Critical temperature and low-energy excitations in gapped spin systems with defects

Abstract

We discuss theoretically the magnetically ordered phase induced by magnetic and nonmagnetic impurities in three-dimensional and quasi-low-dimensional systems with singlet ground states separated by a gap from the excited triplet states. Using ideas of the percolation theory, we estimate the transition temperature TN (n) to the Néel phase and derive the density of states of low-energy elementary excitations at a small concentration n of defects. Our expression for TN (n) describes well available experimental findings obtained in various appropriate systems: spin-1 2 dimer materials, spin-ladder compounds, spin-Peierls and Haldane chain materials. However, our expression for TN (n) differs considerably from those proposed before.