本研究以Mn₂.₉₀V₃.₁₀O₈為研究對象，探討其結構、價態與磁性之間的關聯。微觀結構分析顯示，EDS mapping 中Mn、V與 O元素在顆粒中的分布相對均勻，TEM與HRTEM則顯示樣品具有良好的局部結晶性。FFT圖樣大致可沿I4₁/amd結構之 [001] zone axis進行索引，此結果表示前述結構與價態特徵應可視為樣品本身的性質，而非局部成分分離所造成。結構分析以變溫中子繞射顯示材料在本研究量測溫區內始終維持四方扭曲的尖晶石相關結構，並未出現明確的 cubic-to-tetragonal 結構相變；其四方扭曲程度隨溫度升高而逐漸減弱。局部配位分析顯示，鍵長與鍵角於磁有序溫度附近呈現明顯變化，其中 B-site planar 方向的結構改變較為顯著，顯示該溫區的局部結構調整可能與八面體平面方向晶格扭曲及 Jahn–Teller 作用有關。 本研究分別利用磁化量測所得的有效磁矩，在電荷中性與不同價態離子自旋貢獻的限制下進行自洽計算，並與中子粉末繞射的佔位率精算結果比較。磁性分析顯示，A 位點的 Mn 與 V 佔位比例分別為 0.89(2) 與 0.11(2)，B 位點則分別為 0.28(1) 與 0.72(1)，對應的化學組成為 [Mn1.78(4)V0.22(4)]A[Mn1.12(4)V2.88(4)]BO，總組成為 Mn2.90(6)V3.10(6)O8。中子繞射精算得到 A 位點的 Mn 與 V 佔位比例分別為 0.822(30) 與 0.178(30)，B 位點則為 0.269(34) 與 0.731(34)，對應組成為 [Mn1.64(6)V0.36(6)]A[Mn1.12(4)V2.88(4)]BO8，總組成為 Mn2.72(15)V3.28(15)O8。兩種方法在定量結果上存在一定差異，但均顯示 Mn 離子主要佔據 A 位點，而 V 離子主要分布於 B 位點。考量有效磁矩分析同時受到電荷中性、離子價態及自旋貢獻的限制，本研究以 Mn₂.₉₀V₃.₁₀O₈ 作為後續平均磁性與總磁矩討論的主要組成。 價態分析方面，Mn 與V K-edge XANES結果皆落在不同價態標準樣品之間，顯示兩者皆具有混合價態特徵。BVS結果則指出A-site 平均價數接近 +2、B-site平均價數接近 +3。然而，若結合中子繞射精算所得之佔位比例進一步分析，可發現樣品並非理想正尖晶石中的完全有序價態分布，而是同時具有A、B site混合佔據與混合價數的特性；其中A site仍以Mn佔據為主，B site則除V外亦存在反位Mn，並呈現較高價態的特徵。這些結果顯示Mn₂.₉₀V₃.₁₀O₈的局部電子態與鍵結環境已偏離理想尖晶石圖像。 磁性量測結果顯示，Mn₂.₉₀V₃.₁₀O₈於低溫下具有明顯磁化訊號與磁滯行為，ZFC與FC曲線在低溫區出現分岔，隨溫度升高，磁化強度快速下降，磁化率隨溫度之一階微分訊號在約58 K左右具有最大值，顯示巨觀磁化量測之磁有序溫度。Curie–Weiss 擬合得到有效磁矩約 10.02(1) μB / f.u.、Curie–Weiss 溫度 θCW = 138(1) K，系統中主要交換作用傾向反平行排列；若以58 K估算，其挫折參數約為 2.38。另一方面，M–H 曲線顯示樣品在4 K具有有限淨磁矩與磁滯，飽和磁矩由4 K的1.96(4) μB/f.u.隨溫度升高而系統性下降，至75 K數據已明顯衰減，顯示其低溫磁有序較適合描述為具有淨磁矩的亞鐵磁或傾斜亞鐵磁磁有序。變溫中子繞射結果進一步顯示，3.5 K的繞射圖譜可由四方晶系核結構 I4₁/amd 搭配磁結構模型 I4₁/am′d′良好描述；相較之下，300 K時低角度區的額外磁散射已不再明顯，對應高溫下無長程磁有序的狀態。磁結構精算結果指出，A-site與B-site子晶格磁矩分量在升溫過程中存在重新分配，A位磁矩大小主要沿著c軸方向縮小，而B位磁矩的大小變化相對較弱，並伴隨著磁有序溫度以下y和z分量的調整。將中子繞射精算所得總磁矩以臨界指數冪定律擬合，可得其磁有序溫度為56(2) K，低溫極限有序磁矩約 1.40(2) μB，且與 VSM 所得 4 K 飽和磁矩 1.96(4) μB/f.u.接近。考量巨觀磁性量測可反映整體樣品的平均磁性響應，本研究以磁化率量測所得的TN=58 K作為主要的有序溫度。在A、B site 的有序磁矩隨溫度變化呈現不同的臨界行為，其臨界指數分別為 βA = 0.29(1) 與 βB = 0.20(2)，其中，A site 的臨界行為較接近三維 Ising 模型，B site 則較偏向二維 Ising 模型，顯示兩個磁性子晶格可能具有不同的有效交換維度。 A、B site 的 BVS 於TN附近呈現同步變化，並伴隨鍵長、鍵角與有序磁矩的調整，顯示磁性轉變涉及局部價態、鍵結環境與晶格扭曲的重新配置。綜合結構、價態與磁性分析結果，Mn₂.₉₀V₃.₁₀O₈ 的亞鐵磁有序與具方向性的交換路徑密切相關，並於TN附近呈現自旋—軌道耦合行為。;This study investigates the relationships among the crystal structure， valence states， and magnetic properties of Mn₂.₉₀V₃.₁₀O₈. Microscopic characterization showed that Mn， V， and O were distributed relatively uniformly within the particles， as revealed by energy-dispersive X-ray spectroscopy (EDS) mapping. Transmission electron microscopy (TEM) and high-resolution TEM (HRTEM) further demonstrated good local crystallinity. The fast Fourier transform (FFT) pattern could be approximately indexed along the [001] zone axis of the I4₁/amd structure， suggesting that the observed structural and valence characteristics are intrinsic to the sample rather than arising from local compositional segregation. Variable-temperature neutron diffraction showed that the material retained a tetragonally distorted spinel-related structure throughout the measured temperature range， without a distinct cubic-to-tetragonal structural transition. The degree of tetragonal