Quantum tunneling of the magnetization (QTM) of the spin-1/2 Vanadium-15 (V15) single molecular magnets (SMMs) is investigated by means of the effective field theory developed by Kaneyoshi. We deal with the two hexagon layers (shell, VS) and one triangular interlayer (core, VC) with the spin-1/2 Ising particles. We find that the V15 has a normal ferromagnetic hysteresis behavior for its all spins are up (parallel). However, V15 has a staircase-like hysteresis behavior that is the signature of the QTM for the spin-down orientation (antiparallel) of the core. QTM appears with the splitting of the magnetizations versus temperature (M–T) and external field (M–H) curves. Namely, QTM occurs from +mVC1 to −mVC2(|mVC1|>|mVC2|) in the core, from +mVS1 to +mVS2 (|mVS1|>|mVS2|) in the shell (only mVS–H curves at T> 0.1) and from +M1V15 to +M2V15 (|M1V15|>|M2V15|) in the total V15. By considering these different splitting behaviors of the magnetizations of the shell, core and total V15 at T<TC and T>TC, we suggest three different kinds of QTM: 1-ferromagnetic QTM (FMQTM) at T<TC for the shell, 2-antiferromagnetic QTM (AFMQTM) at T<TC for the core and 3-paramagnetic QTM (PMQTM) at T>TC for the shell, core and total V15 SMM. Moreover, it is found that there is a relationship between the QTM and type II and surface superconductivity. The EFT results of QTM in V15 are in good agreement with the other theoretical and experimental results of the V15 and other SMMs.

中文翻译：

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磁化的自旋诱导量子隧道效应

自旋 1/2 钒 15 (V) 磁化强度的量子隧穿 (QTM)15)单分子磁体 (SMM) 通过 Kaneyoshi 开发的有效场理论进行了研究。我们处理两个六边形层（shell，V小号)和一个三角形夹层（核心，VC)自旋 1/2 Ising 粒子。我们发现 V15具有正常的铁磁滞后行为，因为它的所有自旋都向上（平行）。然而，V15具有阶梯状的滞后行为，这是 QTM 的特征，用于核心的自旋向下方向（反平行）。QTM 随着磁化强度随温度的分裂而出现（米–吨)和外场（米–H)曲线。即，QTM 发生于+米风险投资1到-米风险投资2(|米风险投资1|>|米风险投资2|)在核心，从 +米VS1到+米VS2 (|米VS1|>|米VS2|)在外壳中（仅米VS–H曲线在吨>0.1) 和从+米1五15到+米2五15 (|米1五15|>|米2五15|)在总V15. 通过考虑壳、芯和总磁化的这些不同的分裂行为五15在吨<吨C和吨>吨C，我们建议三种不同类型的 QTM： 1-铁磁 QTM (FMQTM)吨<吨C对于壳，2-反铁磁 QTM (AFMQTM) 在吨<吨C对于核心和 3-顺磁 QTM (PMQTM) 在吨>吨C壳、核和总 V15SMM。此外，发现QTM和II型与表面超导性之间存在关系。V中QTM的EFT结果15与V的其他理论和实验结果非常吻合15和其他 SMM。