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The development of resonant X-ray magnetic scattering is reviewed. Resonant X-ray magnetic scattering has become a unique probe among several useful techniques for studying magnetism in matter since the pioneering works of the 1980s. In contrast to neutron diffraction, which gives quantitative information on the spatial distribution of magnetic moments, resonant X-ray scattering is sensitive to the orbital and spin states of magnetic ions. The wavelengths of the K-edge resonance in 3d/4d transition elements and the L\(_{2,3}\)-edge resonance in lanthanide elements are located in the hard X-ray range, and are hence sufficiently short for diffraction measurement in most magnetic crystals, while the resonant enhancement is not very large. Recently, the electric dipole excitation between 2p and 5d orbitals has become a remarkably useful technique to explore novel electronic states in 5d transition-metal oxide compounds, where the spin and orbital are found to be strongly entangled with each other. Unique X-ray responses caused by an interference between the electric dipole and quadrupole transitions are also discussed.

The objective of molecular quantum spintronics is to combine the concepts of spintronics, molecular electronics and quantum computing in order to fabricate, characterize, and study molecular devices (for example molecular spin-transistors and molecular spin-valves) allowing the read-out and manipulation of the spin states of one or several molecules. The main first goal is to perform basic quantum operations. The visionary concept of molecular quantum spintronics is underpinned by worldwide research on molecular magnetism and supramolecular chemistry. Indeed, chemists have acquired a strong expertise in tuning, controlling and manipulating the properties of the molecules (spin, anisotropy, redox potential, light, electrical field…) allowing the creation of tuneable devices with new functionalities. This chapter summarizes the concepts and the first important results in this new research area, which open up prospects for new spintronic devices with quantum properties.

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 symmetry 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 possesses rigorous D 2h symmetry (or C ∞ 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.

The layered cobalt oxides with the \(\mathrm{CdI }_2\)-type \(\mathrm{CoO }_2\) block have been extensively studied as good thermoelectric materials at high temperatures since the discovery of large thermoelectric power factor in a \(\mathrm{Na }_x\mathrm{CoO }_x\) single crystal in 1997. In this chapter, we discuss why and how the thermoelectric performance is enhanced in the layered cobalt oxides. We further discuss their peculiar electronic states by comparing the physical properties with those of the layered rhodium oxides, and by controlling the spin state of the cobalt ions in the perovskite-related cobalt oxides.

This is a review of spin-dependent (polarization) properties of multicomponent exciton-polariton condensates in conditions when quasi-equilibrium mean-field Gross-Pitaevskii description can be applied. Mainly two-component (spin states ±1) polariton condensates are addressed, but some properties of four-component exciton condensates, having both the bright (spin ±1) and the dark (spin ±2) components, are discussed. Change of polarization state of the condensate and phase transitions in applied Zeeman field are described. The properties of fractional vortices are given, in particular, I present recent results on the warping of the field around half-vortices in the presence of longitudinal-transverse splitting of bare polariton bands, and discuss the geometrical features of warped half-vortices (in the framework of the lemon, monstar, and star classification).

Spin crossover complexes are characterized by the ability of a transition metal center to undergo a change in electronic configuration in response to external inputs such as heat, light, pressure or changes in magnetic field. Spin crossover is one of the oldest molecular switching phenomena known, and perhaps the most vital, considering its central role in haemoglobin-based respiration.

Exciton–polaritons in microcavities form an unusual gas of weakly interacting bosons. It has no direct analogy in cold atomic gases, superfluids or superconductors due to its two-component spin structure: in typical planar microcavities the polaritons have two allowed spin projections to the structure axis. This is why the order parameter of a polariton condensate is a complex spinor. The magnitude and, possibly, sign of polariton–polariton interaction constant depends on the spin state of polaritons. The energy of an exciton–polariton condensate is also spin-dependent. These specific features make polariton condensates a unique laboratory for studies of spin effects in interacting Bose gases. Several new spin-dependent effects in polariton condensates have been theoretically predicted and experimentally observed during the recent decade. This review chapter addresses some of these effects: polarisation multistability, spin switching, spin rings and spin Meissner effect. In the last section we address the perspective of observation of spin superfluidity in microcavities.

