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Absence of Spin Frustration in the Kagomé Layers of Cu2+ Ions in Volborthite Cu3V2O7(OH)2x2H2O and Observation of the Suppression and Re-entrance of Specific Heat Anomalies in Volborthite Under External Magnetic Field

We determined the spin exchanges between the Cu2+ ions in the kagome layers of volborthite, Cu3V2O7(OH)2x2H2O, by performing the energy-mapping analysis based on DFT+U calculations, to find that the kagomé layers of Cu2+ ions are hardly spin-frustrated, and the magnetic properties of volborthite below ~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)2x2H2O but also its deuterated analogue Cu3V2O7(OD)2x2D2O 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 ~1.5 K and on raising the external magnetic field B. We discovered that the specific heat anomalies of volborthite observed below ~1.5 K at B = 0 are suppressed by raising the magnetic field B to ~4.2 T, that a new specific heat anomaly occurs when B is increased above ~5.5 T, and that the imposed three sets of entropy spectra are responsible for the field-dependence of the specific heat anomalies.