Two-dimensional quantum ferromagnet, magnetic chains, and oxygen ordering in La$_2$NiO$_{4.125}$ single crystals

The temperature dependence of the magnetic susceptibility $\chi (T)$ is studied in the region of the magnetic and charge ordering of La$_2$NiO$_{4.125}$ single crystals that differ in the degree of ordering of the excess oxygen. In the absence of the ordering of the excess oxygen, $\chi (T)$ obeys the dependence $\chi (T)\approx C/tT^2$, which is explained by the formation of 1D FM Heisenberg chains of impurity states with $S$=1/2. The ordering of oxygen creates favorable conditions for the formation of 2D FM Heisenberg lattices of impurity states with $S=1/2$ that obey the exponential dependence $\chi (T)\approx C(T)^2\exp(4\pi JS^2/ kT)$, which is an indication of the formation of a 2D quantum Heisenberg ferromagnet.