A Chronicle About the Development of Electronic Structure Theories for Transition Metal Complexes.- Orbital Models and Electronic Structure Theory.- Sturmians and Generalized Sturmians in Quantum Theory.- Chemistry as a "Manifestation of Quantum Phenomena" and the Born-Oppenheimer Approximation? From Ligand Field Theory to Molecular Collision Dynamics: A Common Thread of Angular Momentum.- A Modern First-Principles View on Ligand Field Theory Through the Eyes of Correlated Multireference Wavefunctions.- The Phase Rule: Beyond Myopia to Understanding.

Quantum mechanics deals with statistical statements about the result of measurements on an ensemble of states (particles, beams, targets). In other words: by giving an expectation value of operators it provides probabilitites (better: probability amplitudes) for the result of a measurement on an ensemble. Here two limiting cases can be distinguished.

Particles with short-range interactions that produce a large scattering length have universal properties that depend only on the scattering length [1]. A system consisting of such particles is strongly interacting in the sense that there are effects of the interactions that must be treated nonperturbatively. These strong interactions give rise to strong correlations among the particless. Many theoretical methods, even if they are nonperturbative, are inadequate for dealing with such strong correlations. However, such a system is also governed by universal relations that follow from the short-distance and short-time dynamics associated with the large scattering length. These universal relations provide powerful constraints on the behavior of the system. They hold for any state of the system: few-body or many-body, ground state or nonzero temperature, homogeneous or in a trapping potential, normal state or superfluid, balanced in the two spin states or imbalanced. They connect various properties of the system, ranging from thermodynamic variables to large-momentum and high-frequency tails of correlation functions.

We review the development of conductive organic molecular assemblies including organic metals, superconductors, single component conductors, conductive films, conductors with a switching function, and new spin state (quantum spin liquid state). We emphasize the importance of the ionicity phase diagram for a variety of charge transfer systems to provide a strategy for the development of functional organic solids (Mott insulator, semiconductor, superconductor, metal, complex isomer, neutral-ionic system, alignment of chemical potentials, etc.). For organic (super)conductors, the electronic dimensionality of the solids is a key parameter and can be designed based on the self-aggregation ability of a molecule. We present characteristic structural and physical properties of organic superconductors.

Studies that are related to temperature-induced phase transitions and photo-induced phase transitions are extensively investigated in solid-state chemistry [1–4]. Temperature-induced phase transition phenomena are observed in spin crossover or intramolecular electron transfer. In a spin crossover complex, a transition metal ion can be in either the low-spin or the high-spin state depending on the strength of the ligand field. When the thermal energy is close to the exchange energy that corresponds to the crossover, a spin transition occurs between the two spin states. This phenomenon is observed in octahedral coordinate iron transition metal complexes [5–7].

A clear advantage of broken symmetry (BS) unrestricted density functional theory DFT is qualitatively correct description of bond dissociation process, but its disadvantage is that spin-polarized Slater determinant is no longer a pure spin state (a.k.a. spin contamination). We propose a new approach to eliminate the spin-contamination, based on canonical Natural Orbitals (NO). We derive an expression to extract the energy of the pure singlet state given in terms of energy of BS DFT solution, the occupation number of the bonding NO, and the energy of the higher state built on these bonding and antibonding NOs (as opposed to self-consistent Kohn-Sham orbitals). Thus, unlike spin-contamination correction schemes by Noodleman and Yamaguchi, spin-correction is introduced for each correlated electron pair individually and thus expected to give more accurate results. We validate this approach on two examples, a simple diatomic H2 and transition metal hydride MnH.

