Absence of Spin Frustration in the Kagome Layers of Cu2+ Ions in Volborthite Cu3V2O7(OH)(2)center dot 2H(2)O and Observation of the Suppression and Re-Entrance of Specific Heat Anomalies in Volborthite under an External Magnetic Field

We determined the spin exchanges between the Cu2+ ions in the kagome layers of volborthite, Cu3V2O7(OH)(2)center dot 2H(2)O, by performing the energy-mapping analysis based on DFT+U calculations, to find that the kagome layers of Cu2+ ions are hardly spin-frustrated, and the magnetic properties of volborthite below similar to 75 K should be described by very weakly interacting antiferromagnetic uniform chains made up of effective S = 1/2 pseudospin units. This conclusion was verified by synthesizing single crystals of not only Cu3V2O7(OH)(2)center dot 2H(2)O but also its deuterated analogue Cu3V2O7(OH)(2)center dot 2H(2)O and then by investigating their magnetic susceptibilities and specific heats. Each kagome layer consists of intertwined two-leg spin ladders with rungs of linear spin trimers. With the latter acting as S = 1/2 pseudospin units, each two-leg spin ladder behaves as a chain of S = 1/2 pseudospins. Adjacent two-leg spin ladders in each kagome layer interact very weakly, so it is required that all nearest-neighbor spin exchange paths of every two-leg spin ladder remain antiferromagnetically coupled in all spin ladder arrangements of a kagome layer. This constraint imposes three sets of entropy spectra with which each kagome layer can exchange energy with the surrounding on lowering the temperature below similar to 1.5 K and on raising the external magnetic field B. We discovered that the specific heat anomalies of volborthite observed below similar to 1.5 K at B = 0 are suppressed by raising the magnetic field B to similar to 4.2 T, that a new specific heat anomaly occurs when B is increased above similar to 5.5 T, and that the imposed three sets of entropy spectra are responsible for the field-dependence of the specific heat anomalies.