distortion gradually decreased with increasing temperature. Local coordination analysis revealed pronounced changes in the bond lengths and bond angles near the magnetic ordering temperature. These changes were more evident within the B-site octahedral plane， suggesting that the local structural response in this temperature region may be associated with in-plane lattice distortion of the octahedra and the Jahn–Teller effect. Self-consistent calculations were performed using the effective magnetic moment obtained from magnetic susceptibility measurements under the constraints of charge neutrality and the spin contributions of ions with different valence states. The results were compared with the site occupancies refined from neutron powder diffraction. The magnetic analysis yielded Mn and V occupancies of 0.89(2) and 0.11(2)， respectively， at the A site， and 0.28(1) and 0.72(1)， respectively， at the B site. These values correspond to [Mn₁.₇₈₍₄₎V₀.₂₂₍₄₎]A[Mn₁.₁₂₍₄₎V₂.₈₈₍₄₎]BO₈， with an overall composition of Mn₂.₉₀V₃.₁₀O₈. Neutron diffraction refinement yielded Mn and V occupancies of 0.822(30) and 0.178(30)， respectively， at the A site， and 0.269(34) and 0.731(34)， respectively， at the B site. The corresponding composition was [Mn1.64(6)V0.36(6)]A[Mn1.12(4)V2.88(4)]BO8， with an overall composition of Mn2.72(15)V3.28(15)O8. Although the two methods yielded some quantitative differences， both indicated that Mn preferentially occupies the A site， whereas V is primarily distributed over the B site. Because the effective-moment analysis is simultaneously constrained by charge neutrality， ionic valence states， and spin contributions， Mn₂.₉₀V₃.₁₀O₈ was adopted as the representative composition for the subsequent discussion of the average magnetic properties and total magnetic moment. Regarding the valence states， the Mn and V K-edge X-ray absorption near-edge structure (XANES) spectra were located between those of reference compounds with different oxidation states， indicating mixed-valence characteristics for both elements. Bond-valence-sum (BVS) analysis showed that the average valence was close to +2 at the A site and +3 at the B site. Combined with the site occupancies obtained from neutron diffraction refinement， these results indicate that the sample deviates from the fully ordered valence distribution expected for an ideal normal spinel and instead exhibits mixed A/B-site occupancy and mixed valence. The A site remains predominantly occupied by Mn， whereas the B site contains antisite Mn in addition to V and exhibits characteristics associated with higher oxidation states. These findings demonstrate that the local electronic states and bonding environments of Mn₂.₉₀V₃.