本篇論文旨在說明，利用構想出的各種不同磁性組態來研究ZnFe2O4這種物質的磁性與結構特性。我們發現計算出ZnFe2O4最低能量結構與一般認為它應有的磁性結構不同。利用海森堡模型並考慮到第四鄰近鄰居所產生之交互作用現象來描述這七種不同的磁性結構總能量，因而獲得材料中鐵原子間的磁矩交互作用能。若只考慮到第二鄰近鄰居之影響，我們發現第一鄰近鄰居與第二鄰近鄰居所引起的交互作用性質分別屬於反鐵磁性與鐵磁性，而在作用能大小上第一鄰近大約為第二鄰近的三倍大。然而當我們在ZnFe2O4七種不同磁性組態下，把第四鄰近鄰居對總能量的影響考慮進去時，發現計算出來的交互作用能較無一致性之結果。同時我們用不同的限制條件（如:固定形狀、允許形狀改變、只允許氧原子位置改變）來鬆弛結構，使其達到最佳化過程也發現與上述相同之結論。在我們使用海森堡模型並考慮到第四鄰近鄰居之作用後，所產生的不一致性說明了材料在磁性排列上之複雜性，而未來的研究上我們應該把不同的交換路徑影響與磁矩間可能並非各向均為線性排列關係等因素考慮進去。

In this thesis, structures of different configurations in magnetic ordering for ZnFe2O4 were constructed to investigate the magnetic and structural properties of this material. The calculated lowest energy structure was found to be different from the conventionally regarded magnetic structure of ZnFe2O4. The Heisenberg model with up to the 4th neighbour interactions was employed to describe the total energies of the seven structures with different magnetic ordering to obtain the interaction energies between the magnetic dipole moments of Fe atoms in the material. In case only up to the 2nd nearest-neighbour interactions was included, the nearest-neighbour (nn) and next nearest-neighbour (nnn) interactions were found to be antiferromagnetic and ferromagnetic respectively with the magnitude of the nn interaction about thrice of that of the nnn interaction. However, much lower consistent results were obtained when the 4th neighbour interactions were included in describing the total energies for these seven structures of different magnetic ordering for ZnFe2O4. Similar conclusions were reached when different constraints were applied in the relaxation processes, i.e. relaxation with constrained cubic geometry, relaxation with allowed shape change for unit cell and relaxation with ionic relaxation applied to O atoms only. The inconsistency in applying the Heisenberg model of up to the 4th neighbour interactions indicates the complexity of magnetic ordering in this material and models beyond the present consideration, e.g. including noncolinearity and different interacting paths, need to be included in the future studies.

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