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This book is based on some of the lectures during the Pacific Institute of Theoretical Physics (PITP) summer school on "Quantum Magnetism", held during June 2006 in Les Houches, in the French Alps. The school was funded jointly by NATO, the CNRS, and PITP, and entirely organized by PITP. Magnetism is a somewhat peculiar research field. It clearly has a quantum-mechanical basis – the microsopic exchange interactions arise entirely from the exclusion principle, in conjunction with respulsive interactions between electrons. And yet until recently the vast majority of magnetism researchers and users of magnetic phenomena around the world paid no attention to these quantum-mechanical roots. Thus, eg., the huge ($400 billion per annum) industry which manufactures hard discs, and other components in the information technology sector, depends entirely on room-temperature properties of magnets - yet at the macroscopic or mesoscopic scales of interest to this industry, room-temperature magnets behave entirely classically. This situation has now begun to change, and the quantum collective properties of magnetic systems, for so long of interest only to a few, have begun to move to centre stage. There are several reasons for this. One is the increasing use of low temperatures in industrial and applied research labs, and the recognition that the low-T properties of many new magnetic materials are of great potential use in future devices. Another is the emergence of nanoscience, and its offshoot nanotechnology, as an important new discipline – the majority of high-tech applications of nanotechnology so far envisaged will also be low-temperature ones. All this has meant that collective quantum phenomena, occurring at low T in quantum dots, magnetic molecules, and nanoscopic conductors, have suddenly become interesting to more than just pure physics researchers. The design of new magnetic quantum materials, of spin-based quantum devices in low-dimensional geometries, and quantum nanomagnetic systems, using either physical or chemical techniques, has now become the concern of many applied physicists and chemists. An interesting by-product of this broader interest in collective quantum spin phenomena has been the increasing focus, by applied physicists and even start-up companies, on some of the more exotic theoretical ideas current in quantum magnetism. These draw upon various branches of quantum field theory (including topological field theory, the theory of decoherence, and string theory), quantum computation, and upon older fields like spin glass theory and the theory of quantum phase transitions - all of which are fairly esoteric. Some of these ideas have found more application in cosmology or string theory than in condensed matter physics – so that their use in designing circuit arrays for quantum information processors, or spintronic devices, may seem disconcerting to some. Yet from another point of view it simply confirms the broadly unified nature of the principles and techniques used in theoretical physics. For the PITP/Les Houches school a number of topics of prime interest were selected, and these reflect the interests of a broad community. They were as follows: - MAGNETISM at the MICROSCOPIC SCALE - EXOTIC ORDER in QUANTUM MAGNETS - DISORDERED MAGNETS - QUANTUM NANOMAGNETISM - LARGE-SCALE QUANTUM PHENOMENA IN MAGNETS All of these fields are evolving rapidly – as this volume was going to press, new discoveries were being made on graphene and on the behaviour of dipolar quantum spin glasses, and physicists were digesting the discovery of room-temperature Bose-Einstein condensation of magnons in YIG films. However it is clear that the questions, issues, and techniques in these areas will be of central interest for many years to come.

The resonant multiple Bragg x-ray diffraction is used to study the forbidden (10 (4) over bar) reflection in LaMnO3. Using the interference between the three-beam scattering and resonant scattering we can determine the phase of the resonant scattering. This phase is shown to be consistent with a model in which the resonant scattering is caused by the influence of the Mn-O bond length distortion rather than directly by the orbital ordering on the Mn 4p band structure.

Optical and magneto-optical properties of YVO$_3$ single crystal were studied in FIR, visible, and UV regions. Two structural phase transitions at 75 K and 200 K were observed and established to be of the first and second order, respectively. The lattice has an orthorhombic $Pbnm$ symmetry both above 200 K as well as below 75 K, and is found to be dimerized monoclinic $Pb11$ in between. We identify YVO$_3$ as a Mott-Hubbard insulator with the optical gap of 1.6 eV. The electronic excitations in the visible spectrum are determined by three $d$-bands at 1.8, 2.4, and 3.3 eV, followed by the charge-transfer transitions at about 4 eV. The observed structure is in good agreement with LSDA+$U$ band structure calculations. By using ligand field considerations, we assigned these bands to the transitions to the $^4A_{2g}$, $^2E_{g} + ^2T_{1g}$, and $^2T_{2g}$ states. The strong temperature dependence of these bands is in agreement with the formation of orbital order. Despite the small net magnetic moment of 0.01 $��_B$ per vanadium, the Kerr effect of the order of $0.01^\circ$ was observed for all three $d$-bands in the magnetically ordered phase $T_{\text{N��el}}, Submitted to Phys. Rev. B

We report on an x-ray absorption and resonant photoemission study on single crystals of the high-T-c cuprates La2-xSrxCuO4 and Nd2-xCexCuO4-delta. Using an intrinsic energy reference, we find that the chemical potential of La2-xSrxCuO4 lies near the top of the La2CuO4 valence band whereas in Nd2-xCexCuO4-delta it is situated near the bottom of the Nd2CuO4 conduction band. The data clearly establish that the introduction of Ce in Nd2CuO4 results in electrons being doped into the CuO2 planes. We infer that the states closest to the chemical potential have a Cu 3d(10) singlet origin in Nd2-xCexCuO4-delta and a 3d(9) (L) under bar singlet origin in La2-xSrxCuO4.

