In this paper, the Taylor polynomial method is used to solve the Helmholtz equation. Using the Taylor polynomial for the method, the Helmholtz equation is transformed into solving matrix equation. The error analysis of this equation is given. A numerical experiment is given to prove the efficiency and dependability of the method.

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Rare-earth-doped compounds (Sr1.85Ln0.15)FeMoO6(Ln=Sr, La, Ce, Pr, Nd, Sm and Eu) have been prepared by solid-state reaction. Crystal structure and magnetic properties were investigated by means of X-ray diffraction and magnetic measurements. All the samples are single phase and belong to the I4/m space group. Due to the competing contributions of electron doping and steric effects, the unit-cell volume of the doped compounds changes slightly and does not vary systematically with the ionic radius of the rare-earth ions. The temperature dependence of the magnetization of (Sr1.85Ln0.15)FeMoO6indicates that the Curie temperature of the doped compounds has increased upon doping, except for the Eu-doped compound.

Hole doped double perovskite compounds (Sr, Na)2FeMoO6 with the Na content of x = 0, 0.02, 0.03, 0.07 and 0.17 have been synthesized by sol-gel method. Effects of hole doping on the crystal structure and magnetic properties of Sr2FeMoO6 have been investigated. XRD pattern indicates that all the samples are of single phase and belong to the space group I4/m. The degree of cation ordering in the Na-doped Sr2FeMoO6 compounds shows a non-monotonic variation with the doping level. The saturation magnetization of the compound increases with x for x<0.17. Similar to the electron doped Sr2FeMoO6, provided that the doped hole enters selectively the spin-down band, the variation of the saturation magnetization can be explained in light of the ferrimagnetic model (FIM).

Crystal structure and magnetic properties of the double perovskite compounds Sr2(Fe1-xVx)MoO6 (0 ≤ x ≤ 0.1) have been investigated in this work. Rietveld refinement of the crystal structure shows that the cation ordering decrease monotonously with the V content. Magnetic measurement shows that saturation magnetization of the compounds decrease with increasing x due to the reduced degree of ordering. Analysis of saturation magnetization based on the ferrimagnetic model (FIM) indicates that the V atoms in Sr2(Fe1-xVx)MoO6 selectively occupy the Mo sites instead of Fe sites.