Description of the colossal magnetoresistance of La$_{1.2}$Sr$_{1.8}$Mn$_{2}$O$_{7}$ based on spin-polaron and orientation conductivity mechanisms in the paramagnetic temperature region

The resistance of single-crystal La$_{1.2}$Sr$_{1.8}$Mn$_{2}$O$_{7}$ is studied experimentally and theoretically in the 75–300 K temperature range in magnetic fields varying in intensity from 0 to 90 kOe. The magnetoresistance is governed by spin-polaron and orientation conductivity mechanisms. The observed magnetoresistance of La$_{1.2}$Sr$_{1.8}$Mn$_{2}$O$_{7}$ at 75–300 K is characterized using the method of separation of contributions from different conductivity mechanisms. The calculated and experimental data agree closely. Temperature dependences of the spin-polaron size (in relative units) are calculated in the 75–300 K interval in zero magnetic field and in a 90 kOe field. It is demonstrated that the increasing (along the magnetic field) spin-polaron linear size gives rise to colossal magnetoresistance. In other words, the size change of magnetic inhomogeneities produces the primary contribution to the colossal magnetoresistance value.