It has recently been shown that x-ray diffraction from the doped holes in cuprates can be enhanced by 3-4 orders of magnitude by exploiting resonance effects in the oxygen K shell. This new type of anomalous scattering is direct way of probing ground state inhomogeneity in the mobile carrier liquid of high temperature superconductors. Here we describe a model which quantifies the relationship between experimental count rates and the structure factor for doped holes in this technique. We describe first efforts to detect inhomogeneity in thin films of La2CuO4+delta and report some peculiar observations. We attempt to offer some explanation.

Physical Review Letters

Polarization dependent x-ray-absorption measurements were performed on pure and Cr-doped V2O3 single crystals in the antiferromagnetic insulating, paramagnetic insulating, and metallic phases. The orbital occupation of the V 3d2 ion is found to depend appreciably on the phase, but always with the S = 1 character, requiring an explanation which is beyond the elegant simplicity of the pure one-band Hubbard model or of models in which the a1g orbital is projected out by means of a simple dimerization. The results reveal the critical role of the spin and orbital dependence of the on-site 3d-3d Coulomb energy, and a mechanism is proposed to explain the closing or opening of the band gaps which are of much higher energy scale than the transition temperatures.

We report on a systematic analysis of x-ray photoelectron spectroscopy (XPS) core- and valence-level spectra of clean and well-characterized iron oxide films, i.e., α − Fe 2 O 3 , γ − Fe 2 O 3 , Fe 3 − δ O 4 , and Fe 3 O 4 . All iron oxide films were prepared epitaxially by NO 2 -assisted molecular-beam epitaxy on single crystalline MgO(100) and α − Al 2 O 3 ( 0001 ) substrates. The phase and stoichiometry of the films were controlled precisely by adjusting the NO 2 pressure during growth. The XPS spectrum of each oxide clearly showed satellite structures. These satellite structures were simulated using a cluster-model calculation, which could well reproduce the observed structures by considering the systematic changes in both the Fe 3 d to O 2 p hybridization and the d − d electron-correlation energy. The small difference in the satellite structures between α − Fe 2 O 3 and γ − Fe 2 O 3 resulted mainly from changes in the Fe-O hybridization parameters, suggesting an increased covalency in γ − Fe 2 O 3 compared to α − Fe 2 O 3 . With increasing reduction in the γ − Fe 2 O 3 − F e 3 O 4 system, the satellite structures in XPS became unresolved. This was not only due to the formation of Fe 2 + ions, but also to nonhomogeneous changes in the hybridization parameters between octahedral and tetrahedral Fe 3 + ions.

We demonstrate that it is possible to obtain spin-resolved valence band spectra with a very high degree of spin polarization from antiferromagnetic transition metal materials if the excitation light is circularly polarized and has an energy close to the cation 2p3/2 (L3) white line. We are able to unravel the different spin states in the single-particle excitation spectrum of CuO and show that the top of the valence band is of pure singlet character, which provides strong support for the existence and stability of Zhang-Rice singlets in high-Tc superconductors.

The electronic structure of the perovskite LaCoO$_3$ for different spin states of Co ions was calculated in the LDA+U approach. The ground state was found to be a nonmagnetic insulator with Co ions in a low-spin state. Somewhat higher in energy we found two intermediate-spin states followed by a high-spin state at significantly higher energy. The calculation results show that Co 3$d$ states of $t_{2g}$ symmetry form narrow bands which could easily localize whilst $e_g$ orbitals, due to their strong hybridization with the oxygen 2$p$ states, form a broad $\sigma^*$ band. With the increase of temperature which is simulated by the corresponding increase of the lattice parameter, the transition from the low- to intermediate-spin states occurs. This intermediate-spin (occupation $t_{2g}^5e_g^1$) can develop an orbital ordering which can account for the nonmetallic nature of LaCoO$_3$ at 90 K$, Comment: formatted using LaTeX2e, graphicx and geometry packages

We discuss two-magnon phonon-assisted infrared absorption in two-dimensional Heisenberg systems like the parent insulating high-T-c cuprates (spin 1/2) and nickelates (spin 1). The theoretical line shape is compared with experiments. In the case of the cuprates it explains the mid-infrared peaks observed in the insulator. In the case of the nickelates the predicted line shape is also shown to agree with the experiments. We discuss the possibility to observe these excitations in other experiments.