Resistively Detected ESR and ENDOR Experiments in Narrow and Wide Quantum Wells: A Comparative Study.- Electron-Spin Manipulation in Quantum Dot Systems.- Resistively Detected NMR in GaAs/AlGaAs.- Electron-Spin Dynamics in Self-Assembled (In,Ga)As/GaAs Quantum Dots.- Single-Electron-Spin Measurements in Si-Based Semiconductor Nanostructures.- Si/SiGe Quantum Devices, Quantum Wells, and Electron-Spin Coherence.- Electrical Detection of Electron-Spin Resonance in Two-Dimensional Systems.- Quantitative Treatment of Decoherence.- Measuring the Charge and Spin States of Electrons on Individual Dopant Atoms in Silicon.- Electron Spin as a Spectrometer of Nuclear-Spin Noise and Other Fluctuations.- A Robust and Fast Method to Compute Shallow States without Adjustable Parameters: Simulations for a Silicon-Based Qubit.- Photon-Assisted Tunneling in Quantum Dots.

We propose a new approach in Nuclear Magnetic Resonance (NMR) technology for quantum computing. Two basic elements for quantum computation are qubits and interaction. Traditionnally in NMR, qubits are obtained by considering the spin states of certain atoms of a specific molecule. The interaction that is necessary to create qubit gates such as Control-NOT is then made possible by the spin-spin coupling that exists in such a molecule. One of the drawbacks of this method is the low scalability. More qubits usually means finding an entire different molecule to label the qubits. We take a different view on the NMR approach. We use a water tube as quantum computer where qubits are defined by the spins which have the same frequency resonance in a small interval defined by the NMR linewidth. Two fundamental roadblocks have to be crossed before this method can even be considered as a possible quantum computation technique: single qubits need to be identified and adressed and an interaction between these qubits has to exist to create two-qubit gates. We settle the first of these problems by using a magnetic field gradient applied in the main magnetic field direction. The application of a magnetic field gradient during the RF pulse induces a rotation only of those spins whose resonant frequency is equal to the bandwidth of the RF pulse, therefore a qubit can be defined by its resonant frequency and manipulated by selective RF pulses. The main advantage of creating qubits in this way is scalability. As qubits are no longer atoms of a specific molecule but segments of our water tube, increasing the number of qubits would hypothetically just mean increasing the number of segments by applying a stronger magnetic field gradient. Another potential advantage can be obtained during the initialisation phase of the qubits. The second roadblock, the problem of creating interaction between qubits, is work in progress. As for now we are investigating the use of the dipole-dipole interaction between the spins to generate a coupling between the spins in order to create entanglements.

We review an ongoing effort to demonstrate technologies required for quantum computing with phosphorus donors in silicon. The main aspect of our research is to achieve control over charge and spin states of individual dopant atoms. This work has required the development of new techniques for engineering silicon nanodevices at the atomic level. We follow an approach for implanting single phosphorus ions into silicon substrates with integrated p–i–n detectors. Configuring our devices with radio-frequency single-electron transistors (RF-SETs) allows for charge sensing at low temperatures. In this context, we perform measurements of single-electron charge transfer between individual phosphorus donors. In a parallel effort, we employ nanoscale Schottky contacts for populating and depopulating individual dopant atoms. Of particular interest is coherent manipulation of single-electron charge and spin states on individual dopant atoms. Charge manipulation between coupled donor states may be achieved by either external microwave pumping or intrinsic tunnel coupling. Spin manipulation, on the other hand, involves magnetic resonance. In this context, we pursue electrically detected spin resonance in phosphorus-doped devices with a decreasing number of dopant atoms.

The great amount of theoretical predictions [1 4] on the structure of high lying high-spin states and yrast lines in light nuclei (A 1 0 brought a new impetus to the experimental investigations. However the actual confinement of the experimental knowledge to the region E 10MeV in light nuclei is the use of high-spin selective compound reactions [5, 6]. Together with statistical model calculations the "relative" cross sections yield directly the spins of the high-spin states and the critical angular momentum J~it limiting the formation of the compound nucleus. This method is limited, however, for high spins by the loss of selectivity for spins near J~it [7] and is limited further for high excitation energies (E > 20 MeV) by the high level density of low-spin states [7]. The high level density also affects double and triple angular correlation methods which have a further even lower limitation in excitation energy due to the fact that the sequential decay of these highly excited states cannot be in general expected to proceed via a spin-zero state in the final nucleus. The high level density limits also the accuracy of spin measurements by selective direct transfer reactions [-8, 9]. In the present work a new procedure for identifying highly excited high-spin states will be presented which

