Magnetization Curves of Antiferromagnetic Heisenberg Spin- $\frac{1}{2}$ Ladders

Magnetization processes of spin- $\frac{1}{2}$ Heisenberg ladders are studied using strong-coupling expansions, numerical diagonalization of finite systems, and a bosonization approach. We find that the magnetization exhibits plateaux as a function of the applied field at certain rational fractions of the saturation value. Our main focus is on ladders with three legs where plateaux with magnetization one third of the saturation value are shown to exist.