本論文利用固態合成法合成Mn3V2Ge3O12 (MVGO)石榴石氧化物樣品，並透過實驗室內的X光粉末繞射儀(Rigaku, MiniFlex II)，初步地確認樣品相組成及純度。接著將小塊樣品，利用Quantum design的MPMS3進行AC磁化率、DC磁化率及等溫磁化強度的量測。DC磁化率結果顯示，在外加磁場H = 100 Oe下，MVGO於低溫區呈現兩個磁相變。為進一步釐清其是否具有自旋玻璃行為，本研究透過 AC 磁化率量測觀察峰值隨頻率的變化。結果顯示MVGO 並未展現明顯的頻率相依性，因此可排除自旋玻璃行為的可能性，並確認兩個磁相變溫度分別為TN1 = 4 K 及TN2 = 2.6 K。此外，本研究進行不同外加磁場下的比熱量測，結果顯示兩個相變溫度皆隨磁場增加而往低溫移動，其中TN2 在外加磁場達20 kOe 時被抑制。同時，零場比熱測量顯示磁熵略有降低，在 25 K 時恢復了理論熵值的約 90 %。
根據上述磁性與比熱量測結果，本研究進一步進行隨溫度變化的中子粉末繞射實驗。結果顯示，TN1 主要源自 Mn2+ 反鐵磁有序，而 TN2 則與 Mn2+及V3+ 的反鐵磁有序有關。磁結構精修結果顯示，Mn2+及V3+ 的有序磁矩明顯小於 spin-only 所預期的理論值。本研究最後根據實驗結果與相關文獻，探討造成磁矩降低的可能原因。

This thesis reports the synthesis and investigation of the garnet oxide Mn3V2Ge3O12 (MVGO) prepared by the solid-state reaction method. The phase composition and sample purity were first characterized using a laboratory X-ray powder diffractometer (Rigaku, MiniFlex II). Small pieces of the sample were then measured using a Quantum Design MPMS3 system to perform AC susceptibility, DC susceptibility, and isothermal magnetization measurements.
The DC susceptibility results reveal that MVGO undergoes two magnetic phase transitions in the low-temperature region under an applied magnetic field of H = 100 Oe. To further clarify whether spin-glass behavior exists in this system, AC susceptibility measurements were carried out by examining the frequency dependence of the susceptibility peaks. The results show no obvious frequency dependence, indicating the absence of spin-glass behavior. The two magnetic transition temperatures were determined to be TN1 = 4 K and TN2 = 2.6 K, respectively.
In addition, specific heat measurements under various applied magnetic fields were performed. The results show that both transition temperatures shift toward lower temperatures with increasing magnetic field, and TN2 is suppressed under an applied magnetic field of 20 kOe. Meanwhile, the zero-field specific heat measurements indicate a slight reduction in magnetic entropy, recovering approximately 90 % of the theoretical entropy value at 25 K.
Based on the magnetic and specific heat measurements, temperature-dependent neutron powder diffraction experiments were further conducted. The results indicate that TN1 mainly originates from the antiferromagnetic ordering of Mn2+ ions, whereas TN2 is associated with the antiferromagnetic ordering of both Mn2+ and V3+ ions. Magnetic structure refinements reveal that the ordered magnetic moments of Mn2+ and V3+ are significantly smaller than the theoretical values expected from the spin-only model. Finally, possible origins of the reduced magnetic moments are discussed based on the experimental results and relevant literature.

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