The maximum spin Jmax limiting the sunmlation over the spin J of the compound nucleus 26AI was determined by a simultaneous least squares fit of relative angular distributions of 17 transitions to known spin, as a function of the angular momentum cutoff. The value Jmax=15 Was obtained independent of the choice of level density parameter in a very wide range (Fig.2). This value, obtained for the entrance channel IOB+I60 for E ¢ = 42.5 MeV in 26AI, agrees with values obtained by fusion cross section measurements in the reaction 14N + 12 C 3). 2500 ~°B (~60 d)24Mg .,.d I ~

Chemical and biological photoprocesses which involve bimolecular reactions between non-zero spin intermediates, e.g. doublet molecules 2A+2B, often produce the intermediate molecular pair in a pure overall spin state, e.g. a singlet state 1(2A+2B). and select for the reaction channels again such spin states, e.g. a triplet state 3(2A+2B). The necessery transition 1(2A+2B)→3(2A+2B) is affected by magnetic interactions (hyperfine, Zeeman, zero field splitting) and can be influenced by magnetic fields. Examples are photoinduced electron transfer processes, e.g. the primary reaction of photosynthesis.

DFT is often used to predict the energetics of transition metal compounds. In particular, energy differences between states of different spin are of great interest. This review discusses the accuracy of such computations for spin-state splittings of monometallic complexes where the differences in spin-pairing occur mostly or exclusively on the metal itself. Large differences are found for computed splittings using different functionals, in particular between pure and hybrid functionals. An optimum exact exchange admixture of ~15% seems to yield accurate results in many cases, but experimental and especially theoretical uncertainties suggest that this should not be relied upon, and the development of new functionals is seen to be highly desirable.

Thermal spin transition (spin crossover), one of the most fascinating dynamic electronic structure phenomena occurring in coordination compounds of third row transition metal ions, mostly of iron(II), iron(III) and cobalt(II) with critical ligand field strengths competing with the spin pairing energy, has attracted increasing attention by many research groups. One of the reasons is the promising potential for practical applications. In this chapter we intend to cover essential recent work, primarily accomplished within the European research network on "Thermal and Optical Switching of Molecular Spin States (TOSS)". New spin crossover compounds and their thermal spin transition behaviour, also under applied pressure, novel effects observed by irradiation and magnetic field, will be discussed. Progress in theoretical treatments of spin crossover phenomena, particularly cooperativity, will be briefly outlined. The chapter concludes with a summary of research highlights published by the partner laboratories of the TMR network TOSS.

The mass A = 130 region has been of particular interest both theoretically and experimentally as nuclei in this region are expected to exhibit soft behaviour related to the shape asymmetry parameter γ. The level scheme has been extended considerably up to spin 83/2− with a further possible transition to spin 85/2−.

Multi reference correlation calculations (MR-CI and MR-ACPF) have been performed for small VnOm clusters. VO2 has two doublet states which are so close that it is difficult to predict the symmetry of the ground state. For V2O 4 + and V2O4 we find minimum energy structures of C 2h . symmetry (trans bending of the vanadyl units) in contrast to what has been reported in the literature. The magnetic coupling of the electrons is such that low spin states are favoured (singlet for V2O4, doublet for V2O 4 - ).

Consider steady state current flow in the circuit depicted in Fig. 7.1 [1], where two identical strong ferromagnetic layers (F1 and F2) are arranged with a distance on a thin nonmagnetic metal (N) layer. If Fi (i = 1, 2) is uniformly magnetized and the magnetization M i is strongly oriented, it is a property of F that the current carrying electrons have spin down. When the battery drives a circulation, the current crossing the F1-N interface has a net spin polarization and each electron remains polarized for a mean time T 2. In the diffusive conduction process, each electron is constantly scattered so that its mean free path 1 = vFτ is quite short, where vF and τ are the Fermi velocity and the mean scattering time, respectively. The macroscopic current results from a net drift of electrons, when each electron nudges the one next to it. But only a small fraction, about 1 in 1000 (ie., τ/T 2 ~0.001), of these scattering events alters the spin state of the electron.

