Weak ferromagnetism of quasi-one-dimensional S=1/2 antiferromagnet BaCu${}_2$Ge${}_2$O${}_7$

Weak ferromagnetism of quasi-one-dimensional S = 1/2 antiferromagnet BaCu${}_2$Ge${}_2$O${}_7$ is studied by the magnetization measurement. The spontaneous magnetization appears along the b axis. The local symmetry between the in-chain nearest neighbor spins allows the presence of Dzyaloshinskii-Moriya interaction, and the only possible spatial configuration of the weak ferromagnetic moment per spin determines the sign of the inter-chain interaction. A weak $a$-axis magnetic field can change the direction of the magnetization to the $a$-axis direction, which shows that the spin chain forms a weakly coupled weak-ferromagnetic chain system.