http://sces.phys.utk.edu/mostcited/mc1_1114.pdf

Colossal Magnetoresistant Materials: The Key Role of Phase Separation

The theory of critical phenomena in systems at equilibrium is reviewed at an introductory level with special emphasis on the values of the critical point exponents α, β, γ,..., and their interrelations. The experimental observations are surveyed and the analogies between different physical systems - fluids, magnets, superfluids, binary alloys, etc. - are developed phenomenologically. An exact theoretical basis for the analogies follows from the equivalence between classical and quantal `lattice gases' and the Ising and Heisenberg-Ising magnetic models. General rigorous inequalities for critical exponents at and below Tc are derived. The nature and validity of the `classical' (phenomenological and mean field) theories are discussed, their predictions being contrasted with the exact results for plane Ising models, which are summarized concisely. Pade approximant and ratio techniques applied to appropriate series expansions lead to precise critical-point estimates for the three-dimensional Heisenberg and Ising models (tables of data are presented). With this background a critique is presented of recent theoretical ideas: namely, the `droplet' picture of the critical point and the `homogeneity' and `scaling' hypotheses. These lead to a `law of corresponding states' near a critical point and to relations between the various exponents which suggest that perhaps only two or three exponents might be algebraically independent for any system.

https://iopscience.iop.org/article/10.1088/0034-4885/30/2/306/pdf

The theory of equilibrium critical phenomena

The d1 layer metals TaS2, TaSe2, NbSe2, in all their various polytypic modifications, acquire, below some appropriate temperature, phase conditions that their electromagnetic properties have previously revealed as ‘anomalous’. Our present electron-microscope studies indicate that this anomalous behaviour usually includes the adoption, at some stage, of a superlattice. The size of superlattice adopted often is forecast in the pattern of satellite spotting and strong diffuse scattering found above the transition. Our conclusions are that charge-density waves and their concomitant periodic structural distortions occur in all these 4d1/5d1 dichalcogenides. We have related the observed periodicities of these CDW states to the theoretical form of the parent Fermi surfaces. Particularly for the 1T octahedrally coordinated polytypes the Fermi surface is very simple and markedly two-dimensional in character, with large near-parallel walls. Such a situation is known theoretically to favour the formation of...

Charge-density waves and superlattices in the metallic layered transition metal dichalcogenides

We give a general introduction to quantum phase transitions in strongly-correlated electron systems. These transitions which occur at zero temperature when a non-thermal parameter $g$ like pressure, chemical composition or magnetic field is tuned to a critical value are characterized by a dynamic exponent $z$ related to the energy and length scales $\Delta$ and $\xi$. Simple arguments based on an expansion to first order in the effective interaction allow to define an upper-critical dimension $D_{C}=4$ (where $D=d+z$ and $d$ is the spatial dimension) below which mean-field description is no longer valid. We emphasize the role of pertubative renormalization group (RG) approaches and self-consistent renormalized spin fluctuation (SCR-SF) theories to understand the quantum-classical crossover in the vicinity of the quantum critical point with generalization to the Kondo effect in heavy-fermion systems. Finally we quote some recent inelastic neutron scattering experiments performed on heavy-fermions which lead to unusual scaling law in $\omega /T$ for the dynamical spin susceptibility revealing critical local modes beyond the itinerant magnetism scheme and mention new attempts to describe this local quantum critical point.

https://arxiv.org/pdf/cond-mat/0102119.pdf

Quantum Phase Transitions

Multiferroics, defined for those multifunctional materials in which two or more kinds of fundamental ferroicities coexist, have become one of the hottest topics of condensed matter physics and materials science in recent years. The coexistence of several order parameters in multiferroics brings out novel physical phenomena and offers possibilities for new device functions. The revival of research activities on multiferroics is evidenced by some novel discoveries and concepts, both experimentally and theoretically. In this review, we outline some of the progressive milestones in this stimulating field, especially for those single-phase multiferroics where magnetism and ferroelectricity coexist. First, we highlight the physical concepts of multiferroicity and the current challenges to integrate the magnetism and ferroelectricity into a single-phase system. Subsequently, we summarize various strategies used to combine the two types of order. Special attention is paid to three novel mechanisms for multiferroicity generation: (1) the ferroelectricity induced by the spin orders such as spiral and E-phase antiferromagnetic spin orders, which break the spatial inversion symmetry; (2) the ferroelectricity originating from the charge-ordered states; and (3) the ferrotoroidic system. Then, we address the elementary excitations such as electromagnons, and the application potentials of multiferroics. Finally, open questions and future research opportunities are proposed.