₁₀O₈ deviate from the idealized spinel picture. Magnetic measurements revealed pronounced magnetization and hysteresis at low temperatures. The zero-field-cooled and field-cooled curves exhibited a low-temperature bifurcation， while the magnetization decreased rapidly with increasing temperature. The first derivative of the magnetic susceptibility showed a maximum near 58 K， indicating the magnetic ordering temperature observed by macroscopic magnetic measurements. Curie–Weiss fitting yielded an effective magnetic moment of approximately 10.02(1) μB/f.u. and a Curie–Weiss temperature of θCW = 138(1) K， suggesting that the dominant exchange interactions favor antiparallel spin alignment. Using 58 K as the ordering temperature， the frustration parameter was estimated to be approximately 2.38. The M–H curves showed a finite net magnetic moment and magnetic hysteresis at 4 K. The saturation magnetization decreased systematically from 1.96(4) μB/f.u. at 4 K and was substantially reduced by 75 K， indicating that the low-temperature magnetic state can be described as ferrimagnetic or canted ferrimagnetic order with a finite net moment. Variable-temperature neutron diffraction further showed that the diffraction pattern at 3.5 K could be well described by the tetragonal nuclear structure I4₁/amd combined with the magnetic structure model I4₁/am′d′. At 300 K， the additional low-angle magnetic scattering was no longer evident， consistent with the absence of long-range magnetic order at high temperature. Magnetic structure refinement revealed a redistribution of the magnetic-moment components of the A- and B-site sublattices upon warming. The decrease in the A-site magnetic moment occurred primarily along the c axis， whereas the magnitude of the B-site moment varied less substantially and was accompanied by changes in its y and z components below the magnetic ordering temperature. Fitting the total ordered moment obtained from neutron diffraction refinement using a critical power law yielded a magnetic ordering temperature of 56(2) K and a low-temperature limiting ordered moment of approximately 1.40(2) μB. This value is close to the saturation magnetization of 1.96(4) μB/f.u. measured by VSM at 4 K. Because macroscopic magnetic measurements reflect the average magnetic response of the entire sample， TN = 58 K， determined from the magnetic susceptibility measurements， was adopted as the primary ordering temperature. The temperature-dependent ordered moments of the A and B sites exhibited distinct critical behaviors， with critical exponents of βA = 0.29(1) and βB = 0.20(2)， respectively. The critical behavior of the A site is closer to that of the three-dimensional Ising model， whereas that of the B site tends toward the two-dimensional Ising model， suggesting that the two magnetic sublattices may possess different effective exchange dimensionalities. The BVS values of the A and B sites exhibited correlated changes near TN， accompanied by variations in the bond lengths， bond angles， and ordered magnetic moments. These observations indicate that the magnetic transition involves a reconfiguration of the local valence states， bonding environments， and lattice distortions. The combined structural， valence-state， and magnetic analyses suggest that the ferrimagnetic order in Mn₂.₉₀V₃.₁₀O₈ is closely associated with directional exchange pathways and exhibits spin–orbit coupling near TN.
