all spins, compared to 10% for fits to the curve. This suggests that the apparently quasi-free spins are an emergent property of the (disorder free) system.

Figure 3: (Color online) The temperature dependence of the dispersive (left axis, open symbols) and dissipative (right axis, filled symbols) components of the AC susceptibility. The solid lines are guides to the eye.

The AC susceptibility measured with a field amplitude of 5 Oe and zero DC offset field is shown in Fig. 3. The dispersive part of the AC susceptibility () is almost frequency independent and is comparable to the diverging low temperature DC susceptibility. The dissipative part () shows a frequency dependent maximum between 26 and 70 K. Remarkably, the maximum gradually gets sharper as the frequency increases, instead of weaker as expected for a spin-glass transition. The agreement between the DC susceptibility and below 20 K is a strong indication that the Curie-term can be ascribed to the weakly coupled spins.

The heat capacity associated with the single Mo electron in BaYMoO (as shown in Fig. 4) was obtained from comparison with the heat capacity of the diamagnetic analogue BaYNbO. The heat capacity from phonons of BaYMoO is expected to be lower than for BaYNbO by a factor 0.991 due to the mass difference between the Mo and Nb nuclei. However this is small compared to the experimental error in the sample mass which is known with 10% accuracy. For this reason the heat capacity was measured well into the paramagnetic regime and matched to the heat capacity of BaYNbO above 200 K (150 K) for the zero-field (9 T) measurements (30). The magnetic entropy is gradually released over a wide range of temperatures with a broad maximum around 50 K. No anomalies corresponding to phase transitions are observed, only a gradual freezing, quenching all degrees of freedom associated with the orbitally degenerate electrons. As shown in the inset of Fig. 4, the total entropy recovered JKmol, close to the expected for a quadruplet (the doublet lies at much higher energies (25); (26)). Below 25 K only % of the entropy is released, in agreement with the Curie fit to the low temperature susceptibility which was found to correspond to % of the Mo if these remaining spins have . In a 9 T magnetic field most of the magnetic entropy shifts to lower temperatures.

Figure 4: (Color online) The magnetic heat capacity obtained by subtracting the heat capacity of the diamagnetic analogue BaYNbO in zero field (black dots) and in 9 Tesla (open squares). The experimental error for the 9 T data is comparable to that indicated for the zero field data (grey area). The inset shows the total entropy release as a function of temperature in zero field (black line) and in 9 T (red line).
Figure 5: (Color online) The muon spin relaxation at 120, 5 and 1.4 K. The relaxation follows an exponential decay (, solid lines) with for all but the 1.4 K data, where . The temperature dependence of the relaxation rate is shown in the inset.

To gain a better understanding of the gradual freezing and the appearance of apparently weakly-coupled spins a SR experiment was carried out. The zero-field muon spin relaxation spectra at 120 K, 5 K and 1.4 K are shown in Fig. 5. There is no evidence of muon relaxation due to nuclear spins which confirms that the main muon stopping site is near the O ions. At 120 K there is no muon relaxation, as expected for a paramagnetic state. Remarkably, at 5 K a muon relaxation is still only just detectable. If the maximum in the AC susceptibility is due to a conventional spin-glass transition a Lorentzian Kubo-Toyabe muon relaxation is expected below the spin glass transition, as observed in the related system SrMgReO (23). The very slow muon relaxation observed at 5 K in BaYMoO indicates there are no static moments. At the same time the heat capacity data shows that at 5 K most of the magnetic entropy associated with is quenched, implying static order. The majority of spins must therefore have bound into (non-magnetic) static spin-singlet “valence bonds” in which also the orbital degrees of freedom are quenched. The moderate increase in the muon relaxation rate below 5 K is then due to slowing-down of a small fraction of the spins which are left isolated as domain walls or defects in a (disordered) valence bond crystal (VBC). The best characterization of this state is probably a valence bond glass (VBG) as described in Ref. (17).

The magnetic properties of BaYMoO are very different to those of the related compound SrMgReO (23), where a first order transition to a conventional spin glass state is observed. That the crossover in BaYMoO is not a conventional spin-glass transition is also clear from the unusual frequency dependence of the AC susceptibility. The gradual freezing and cross-over region around 50 K are consistent with a pseudogap predicted for the VBG (17). This gap, which corresponds to a spin-singlet dimerization energy scale, is filled by levels corresponding to emergent weakly-coupled spins which give rise to a diverging susceptibility as the temperature is decreased. In close agreement with Ref. (17) the observed low temperature susceptibility follows a power law with . As noted earlier, this contribution from effectively weakly-coupled spins can not be related one-to-one to any structural disorder but arises as a cooperative effect, due to the amorphous arrangement of spin-singlets. The heat capacity does not become zero at the lowest temperature measured which is consistent with a small residual entropy and an ungapped spectrum as expected for the VBG.

The classical ground-state energy is highest when , at the cross-over between type III () and type II magnetism (the energy per spin is for ). One possibility is that around this cross-over a spin-singlet state is energetically favored. A complete explanation of why spin-singlets stabilize will in the present case also involve the orbital degrees of freedom; It is the valence-bond formation rather than a Jahn-Teller effect that fixes the orbital orientation. This could be accompanied by local structural distortions which do not lead to experimentally observable (24); (29) structural changes because the valence bonds do not form a regular pattern within the crystal. As first observed by Goodenough and Battle (21), the band width is an important factor in understanding the magnetism in double perovskites with and transition metal ions. Because BaYMoO is a relatively wide-band insulator it could also be that the stability of a spin-singet state can be understood in terms of the model (31).

In conclusion, the B-site ordered double perovskite BaYMoO has Mo ions with a singly-occupied degenerate orbital in a cubic crystal field and with . These moments are located on an fcc lattice and coupled antiferromagnetically, with a Weiss temperature of  K. At high temperature the single-ionic moments are strongly reduced by quantum fluctuations, consistent with the formation of stable spin-singlet dimers at low temperatures. Remarkably, the dimerization pattern appears to be disordered, giving rise to emergent effectively unpaired spins with a diverging susceptibility as the temperature is reduced, in agreement with theoretical predictions of a VBG (17). It is proposed that the stabilisation of spin-singlets is a result of the fine-tuning of the ratio to the boundary between the classical type II and type III phases. Clearly the present results provide a strong motivation for further theoretical explorations of the phase diagram of the fcc antiferromagnet and of the interplay between spin and orbital degrees of freedom in and transition metal compounds. This is the first observation of a VBG in a quantum magnet. Further experimental studies are needed to understand the relationship between the structural and magnetic disorder in this class of materials.

The Royal Society of Edinburgh (JWGB) and Leverhulme Trust (ACM) are acknowledged for financial support. C. L. Henley and H. M. Rønnow are gratefully acknowledged for fruitful discussions. S. J. Ray, P. King and P. Baker are gratefully acknowledged for assistance with the SR experiments.


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