This chapter takes a microscopic view of quantum tunneling of magnetization (QTM) in single-molecule magnets (SMMs), focusing on the interplay between exchange and anisotropy. Careful consideration is given to the relationship between molecular symme
try and the symmetry of the spin Hamiltonian that dictates QTM selection rules. Higher order interactions that can modify the usual selection rules are shown to be very sensitive to the exchange strength. In the strong coupling limit, the spin Hamiltonian possess rigorous $D_{2h}$ symmetry (or $C_{infty}$ in high-symmetry cases). In the case of weaker exchange, additional symmetries may emerge through mixing of excited spin states into the ground state. Group theoretic arguments are introduced to support these ideas, as are extensive results of magnetization hysteresis and electron paramagnetic resonance measurements.
A Mn4 single-molecule magnet displays asymmetric Berry-phase interference patterns in the transverse-field (HT) dependence of the magnetization tunneling probability when a longitudinal field (HL) is present, contrary to symmetric patterns observed f
or HL=0. Reversal of HL results in a reflection of the transverse-field asymmetry about HT=0, as expected on the basis of the time-reversal invariance of the spin-orbit Hamiltonian which is responsible for the tunneling oscillations. A fascinating motion of Berry-phase minima within the transverse-field magnitude-direction phase space results from a competition between noncollinear magnetoanisotropy tensors at the two distinct Mn sites.
We present a detailed study of the influence of various interactions on the spin quantum tunneling in a Mn12 wheel molecule. The effects of single-ion and exchange (spin-orbit) anisotropy are first considered, followed by an analysis of the roles pla
yed by secondary influences, e.g. disorder, dipolar and hyperfine fields, and magnetoacoustic interactions. Special attention is paid to the role of the antisymmetric Dzyaloshinski-Moriya (DM) interaction. This is done within the framework of a 12-spin microscopic model, and also using simplified dimer and tetramer approximations in which the electronic spins are grouped in 2 or 4 blocks, respectively. If the molecule is inversion symmetric, the DM interaction between the dimer halves must be zero. In an inversion symmetric tetramer, two independent DM vectors are allowed, but no new tunneling transitions are generated by the DM interaction. Experiments on the Mn12 wheel can only be explained if the molecular inversion symmetry is broken, and we explore this in detail using both models, focussing on the asymmetric disposition and rounding of Berry phase minima associated with quantum interference between states of opposite parity. A remarkable behavior exists for the `Berry phase zeroes as a function of the directions of the internal DM vectors and the external transverse field. A rather drastic breaking of the molecular inversion-symmetry is required to explain the experiments; in the tetramer model this requires a reorientation of the DM vectors on one half of the molecule by nearly 180 degrees. This cannot be attributed to sample disorder. These results are of general interest for the quantum dynamics of tunneling spins, and lead to some interesting experimental predictions.
We present low temperature magnetometry measurements on a new Mn3 single-molecule magnet (SMM) in which the quantum tunneling of magnetization (QTM) displays clear evidence for quantum mechanical selection rules. A QTM resonance appearing only at ele
vated temperatures demonstrates tunneling between excited states with spin projections differing by a multiple of three: this is dictated by the C3 symmetry of the molecule, which forbids pure tunneling from the lowest metastable state. Resonances forbidden by the molecular symmetry are explained by correctly orienting the Jahn-Teller axes of the individual manganese ions, and by including transverse dipolar fields. These factors are likely to be important for QTM in all SMMs.
