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 Ba$_{2}$YNbO$_{6}$ above 200 K (150 K) for the zero-field (9 T) measure- ments [30]. The magnetic entropy is gradually released over a wide range of temperatures with a broad maxi- mum around 50 K. No anomalies corresponding to phase transitions are observed, only a gradual freezing, quench- ing all degrees of freedom associated with the orbitally degenerate t$_{2}$$_{g}$ s = 1 / 2 4 d electrons. As shown in the inset of Fig. 4, the total entropy recovered S$_{tot}$ = 12 ± 2 JK $^{$_{−}$1}$mol$^{$_{−}$1}$, close to the R ln 4 = 11 . 5 expected for a j = 3 / 2 quadruplet (the j = l − s = 1 / 2 doublet lies at much higher energies [25, 26]). Below 25 K only ∼ 5% of the entropy is released, in agreement with the Curie fit to the low temperature susceptibility which was found to correspond to ∼ 5% of the Mo 5+ if these remaining spins have j = 3 / 2. In a 9 T magnetic field most of the magnetic entropy shifts to lower temperatures. To gain a better understanding of the gradual freezing and the appearance of apparently weakly-coupled spins a µ 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 relax- ation due to nuclear spins which confirms that the main muon stopping site is near the O 2$_{−}$ 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 sus- ceptibility is due to a conventional spin-glass transition The magnetic properties of Ba$_{2}$YMoO$_{6}$ are very differ- ent to those of the related compound Sr$_{2}$MgReO$_{6}$ [23], where a first order transition to a conventional spin glass state is observed. That the crossover in Ba$_{2}$YMoO$_{6}$ is not a conventional spin-glass transition is also clear from the unusual frequency dependence of the AC susceptibil- ity. 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 correspond- ing 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 temper- ature susceptibility follows a power law χ ∝ ( T − T$_{s}$ ) $_{−}$γ with γ ≈ 1. As noted earlier, this contribution from effec- tively weakly-coupled spins can not be related one-to-one to any structural disorder but arises as a cooperative ef- fect, 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 a Lorentzian Kubo-Toyabe muon relaxation is expected below the spin glass transition, as observed in the re- lated system Sr$_{2}$MgReO$_{6}$ [23]. The very slow muon re- laxation observed at 5 K in Ba$_{2}$YMoO$_{6}$ indicates there are no static moments. At the same time the heat capac- ity data shows that at 5 K most of the magnetic entropy associated with j = 3 / 2 is quenched, implying static or- der. 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. FIG. 5: (Color online) The muon spin relaxation at 120, 5 and 1.4 K. The relaxation follows an exponential decay ( P ( t ) = exp[ − t/λ ] $^{β}$, solid lines) with β = 1 for all but the 1.4 K data, where β = 0 . 7. The temperature dependence of the relaxation rate λ is shown in the inset. FIG. 4: (Color online) The magnetic heat capacity obtained by subtracting the heat capacity of the diamagnetic analogue Ba 2 YNbO 2 in zero field (black dots) and in 9 Tesla (open squares). The experimental error for the 9 T data is com- parable 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). 3 0 2 4 6 8 10 t ( s) 0.2 0.4 0.6 0.8 1 P 120 K 5 K 1.4 K 1 10 100 T (K) 0 0.02 0.04 0.06 0 50 100 150 200 T (K) 0.05 0.1 0.15 0.2 C/T (JK -2 mol -1 ) zero field 9 Tesla 0 50 100 150 200 T (K) 5 10 15 S tot  (JK -1 mol -1 )