How to Cross an Energy Barrier at Zero Kelvin without Tunneling Effect.

This Letter deals with the broad class of magnetic systems having a single or collective spin S with an energy barrier, such as rare-earth elements and their compounds, single molecule magnets with uniaxial anisotropy, and more generally any other anisotropic quantum system made of single or multiple objects with discrete energy levels. Till now, the reversal of the magnetization of such systems at zero kelvin required making use of quantum tunneling with a significant transverse field or transverse anisotropy term, at resonance. Here, we show that another very simple method exists. It simply consists in the application of a particular sequence of electromagnetic radiations in the ranges of optical or microwave frequencies, depending on the characteristics of the system (spin and anisotropy values for magnetic systems). This produces oscillations of the Rabi type that pass above the barrier, thus extending these oscillations between the two energy wells with mixtures of all the 2S+1 states. In addition to its basic character, this approach opens up new directions of research in quantum information with possible breakthroughs in the current use of multiple quantum bits.

Atomistic theory of thermally activated magnetization processes in Nd2Fe14B permanent magnet.

To study the temperature dependence of magnetic properties of permanent magnets, methods of treating the thermal fluctuation causing the thermal activation phenomena must be established. To study finite-temperature properties quantitatively, we need atomistic energy information to calculate the canonical distribution. In the present review, we report our recent studies on the thermal properties of the Nd2Fe14B magnet and the methods of studying them. We first propose an atomistic Hamiltonian and show various thermodynamic properties, for example, the temperature dependences of the magnetization showing a spin reorientation transition, the magnetic anisotropy energy, the domain wall profiles, the anisotropy of the exchange stiffness constant, and the spectrum of ferromagnetic resonance. The effects of the dipole-dipole interaction (DDI) in large grains are also presented. In addition to these equilibrium properties, the temperature dependence of the coercivity of a single grain was studied using the stochastic Landau-Lifshitz-Gilbert equation and also by the analysis of the free energy landscape, which was obtained by Monte Carlo simulation. The upper limit of coercivity at room temperature was found to be about 3 T at room temperature. The coercivity of a polycrystalline magnet, that is, an ensemble of interactinve grains, is expected to be reduced further by the effects of the grain boundary phase, which is also studied. Surface nucleation is a key ingredient in the domain wall depinning process. Finally, we study the effect of DDI among grains and also discuss the distribution of properties of grains from the viewpoint of first-order reversal curve.

Magnetic-Pole Flip by Millimeter Wave.

In the era of Big Data and the Internet of Things, data archiving is a key technology. From this viewpoint, magnetic recordings are drawing attention because they guarantee long-term data storage. To archive an enormous amount of data, further increase of the recording density is necessary. Herein a new magnetic recording methodology, "focused-millimeter-wave-assisted magnetic recording (F-MIMR)," is proposed. To test this methodology, magnetic films based on epsilon iron oxide nanoparticles are prepared and a focused-millimeter-wave generator is constructed using terahertz (THz) light. Irradiating the focused millimeter wave to epsilon iron oxide instantly switches its magnetic pole direction. The spin dynamics of F-MIMR are also calculated using the stochastic Landau-Lifshitz-Gilbert model considering all of the spins in an epsilon iron oxide nanoparticle. In F-MIMR, the heat-up effect of the recording media is expected to be suppressed. Thus, F-MIMR can be applied to high-density magnetic recordings.

Rapid Faraday Rotation on ε-Iron Oxide Magnetic Nanoparticles by Visible and Terahertz Pulsed Light.

Light- or electromagnetic wave-responsive magnetism is an attractive issue in spin chemistry and optical materials science. Herein we show the magnetization reversal induced by visible-light pulsed laser and the ultrafast dynamic magnetooptical effect caused by terahertz (THz) pulsed laser irradiation onto chemically synthesized magnetic films based on gallium-titanium-cobalt-substituted ε-Fe2O3 (GTC-ε-Fe2O3) and ε-Fe2O3 nanoparticles. Visible-light pulsed laser irradiation switches the sign of the Faraday effect in GTC-ε-Fe2O3 films. On the other hand, irradiating the ε-Fe2O3 film with pulsed THz light induces an ultrafast Faraday rotation in an extremely short time of 400 fs. The time evolution dynamics of these ultrafast magnetooptical effects are theoretically demonstrated by stochastic Landau-Lifshitz-Gilbert calculations of a nanoparticle model that considers all motions of the individual spins. These ε-iron oxide magnetic nanomaterials are expected to contribute to high-density magnetic memory media or high-speed operation circuit magnetic devices.

