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We present two phenomenological models to calculate the grain boundary resistance in polycrystalline and two-phase lanthanum manganites. Using the rst model we demonstrate that it is not the total magnetization, but rather the difference in magnetization of neighboring magnetic grains that plays the most important role in temperature dependences of resistance and magnetoresistance of doped polycrystalline lanthanum manganites with grain boundaries. Our calculations show that, in order to obtain the maximum in temperature dependence of resistance at Tm, grain boundary layers have to be, at least, weakly ferromagnetic. Increase of the ferromagneticity of these layers leads to decrease of resistance, increase of Tm, and decrease of the difference between Tm and Curie temperature TC. Increase in the number of grain boundaries also leads to increase of resistance, but does not affect the value of Tm. The second model is devoted to relation of resistivity and magnetization in two-phase thin lms of lanthanum manganites. Every plane is asumed to be a mixture of two ferromagnetic phases with different magnetizations and concentrations. Thin lm, represented as the system of such planes, is reduced to a circuit of resistances connected in parallel. The grain boundary resistivity is expressed as the difference in magnetization of phases. For such a system we have found that the peak of resistivity Tm decreases and shifts towards higher values of temperature with increase of lm thickness, the result which qualitatively agrees with experimental data.

Modelling of grain boundary resistance in thin films of lanthanum manganites