  We report magnetocaloric and magnetic-torque evidence that in
Cs$_{2}$CuBr$_{4}$ -- a geometrically frustrated Heisenberg $S=1/2$
triangular-lattice antiferromagnet -- quantum fluctuations stabilize a series
of spin states at simple increasing fractions of the saturation magnetization
$M_{s}$. Only the first of these states -- at $M={1/3}M_{s}$ -- has been
theoretically predicted. We discuss how the higher fraction quantum states
might arise and propose model spin arrangements. We argue that the first-order
nature of the transitions into those states is due to strong lowering of the
energies by quantum fluctuations, with implications for the general character
of quantum phase transitions in geometrically frustrated systems.