Quantum Stoner-Wohlfarth Model.

The quantum mechanical counterpart of the famous Stoner-Wohlfarth model-an easy-axis magnet in a tilted magnetic field-is studied theoretically and through simulations as a function of the spin size S in a sweeping longitudinal field. Beyond the classical Stoner-Wohlfarth transition, the sweeping field-induced adiabatic change of states slows down as S increases, leading to a dynamical quantum phase transition. This result gives us new insights to describe the collapse of the metastability from the viewpoint of a critical phenomenon associated with the Landau-Zener tunneling gaps. Furthermore, a beating of the amplitude of the magnetization (the spin-length fidelity) is discovered after the Stoner-Wohlfarth transition. The period of the beating, confirmed analytically, arises from a new type of quantum phase factor.

Condition for emergence of the Floquet-Gibbs state in periodically driven open systems.

We study probability distribution of a steady state of a periodically driven system coupled to a thermal bath by using a quantum master equation in the weak-coupling limit. It is proved that, even when the external field is strong, the probability distribution is independent of the detailed nature of the thermal bath under the following conditions: (i) the Hamiltonian of the relevant system is bounded and the period of the driving field is short, (ii) the Hamiltonians for the driving field at different times commute, and (iii) the Hamiltonians of the driving field and of the interaction between the relevant system and the thermal bath commute. It is shown that the steady state is described by the Gibbs distribution of the Floquet states of the relevant system at the temperature of the thermal bath.

Electron transport dynamics in redox-molecule-terminated branched oligomer wires on Au(111).

Dendritic bis(terpyridine)iron(II) wires with terminal ferrocene units were synthesized on a Au(111) surface by stepwise coordination using a three-way terpyridine ligand, a ferrocene-modified terpyridine ligand, and Fe(II) ions. Potential-step chronoamperometry, which applied overpotentials to induce the redox of the terminal ferrocene, revealed an unusual electron-transport phenomenon. The current-time profile did not follow an exponential decay that is common for linear molecular wire systems. The nonexponentiality was more prominent in the forward electron-transport direction (from the terminal ferrocene to the gold electrode, oxidation) than in the reverse direction (from the gold electrode to the terminal ferrocenium, reduction). A plateau and a steep fall were observed in the former. We propose a simple electron transport mechanism based on intrawire electron hopping between two adjacent redox-active sites, and the numerical simulation thereof reproduced the series of "asymmetric" potential-step chronoamperometry results for both linear and branched bis(terpyridine)iron(II) wires.

Noise effects in a finite-size Ising-like model.

We study finite-size effects on properties of stationary state and also transient process of a bistable system with long range interaction. We adopt an Ising-like model with infinite range interaction (Husimi-Temperlay model). In particular, we formulate this problem in light of the Langevin equation and investigate study the effects of various types of noises. We study characteristics of the probability of stationary state of a finite system and find that there exist two types of regions in the ordered state: the saturated region in which the maximum of the distribution locates at the maximum value of the Ising variable (±1) and the transient region in which the maximum of the distribution locates at a nonsaturated value. We introduce an additional type of noise that represents fluctuation due to direct coupling to the thermal bath. Finally we also study the finite-size effects on the dynamical aspect by studying the mean first-passage times.

Macroscopic nucleation phenomena in continuum media with long-range interactions.

Nucleation, commonly associated with discontinuous transformations between metastable and stable phases, is crucial in fields as diverse as atmospheric science and nanoscale electronics. Traditionally, it is considered a microscopic process (at most nano-meter), implying the formation of a microscopic nucleus of the stable phase. Here we show for the first time, that considering long-range interactions mediated by elastic distortions, nucleation can be a macroscopic process, with the size of the critical nucleus proportional to the total system size. This provides a new concept of "macroscopic barrier-crossing nucleation". We demonstrate the effect in molecular dynamics simulations of a model spin-crossover system with two molecular states of different sizes, causing elastic distortions.

