Low-temperature magnetization of the antiferromagnetically coupled Heisenberg bilayer with ferromagnetic-intralayer long-range and near-neighbor interactions

In this paper, the spin wave theory is used to investigate the low-temperature magnetization of the Heisenberg bilayer with three kinds of spatially anisotropic interactions, which are the long-range ferromagnetic intralayer interaction (which decays as J/r p with distance r), nearest-neighbor ferromagnetic intralayer interaction K, and antiferromagnetic interlayer interaction J 1 . The effects of quantum and thermal fluctuations induced by spatially anisotropic interactions on both layer magnetization per site m and total magnetization per site M are obtained within the linear spin-wave theory approximation at zero field and finite magnetic fields, respectively. At the temperatures T ≠ 0, both m and M have not only the J 1 -dependent behaviors with the maxima in the small J 1 region, but also the T-dependent behaviors with the crossovers for the different values of J 1 . The layer magnetization m exhibits the non-monotonic dependence on the long-range exponent p at the temperatures T ≥ 0, including the emergence of a minimum in the region 2 < p < 3; while for M, due to the field-induced effect, only the minimum appears in the finite-temperature region. It is shown that in the region 2 < p < 3, there exist two types of finite-temperature phase transitions, which are from the antiferromagnetic collinear and non-collinear states to paramagnetic state at zero and low fields respectively. Both critical temperatures display the p-dependent behaviors with the minima in the large-p region. It is found that the heights and locations of the maxima, minima and crossovers for the magnetizations and critical temperatures, are strongly affected by spatially anisotropic couplings in low-temperature and low-field region. Our results of the magnetization obtained by the spin-wave theory are in agreement with the experimental data of the perovskites Pr 0.5 S r0.5 MnO 3 .