The drive to build a framework for coherent semiconductor spintronic devices provides a strong motivation for understanding the coherent evolution of spin states in semiconductors [1,2]. The fundamental aim in this context is to discover regimes in which carefully prepared quantum states based upon spin can evolve coherently long enough to allow the storage, manipulation and transport of quantum information in devices. Such devices might exploit, for instance, the interference between two coherently-occupied spin states whose time variation occurs at a frequency ΔE/h, where ΔE is their energy separation. Since typical spin splittings in semiconductors are in the range of meV, the rapidly varying oscillations of a classical observable such as the spin orientation (magnetization) can occur at GHz-THz frequencies, providing the basis for ultrafast devices. Another possibility is that this quantum interference may actually be used as part of a calculation within the context of quantum computing algorithms [3]. It is hence crucial to develop experimental tools that probe spin coherence in semiconductors and that allow one to map out schemes for its manipulation, storage and transport. The previous chapter formulated the theoretical foundations underlying coherent spin dynamical phenomena in semiconductors and introduced specific mechanisms that may be responsible for spin relaxation and spin decoherence, pointing out the important physical distinctions between longitudinal and transverse spin relaxation times (T 1 and T 2, respectively) [4]. We note that it is the latter timescale that is of direct relevance to coherent spin devices and hence we focus on experimental techniques that probe the transverse spin relaxation time in semiconductors.

Numerical and analytical results are reviewed, which support SO(5) symmetry as a concept unifying superconductivity and antiferromagnetism in the high-temperature superconductors. Exact cluster diagonalizations verify that the low-energy states of the two-dimensional t-J and Hubbard models, widely used microscopic models for the high-Tc cuprates, form SO(5) symmetry multiplets. Apart from a small standard deviation ~J/10, these multiplets become degenerate at a critical chemical potential (transition into doped system). As a consequence, the d-wave superconducting states away from half-filling are obtained from the higher spin states at half-filling through SO(5) rotations. Between one and two dimensions, using weak-coupling renormalization, a rather general ladder Hamiltonian including next-nearest-neighbor hopping can be shown to flow to an SO(5) symmetric point. Experimental tests and consequences such as the existence of a pi-Goldstone mode both in the insulator and superconductor and, in particular, the relationship between the photoemission spectra of the insulator and superconductor, are emphasized.

We explore theoretically how the correlation effects involving spins can appear in transport properties when we put zero dimensional (0D: quantum dots), ID (quantum wires) or in 2D correlated systems in magnetic fields. We show that the correlation induces a spin blockade through ‘electron molecules’ in quantum dots, a spin polarised current in a Tomonaga-Luttinger liquid and a negative magnetoresistance in partly flat bands.

Hahn echoes arise when the spins are reoriented by RF pulses while the field inhomogeneities are stationary. The recovery of spin coherences is a matter of suitably manipulated spin states. By contrast, the principle of solid echoes due to dipolar (or quadrupolar) interaction is that the spin couplings as the coherence defocusing elements are also affected by the RF pulses. Solid echoes [322, 390] are the consequence of spin-state as well as spin-interaction manipulations. This is the reason why the RF pulse sequences, albeit very similar in many respects, require different pulse phases and flip angles to provide optimal solid-echo amplitudes.

The traditional approach to the electronic structure of transition metal complexes (which is the subject of the next chapter) is to assume that the only effect of the ligands is to produce an electrostatic field which relieves the degeneracy of the d orbitals of the central metal ion. The most serious defect of this model is that it does not recognize the existence of overlap, and hence the existence of specific bonding interactions, between the ligands and the metal orbitals. Yet calculations which assume reasonable sizes for the orbitals (together with a considerable body of physical evidence which will be reviewed in Chapter 12) point to the existence of overlap. How should this be taken account of? The simplest answer is to be found in the application of symmetry ideas to the problem, and this is the subject of this chapter. In it the reader will be assumed to have some familiarity with the basics of group theory. Appendix 3 gives an introduction to the subject; the following lines are intended to provide a brief overview of aspects needed to make a start on the present chapter.