Nonmonotonic dynamics in a frustrated Ising model with time-dependent transverse field.

We study how the degree of ordering depends on the strength of the thermal and quantum fluctuations in frustrated systems by investigating the correlation function of the order parameter. Concretely, we compare the equilibrium spin correlation function in a frustrated lattice which exhibits a nonmonotonic temperature dependence (reentrant type dependence) with that in the ground state as a function of the transverse field that causes the quantum fluctuation. We find the correlation function in the ground state also shows a nonmonotonic dependence on the strength of the transverse field. We also study the real-time dynamics of the spin-correlation function under a time-dependent field. After sudden decrease in the temperature, we found nonmonotonic changes of the correlation function reflecting the static temperature dependence, which indicates that an effective temperature of the system changes gradually. For the quantum system, we study the dependence of changes of the correlation function on the sweeping speed of the transverse field. Contrary to the classical case, the correlation function varies little in a rapid change of the field, though it shows a nonmonotonic change when we sweep the field slowly.

Phase transition in spin systems with various types of fluctuations.

Various types ordering processes in systems with large fluctuation are overviewed. Generally, the so-called order-disorder phase transition takes place in competition between the interaction causing the system be ordered and the entropy causing a random disturbance. Nature of the phase transition strongly depends on the type of fluctuation which is determined by the structure of the order parameter of the system. As to the critical property of phase transitions, the concept "universality of the critical phenomena" is well established. However, we still find variety of features of ordering processes. In this article, we study effects of various mechanisms which bring large fluctuation in the system, e.g., continuous symmetry of the spin in low dimensions, contradictions among interactions (frustration), randomness of the lattice, quantum fluctuations, and a long range interaction in off-lattice systems.

Asymptotic forms and scaling properties of the relaxation time near threshold points in spinodal-type dynamical phase transitions.

We study critical properties of the relaxation time at a threshold point in switching processes between bistable states under change in external fields. In particular, we investigate the relaxation processes near the spinodal point of the infinitely long-range interaction model (the Husimi-Temperley model) by analyzing the scaling properties of the corresponding Fokker-Planck equation. We also confirm the obtained scaling relations by direct numerical solution of the original master equation, and by kinetic Monte Carlo simulation of the stochastic decay process. In particular, we study the asymptotic forms of the divergence of the relaxation time near the spinodal point and re-examine its scaling properties. We further extend the analysis to transient critical phenomena such as a threshold behavior with diverging switching time under a general external driving perturbation. This models photoexcitation processes in spin-crossover materials. In the ongoing development of nanosize fabrication, such size-dependence of switching processes should be an important issue, and the properties obtained here will be applicable to a wide range of physical processes.

Comparison among various expressions of complex admittance for quantum systems in contact with a heat reservoir.

Relation among various expressions of the complex admittance for quantum systems in contact with heat reservoir is studied. Exact expressions of the complex admittance are derived in various types of formulations of equations of motion under contact with heat reservoir. Namely, the complex admittance is studied in the relaxation method and the external-field method. In the former method, the admittance is calculated using the Kubo formula for quantum systems in contact with heat reservoir in no external driving fields, while in the latter method the admittance is directly calculated from equations of motion with external driving terms. In each method, two types of equation of motions are considered, i.e., the time-convolution (TC) equation and time-convolutionless (TCL) equation. That is, the full of the four cases are studied. It is turned out that the expression of the complex admittance obtained by using the relaxation method with the TC equation exactly coincides with that obtained by using the external-field method with the TC equation, while other two methods give different forms. It is also explicitly demonstrated that all the expressions of the complex admittance coincide with each other in the lowest Born approximation for the system-reservoir interaction. The formulas necessary for the higher-order expansions in powers of the system-reservoir interaction are derived, and also the expressions of the admittance in the nth order approximation are given. By transforming inverse-temperature integrals into time integrals, the admittances are also given in the formulas with time-integrals alone. To characterize the TC and TCL methods, we study the expressions of the admittances of two exactly solvable models. Each exact form of admittance is compared with the results of the two methods in the lowest Born approximation. It is found that depending on the model, either of TC and TCL would be the better method.

