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We determined the spin exchanges between the Cu2+ ions in the kagome layersof volborthite, Cu3V2O7(OH)2x2H2O, by performing the energy-mapping analysisbased on DFT+U calculations, to find that the kagom\'e layers of Cu2+ ions arehardly spin-frustrated, and the magnetic properties of volborthite below ~75 Kshould be described by very weakly interacting antiferromagnetic uniform chainsmade up of effective S=1/2 pseudospin units. This conclusion was verified bysynthesizing single crystals of not only Cu3V2O7(OH)2x2H2O but also itsdeuterated analogue Cu3V2O7(OD)2x2D2O and then by investigating their magneticsusceptibilities and specific heats. Each kagome layer consists of intertwinedtwo-leg spin ladders with rungs of linear spin trimers. With the latter actingas S=1/2 pseudospin units, each two-leg spin ladder behaves as a chain of S=1/2pseudospins. Adjacent two-leg spin ladders in each kagome layer interact veryweakly, so it is required that all nearest-neighbor spin exchange paths ofevery two-leg spin ladder remain antiferromagnetically coupled in all spinladder arrangements of a kagome layer. This constraint imposes three sets ofentropy spectra with which each kagome layer can exchange energy with thesurrounding on lowering the temperature below ~1.5 K and on raising theexternal magnetic field B. We discovered that the specific heat anomalies ofvolborthite observed below ~1.5 K at B = 0 are suppressed by raising themagnetic field B to ~4.2 T, that a new specific heat anomaly occurs when B isincreased above ~5.5 T, and that the imposed three sets of entropy spectra areresponsible for the field-dependence of the specific heat anomalies.

condensed matter

Absence of Spin Frustration in the Kagom\'e 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