In a recent Letter [1], Wernsdorfer et al. report an experimental study of a Mn12 molecular wheel which shows essentially identical behavior to the Mn12 wheel studied by Ramsey et al. [2]. In their Letter, Wernsdorfer et al. use the same model of a d
imer of two exchange-coupled spins used in [2] as a basis to extend the study of the influence of the Dzyaloshinskii-Moriya (DM) interaction on the quantum tunneling of the magnetization of this system; in particular, they show that a tilt of the DM vector away from the uniaxial anisotropy axis can account for the asymmetric nature of the quantum interference minima associated with resonances between states of opposite parity, e.g., k = 1(A). We want to stress that the inclusion of DM interactions in a system with inversion symmetry cannot mix states of opposite parity; i.e., the parity operator commutes with the Hamiltonian. Consequently, the use by Wernsdorfer et al. of a single DM vector in a centrosymmetric dimer is strictly forbidden since it implicitly violates parity conservation. The authors correctly point out that the lack of an inversion center between each pair of manganese ions on the wheel justifies the possibility of local DM interactions, even though the complete molecule has an inversion center. However, these local DM interactions must also satisfy the molecular inversion symmetry; i.e., they cannot mix states of opposite parity.We agree that such DM interactions are not always completely innocuous; e.g., they can mix spin states having the same parity. Indeed, in kagome systems [3] (cited in [1]), this can lead to weak ferromagnetism. Nevertheless, the inversion symmetry of the lattice is preserved and parity is still conserved.
In this article we discuss the design and implementation of a novel microstrip resonator which allows for the absolute control of the microwaves polarization degree for frequencies up to 30 GHz. The sensor is composed of two half-wavelength microstri
p line resonators, designed to match the 50 Ohms impedance of the lines on a high dielectric constant GaAs substrate. The line resonators cross each other perpendicularly through their centers, forming a cross. Microstrip feed lines are coupled through small gaps to three arms of the cross to connect the resonator to the excitation ports. The control of the relative magnitude and phase between the two microwave stimuli at the input ports of each line allows for tuning the degree and type of polarization of the microwave excitation at the center of the cross resonator. The third (output) port is used to measure the transmitted signal, which is crucial to work at low temperatures, where reflections along lengthy coaxial lines mask the signal reflected by the resonator. EPR spectra recorded at low temperature in an S= 5/2 molecular magnet system show that 82%-fidelity circular polarization of the microwaves is achieved over the central area of the resonator.
We present here an exact version of our response (dated April 27) to Wernsdorfers correspondence submitted to Nature Physics on March 31, 2008. After consultation with a referee, Nature Physics chose not publish any part of this exchange. We would th
erefore like to point out that our original study has now been considered favorably by four separate referees chosen by Nature Physics. Unfortunately, Wernsdorfer subsequently posted two further variations of his correspondence on this archive (arXiv:0804.1246v1 and arXiv:0804.1246v2). We note that aspects of the most recent posting (dated after submission of our response) contradict the version submitted to Nature Physics. However, none of the revisions add weight to Wernsdorfers original correspondence.
A sensor that integrates high sensitivity micro-Hall effect magnetometry and high-frequency electron paramagnetic resonance spectroscopy capabilities on a single semiconductor chip is presented. The Hall-effect magnetometer was fabricated from a two
dimensional electron gas GaAs/AlGaAs heterostructure in the form of a cross, with a 50x50 um2 sensing area. A high-frequency microstrip resonator is coupled with two small gaps to a transmission line with a 50 Ohms impedance. Different resonator lengths are used to obtain quasi-TEM fundamental resonant modes in the frequency range 10-30 GHz. The resonator is positioned on top of the active area of the Hall-effect magnetometer, where the magnetic field of the fundamental mode is largest, thus optimizing the conversion of microwave power into magnetic field at the sample position. The two gaps coupling the resonator and transmission lines are engineered differently. The gap to the microwave source is designed to optimize the loaded quality factor of the resonator (Q = 150) while the gap for the transmitted signal is larger. This latter gap minimizes losses and prevents distortion of the resonance while enabling measurement of the transmitted signal. The large filling factor of the resonator permits sensitivities comparable to that of high-quality factor resonant cavities. The integrated sensor enables measurement of the magnetization response of micron scale samples upon application of microwave fields. In particular, the combined measurement of the magnetization change and the microwave power under cw microwave irradiation of single crystal of molecular magnets is used to determine of the energy relaxation time of the molecular spin states. In addition, real time measurements of the magnetization dynamics upon application of fast microwave pulses are demonstrated