Master equation approach to line shape in dissipative systems.

We propose a formulation to obtain the line shape of a magnetic response with dissipative effects that directly reflects the nature of the environment. Making use of the fact that the time evolution of a response function is described by the same equation as the reduced density operator, we formulate a full description of the complex susceptibility. We describe the dynamics using the equation of motion for the reduced density operator, including the term for the initial correlation between the system and a thermal bath. In this formalism, we treat the full description of non-Markovian dynamics including the initial correlation. We present an explicit and compact formula up to the second order of cumulants, which can be applied in a straightforward way to multiple-spin systems. We also take into account the frequency shift by the system-bath interaction. We study the dependence of the line shape on the type of interaction between the system and the thermal bath. We demonstrate that the present formalism is a powerful tool for investigating various kinds of systems and we show how it is applied to spin systems, including those with up to three spins. We distinguish the contributions of the initial correlation and the frequency shift and make clear the role of each contribution in the Ohmic coupling spectral function. As examples of applications to multispin systems, we obtain the dependence of the line shape on the spatial orientation in relation to the direction of the static field (Nagata-Tazuke effect), including the effects of the thermal environment, in a two-spin system, along with the dependence on the arrangement of a triangle in a three-spin system.

Two-electron reduction of a Rh-Mo-Rh dithiolato complex to form a triplet ground state associated with a change in CO coordination mode.

We synthesized a dithiolato-bridged heterometal trinuclear complex [{(eta(5)-C(5)Me(5))Rh(S(2)C(6)H(4))}(2)Mo(CO)(2)] (1) in which two rhodadithiolene complex units are bridged by a Mo(CO)(2) moiety. Complex 1 with a Rh(III)-Mo(0)-Rh(III) bond exhibits reversible one-step two-electron reduction with potential inversion. This redox process between 1 and 1(2-) accompanies a reversible structural change, which is an alternation in the CO coordination mode between semibridging and bridging. The ground state of dianion 1(2-) with a Rh(II)-Mo(0)-Rh(II) bond is assigned to spin triplet. These alternations of CO coordination mode and spin state are fully consistent with the density functional theory calculation results. This is the first example of multinuclear metalladithiolene complex which was successful in elucidating a reversible multielectron redox process associated with structural change and spin state change.

Molecular dynamics and transfer integral investigations of an elastic anharmonic model for phonon-induced spin crossover.

Based on a vibronic description of the spin-crossover (SC) molecule, the electronic and elastic properties of a chain of anharmonically coupled SC molecules are studied by means of transfer integral (TI) and molecular dynamics (MD) simulations. The thermodynamical properties (high spin fraction and lattice deformation) are derived and show the existence of a first-order transition driven by the phonon field. The MD investigations of the velocity autocorrelation function evidenced that the density of phonon states shows a redshift and a broadening at high temperature, attributed to the enhancement of the phonon entropy. This result is discussed in relation to the thermal dependence of the dispersion relation omega(q) and that of the effective intermolecular elastic constant.

Monte Carlo simulation of pressure-induced phase transitions in spin-crossover materials.

Pressure-induced phase transitions of spin-crossover materials are studied in a microscopic model taking into account the elastic interaction among distortions of lattice due to the difference of the molecular sizes between the high-spin state and the low-spin state. We perform Monte Carlo simulations in the constant pressure ensemble and reproduce several important properties of the pressure effect in a unified way with a microscopic mechanism for the first time. The simulation newly reveals how the temperature dependence of the ordering process changes with the pressure.

Simple two-dimensional model for the elastic origin of cooperativity among spin states of spin-crossover complexes.

We study the origin of the cooperative nature of spin crossover (SC) between low-spin and high-spin (HS) states from the viewpoint of elastic interactions among molecules. As the size of each molecule changes depending on its spin state, the elastic interaction among the lattice distortions provides the cooperative interaction of the spin states. We develop a simple model of SC with intra and intermolecular potentials which accounts for the elastic interaction including the effect of the inhomogeneity of the spin states and apply constant temperature molecular dynamics based on the Nosé-Hoover formalism. We demonstrate that, with increase of the strength of the intermolecular interactions, the temperature dependence of the HS component changes from a gradual crossover to a first-order transition.