Effects of Magnetic Impurities in Quasi-One-Dimensional Magnets

In the low-dimensional gapped magnets such as CuGeO$_3$ and PbNi$_2$V$_2$0$_8$, doping effects of non-magnetic impurities have been studied and novel order-by-disorder phenomena such as the non-magnetic-impurity-induced phase transitions have been found. Recently, the effects of magnetic impurities was experimentally investigated in the Haldane material PbNi$_2$V$_2$O$_8$ and the impurity-induced transition temperature was found to have strange non-monotonic dependence on the magnitude of the impurity spin. Motivated by this recent progress, we study the non-magnetic and magnetic impurity effects in the gapped quasi-one-dimensional system, namely, the weakly coupled spin-1 antiferromagnetic Heisenberg chains on a simple cubic lattice. We utilize the quantum Monte Carlo method with the continuous-time loop algorithm and determine numerically the impurity-induced transition temperature for the systems with non-magnetic impurities and also with the magnetic impurities with spin magnitude $S=1/2$, $3/2$, $2$, and $5/2$. Our simulation results are compared to the experimental data and the picture for the impurity-induced ordered state is discussed.