On the Origin of the Magnetic Anisotropy Energy of Ferrites
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概要
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Possible sources of the anisotropy energy are investigated for ferromagnetic ferrites, i.e., Ni-, Co-, Fe- and Mn-ferrites. The cubic anisotropy energy which arises from the anisotropy of the crystalline field acting on magnetic ions and is described by the function of the spin operator of one ion identically vanishes for iors with spin less than 2, so that this kind of anisotropy energy vanishes for Ni^<2+> and Co^<2+> ions. The anisotropy energy arising from the magnetic dipole-dipole interaction which appears for cubic crystals in its second order perturbation was calculated for Mn- and Ni-ferrites and that arising from the anisotropic exchange interaction calculated for Ni-ferrite but they were found to be too small to account for the experimental values. Therefore, it is concluded that the major part of the anisotropy energy for Ni-ferrite arises from the anisotropy energy of Fe^<3+> ions, for magnetite from the anisotropy energy of Fe^<2+> and Fe^<3+> ions, and for Mn-ferrite from the anisotropy energy of Fe^<3+> and Mn^<2+> ions. Especially it is shown that the experimental anisotropy energy of magnetite extrapolated to the absolute zero of temperature is in good agreement with the sum of the experimental anisotropy energy of Ni-ferrite and the calculated value of the anisotropy energy of Fe^<2+> ions. For Co-ferrite, its large anisotropy energy seems to come from the pseudo-quadrupole and anisotropic exchange interactions among Co and Fe ions, but the situation is too complex to carry out the calculation of the anisotropy energy in this case. Finally, the temperature dependence of the cubic anisotropy energy is calculated for Mn-ferrite, and is shown to decrease as(T_c-T)^2 near the Curie temperature. Further, the sum of the coefficient, a of the cubic anisotropy Hamiltonian for Mn^<2+> and Fe^<3+> ions of the octahedral sites and that for Fe^<3+> ion of the tetrahedral sites have been determined for Mn-ferrite by adjusting the calculated anisotropy energy vs. temperature curve so as to fit the experimental one, and it is found, neglecting the small a-value of Mn^<2+> ions, that the a-value of Fe^<3+> ions on octahedral sites has five times as large an absolute value as that of Fe^<3+> ions on tetrahedral sites and that the former has the opposite sign to the latter.
- 理論物理学刊行会の論文
- 1957-03-00
著者
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Yosida Kei
Department Of Physics Faculty Of Science And Technology Science University Of Tokyo
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Tachiki Masashi
Department Of Chemistry Faculty Of Science Osaka University:(present Address) The Research Institute
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YOSIDA Kei
Department of Physics, Osaka University
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TACHIKI Masashi
Department of Physics, Osaka University
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