In Hg$_{1-x}$Mn$_x$Te (x$geq$0.16) monocrystal, the giant-diamagnetic (GDM) and magnetization-step phenomena have been observed in spin glass (SG) regime. The susceptibility of GDM is about 100-1000 times than that of classic diamagnetic. It can be i
nterpreted that: due to the long-range antiferromagnetic (AF) exchange interactions and the non-uniform random distribution of Mn$^{2+}$ ions in Hg$_{1-x}$Mn$_x$Te, a quasi-static spin wave forms and produces the GDM phenomenon below the critical temperature and magnetic field. Meanwhile, this theory is proved by Monte Carlo simulations in a two-dimensional AF cluster based on XY model. Hence, it is possible to emerge long-range magnetic order structure in SG state.