Although little use is made now of the theory presented in this chapter, it contains the basis of all of those that are used. It provides the foundation, particularly for the understanding of spectral and magnetic properties; all else is elaboration and refinement. A knowledge of simple crystal field theory is therefore essential to an understanding of the key properties of transition metal complexes and particularly those covered in Chapters 8 and 9. This chapter deals exclusively with transition metal complexes. In one or more of their valence states, the ions of transition metals have their d orbitals incompletely filled with electrons. As a result, their complexes have characteristics not shared by complexes of the main group elements. It is the details of the description of these incompletely filled shells which is our present concern; this is in contrast to the discussion of the previous chapter where the topic was scarcely addressed. Ions of the lanthanides and actinides elements have incompletely filled f orbitals and so necessitate a separate discussion which will be given in Chapter 11.

One of the strange features in the Cu-NQR experiments in the CuO2 plane of high-Tc Cu oxides is the existence of several distinctly separated NQR lines in the most of the doped cases with mixed valences. Since the NQR frequency in these Cu sites manifests itself the occupancy of the holes in the Cu d-orbital, hence the charged state, the experimental observation clearly demonstrates a “charge differentiation” in the CuO2 plane. On the contrary, the spin state observed from the Cu Knight shift experiment has a uniform characteristic in the plane because only single NMR line has been observed for all the cases. This fact makes a great contrast to the case of vanadium oxides where the “spin differentiation” has been observed in the 51V NMR shift measurements. We are forced to argue that the above facts obtained by the Cu NMR and NQR for the CuO2 plane are associated with a kind of “spin-charge separation”, namely the energy scale for the spin and charge fluctuations are well differentiated with respect to the NMR time scale (∼10−8 sec). This is one of the most important characteristics of the electronic state in high-Tc’s.

We discuss an important effect of the magnetic field tilted from the direction perpendicular to the electron plane viz., the subband-Landau-level coupling, in the fractional quantum Hall effect regime. We also present new theoretical results on recombination radiation in two-dimensional electron systems which might be an interesting route to investigate the spin states of various filling fractions.

Spin states of antiferromagnetic CuO2 planes in high-T c superconductors with small doping (of alcali-earth metals and oxygen) are considered in the framework of microscopic approach. The reasons for hole localization near different types of acceptors are studied and indirect spin interaction between holes via exchange by virtual magnons is calculated. It is shown that within insulating phase the variable sing interaction is present and, though it teraction is present and, though it prevents from long-range spin ordering in the system of chaotically distributed hole spins, is insufficient for effective destroying of antiferromagnetism in CuO2 planes. It is established that the irreversible loss of order can be produced by random deformation fields from impurity ions. The magnetic phase diagram in localized hole concentration vs temperature is obtained for high-T c superconductors.

We investigate the energy spectrum and the Hall effect of electrons on the square lattice with next-nearest-neighbor (NNN) hopping as well as nearest-neighbor hopping. General rational values of magnetic flux per unit cell φ = p/q are considered. In the absence of NNN hopping, the two bands at the center touch for q even, thus the Hall conductance is not well defined at half filling. An energy gap opens there by introducing NNN hoping. When φ =1/2, the NNN model coincides with the mean field Hamiltonian for the chiral spin state proposed by Wen, Wilczek and Zee (WWZ). The Hall conductance is calculated from the Diophantine equation and the E-φ diagram. We find that gaps close for other fillings at certain values of NNN hopping strength. The quantized value of the Hall conductance changes once this phenomena occurs. In a mean field treatment of the t-J model, the effective Hamiltonian is the same as our NNN model. From this point of view, the statistics of the quasi-particles is not always semion and depends on the filling and the strength of the mean field.

