Magnetic properties of defects in spin-gap magnets

The magnetic properties of defects were studied in spin-gap magnets such as spin-Peierls magnet CuGeO$_3$, Haldane magnet PbNi$_2$V$_2$O$_8$, and charge-ordered ladder magnet NaV$_2$O$_5$. Doping of these systems with nonmagnetic impurities leads to additional magnetic degrees of freedom, which manifest themselves at low temperatures, where the intrinsic magnetic susceptibility of a spin-gap system is close to zero. Magnetic susceptibility appears due to the local destruction of the singlet ground state as a result of impurity-induced breakage of spin chains. Antiferromagnetically correlated areas arise near the spin-chain breaks. The sizes of these areas and the effective spin of these specific spin clusters are estimated. The order parameter and its spatially modulated depth are determined for impurity-induced magnetically ordered phases. The magnetic properties of defects for the NaV$_2$O$_5$ ladder structure are explained in the model of electrons «hopping» near the chain break. The hopping degree of freedom effectively influences the total spin of a spin-chain fragment and magnetization of the system.