Dissipative Landau-Zener transition with decoherence rate

An innovative microscopic model with a minimal number of parameters: tunneling splitting gap, external field sweeping velocity, and decoherence rate is used to describe dynamics of the dissipative Landau-Zener transition in the presence of the decoherence. In limiting cases, the derived equation of motion gives rise to the well-known Landau-Zener and Kayanuma formula. In a general case, the description demonstrates a non-monotonic flipping probability with respect to the sweeping velocity, which is also found in some other models. This non-monotony can be explained by considering the competition and timescale of the quantum tunneling, crossing period, and decoherence process. The simplicity and robustness of the theory offer a practical and novel description of the Landau-Zener transition. In addition, it promises an alternative method to the electron paramagnetic resonance in measuring the effective decoherence rate of relevant quantum systems.Comment: 8 pages, 2 figure

Quantum tunneling of magnetization in molecular spin

We examine the quantum tunneling of magnetization in molecular spin in weak interaction with a bath subject to Redfield master equation. By designing a microscopic model for a multilevel spin system using only a generic Hamiltonian and applying stationary approximation for excited doublets/singlets, we derive a key equation of motion for the quantum tunneling of magnetization process which is applicable in the whole temperature domain. From this equation, we find that in general three tunneling rates are needed to accurately describe the quantum tunneling process. More importantly, behavior of the quantum tunneling in the intermediate temperature domain where there exists a transition between incoherent and coherent quantum tunneling is also unraveled for the first time. Limiting cases at low and high temperature and/or low magnetic field are also worked out where some popular well-known results are reproduced. Last but not least, a new interpretation of the quantum tunneling of magnetization is proposed where we reveal the similarity between this relaxation process with a driven damped harmonic oscillator.Comment: 11 pages, 5 figure

Non-monotonic temperature dependence and first-order phase transition of relaxation times in molecular spin

We derive a simple system of equations to describe the magnetization relaxation of a molecular spin in weak interaction with a thermal bath for the whole temperature domain. Using this for the intermediate temperature domain where the transition from coherent to incoherent relaxation occurs, we find that the slowest relaxation mode shows a first-order phase transition. Associated with this transition, an unusual non-monotonic temperature-dependence of the relaxation rate of this mode is also demonstrated. Contrary to the popular belief, this non-monotony gives rise to a peculiar but observable behavior where increasing temperature will not only result in a smaller rate of the slowest relaxation mode but also may lead to a slower decaying of the magnetization after some relaxing time. Additionally, it is also shown that magnetization relaxation in this intermediate temperature domain can only be accurately described by a bi- or tri-exponential form. The physical reason underlying these features can be attributed to the role of the quantum tunneling effect and different but comparative relaxation modes. A simple experiment to confirm our findings on the first-order phase transition and the non-monotony of the relaxation rate is accordingly proposed.Comment: 7 pages, 5 figure

Coherence/incoherence transition temperature in molecular spin

We examine the coherence/incoherence transition temperature of a generic molecular spin. Our results demonstrates that a molecular spin with a high coherence/incoherence transition temperature should possess a low spin number and low axiality, or high spin number and high axiality. Interestingly, the latter is better protected from the magnetic noises than the former and thus be the best candidate for a robust electron-based molecular spin qubit/qudit. The transition temperature can be further optimized if a large non-axial component of the spin Hamiltonian exists.Comment: 8 pages, 6 figure

Highly Oxidized States of Phthalocyaninato Terbium(III) Multiple‐Decker Complexes Showing Structural Deformations, Biradical Properties and Decreases in Magnetic Anisotropy

Presented here is a comprehensive study of highly oxidized multiple‐decker complexes composed of Tb$_{III}$ and Cd$_{III}$ ions and two to five phthalocyaninato ligands, which are stabilized by electron-donating n-butoxy groups. From X-ray structural analyses, all the complexes become axially compressed upon ligand oxidation, resulting in bowl-shaped distortions of the ligands. In addition, unusual coexistence of square antiprism and square prism geometries around metal ions was observed in +4e charged species. From paramagnetic $^{1}$H NMR studies on the resulting series of triple, quadruple and quintuple-decker complexes, ligand oxidation leads to a decrease in the magnetic anisotropy, as predicted from theoretical calculations. Unusual paramagnetic shifts were observed in the spectra of the +2e charged quadruple and quintuple-decker complexes, indicating that those two species are actually unexpected triplet biradicals. Magnetic measurements revealed that the series of complexes show single-molecule magnet properties, which are controlled by the multi-step redox induced structural changes