Even minimally adequate coverage of the application of orbital symmetry criteria to inorganic reactions would increase the scope of this book inordinately and — in any case — is outside the author’s competence. The modest attempt to address them in the final pages of this book does not merit Part status, so the chapter is included as a matter of necessity in Part IV: Spin and Photochemistry. A somewhat labored justification might run as follows: The principal new element that distinguishes inorganic from organic reactions is the ever-present possibility that d orbitals have to be taken into account. As we will see, the need to consider them when dealing with reactions of the main-group elements arises in connection with their photochemistry. They achieve crucial importance in the reactions of transition metal complexes, where they determine one of the essential properties of the reacting molecule or ion: its spin state.

Spin-state transitions in metal complexes which are driven by a change of temperature T or pressure p are always associated with a considerable reorganization of molecular geometry. The change involves metal-ligand bond lengths R, bond angles, and a variation of ligand orientation. In particular, the elongation 4R by up to ∼ 10% occurring in the course of the LS → HS conversion produces an expansion of molecular volume ΔV ≌ 25 A3 per metal atom. The average crystal structure for given values of T and p is reproduced by the fractional occupancy of the individual structures of the high-spin (HS) and low-spin (LS) isomer. The transitions are reasonably well described by a number of theoretical models which are equivalent to the Bragg and Williams approximation of the Ising model. The dynamics of the spin-state transitions in solution, based on measurements by ultrasonic and photo-perturbation techniques, is in general rapid with rate constants between 4 × 105 and 3 × 108 s−1. Similar results are obtained for the spin conversion in solid complexes where the line shape analysis of Mossbauer spectra based on the theory of Blume and Tjon is applied. The dynamics may be rationalized employing one-dimensional cross sections through Gibbs free-energy surfaces G = G(R), an alternative being the comparison of the results with quantum-mechanical calculations for a radiationless non-adiabatic multiphonon process.

The authors report Cu NMR studies of YBa2Cu3O7−δ (Tc = 90K) in the normal state (using oriented single crystals) and superconducting state (using oriented powders). In the normal state they measure the electric field gradient tensor, the magnetic shift tensor, the spin-lattice relaxation tensor, and the time dependence of the transverse decay (spin-echo envelope) and draw conclusions about the charge and spin states of the Cu atoms. In the superconducting state they measure the shift tensor, using the 89Y resonance to measure the internal field in the sample. The data are compared with various detailed models of spin pairing.

Radical anions, triplet dianions, and radical trianions of phenyl substituted 1,2:9,10-dibenzo[2.2]paracyclophanes 2, 3, and 4 have been characterized by ESR, ENDOR, and TRIPLE resonance spectroscopy.

Short-lived radical pairs are, presently, the subject of permanent scientific attention caused by both the radical pair chemical transformation proper, and their specific role in the appearance of such phenomena as the chemically-induced polarization of electrons and nuclei, the effect of external magnetic field and the resonance microwave (mw) fields on radical reaction, magnetic isotopic effect (see e.g. (1)). Unfortunately, the ISR spectra of radical pairs in solutions cannot be detected by means of a conventional ESR technique due to their low stationary concentration. The present review is concerned with more sensitive methods based on the radical pair spin state modulation, and, hence, its reaction under the action of the resonance mw radiation, and the intrinsic interactions of the magnetic nature in pair radicals. In the broad sense, they may be referred to the methods based on the reaction yield detected magnetic resonance (2).

It is well known that the transfer-matrix method is very useful in the statistical mechanics of classical systems [1,2]. For example, the partition function of the three-dimensional (3D) Ising model is formulated in terms of the transfer matrix. If the size of the lattice is N=l×m×n, the partition function can be written as $$\text{Z=Tr }{{T}^{n}}$$ (1.1) where the transfer matrix T acts on the spin states of the 2D layer of l×m sites sliced from the 3D lattice. The transfer matrix can be pictured as an operator which governs the evolution of spin states from layer to layer. Since each layer has 2 lm spin states, the size of the matrix T is 2 lm ×2 lm . In the limit n →∞ the partition function is dominated by the maximum eigenvalue Λ of T: $$\text{Z}\sim {{\Lambda }^{n}}$$ (1.2)