Purely entropy-driven magnetic phase transitions in the kagom\'e system volborthite.

We demonstrate that the low-temperature magnetic properties of volborthite, Cu3V2O7(OH)2 * 2H2O, possessing kagome layers of Cu2+ ions, are very well described by S = 1/2 Heisenberg chains with antiferromagnetic nearest-neighbor exchange coupling. The spin exchanges divide each kagome layer into weakly coupled two-leg ladders with rungs of S=1/2 pseudospins. Adjacent spin ladders are entangled with overlapping legs so that ordering between spin ladders is topologically constrained. Possible arrangements of adjacent spin ladders lead to three entropy spectra of identical enthalpy. Reentrant magnetic ordering is observed in high magnetic fields due to a purely entropy-driven mechanism.