Multiferroicity: the coupling between magnetic and polarization orders

An investigation of the classical Heisenberg exchange energy has led to the discovery of a new spin configuration, called a ferrimagnetic spiral. The explicit construction of this state is accomplished by application of Lyons-Kaplan generalization of the Luttinger-Tisza method (GLT). For all $B\ensuremath{-}B$ interactions which are sufficiently large to destabilize the N\'eel (collinear) configuration, this spiral has lower energy than all previously proposed spin configurations including those of N\'eel and Yafet-Kittel. Furthermore, this ferrimagnetic spiral is found to be stable against arbitrary small deviations of the spin vectors over a range of interactions that is contiguous with the N\'eel range. It is also shown, by further application of the GLT method, to have the lowest energy over an additional large class of spin configurations. In view of these results, it is likely that the ferrimagnetic spiral is the ground state over its range of local stability.The complete class of configurations possessing "equal relative angles" (i.e., invariance of the angles between spins under lattice translations) is elucidated for the first time. It is shown that the ferrimagnetic spiral has the lowest energy over this class of configurations for a range of interactions which includes the range of stability, and extends beyond it. It follows that for interactions in the latter range, the relative angles in the ground state must not possess translational invariance, in contradiction to earlier hypotheses.The neutron diffraction pattern resulting from general magnetic spirals is discussed. The striking agreement between our theoretical results and the complex pattern found by Corliss and Hastings for manganese chromite supports the theory. In addition, the spin configuration at the Curie point, in the molecular field approximation, is shown to be in accord with the observed temperature dependence in manganese chromite.

Classical Theory of the Ground Spin-State in Cubic Spinels

We report the unexpected evolution, with thermal and magnetic-field (H) variations, of the interrelation between the polarization P, magnetization M, and spiral wave vector Q in CoCr2O4, which has a ferrimagnetic conical-spiral magnetic order. For example, P suddenly jumps and changes its sign at the magnetic lock-in transition (T_{L}) with thermal variation, or with isothermal variation of H (without changing its direction) at T_{L}, which surprisingly occurs without change in spiral handedness (i.e., the sign of Q). The presence of multiple spiral sublattices may be behind this unusual behavior.

https://ir.nctu.edu.tw:443/bitstream/11536/149745/1/54b8ce3f52a711f4a79a88655acc585b.pdf

Thermally or magnetically induced polarization reversal in the Multiferroic CoCr2O4.

The Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction $\ensuremath{\Phi}(\mathrm{R})$ is generalized for the case of nonspherical Fermi surfaces. In general $\ensuremath{\Phi}(\mathrm{R})$ is found to fall off as $\frac{1}{{R}^{3}}$, and to oscillate with a period corresponding to a calipering of the Fermi surface in the R direction. For the special cases of parallel or cylindrical regions of the Fermi surface, a slower falloff of $\ensuremath{\Phi}(\mathrm{R})$ ($\frac{1}{R}$ and $\frac{1}{{R}^{2}}$, respectively) is obtained. The general expression for the Fourier transform $\ensuremath{\varphi}(\mathrm{q})$ is also considered and displays Kohn anomalies whose form depends on the shape of the Fermi surface in the vicinity of calipering pairs of points. The usual infinite slope in $\ensuremath{\varphi}(\mathrm{q})$ for the spherical Fermi surfaces changes in the more general case and becomes a discontinuous slope for a "waist" and a logarithmic singularity in $\ensuremath{\varphi}(\mathrm{q})$ for parallel regions of the Fermi surface. A number of possible applications of the results are discussed.

Generalization of the Ruderman-Kittel-Kasuya-Yosida Interaction for Nonspherical Fermi Surfaces

Series Preface. Preface. Thermodynamics of the Double Exchange System N. Furukawa. Phase Separation in Models for Manganites: Theoretical Aspects and Comparison with Experiments E. Dagotto et al. Two Ferromagnetic States in Magnetoresistive Manganites: First Order Transition Driven by Orbitals S. Maekawa et al. Magnetism and Electronic States of Systems with Strong Hund Coupling K. Kubo et al. Density Functional Studies of Magnetic Ordering, Lattice Distortion, and Transport in Manganites W.E. Pickett et al. Optical Conductivity of Doped Manganites: Comparison of Ferromagnetic Kondo Lattice Models with and without Orbital Degeneracy F. Mack, P. Horsch. Electron-Lattice Interactions in Manganese-Oxide Perovskites J.B. Goodenough. Spin Waves in Doped Manganites T.A. Kaplan, S.D. Mahanati. Spin Dynamics of Magnetoresistive Oxides J.W. Lynn. Metal-Insulator Phenomena Relevant to Charge/Orbital Ordering in Perovskite Manganites Y. Tomioka et al. Optical Properties of Colossal Magnetoresistance Manganites T.W. Noh et al. Polarons in Manganites Now You See Them Now You Don't S.J.L. Billinge. Oxygen Isotope Effects in Manganites: Evidence for (BI)Polaronic Charge Carriers G. Zhao et al. Electronic Transport in La-Ca Manganites M. Jaime, M.B. Salamon. Spin Injection in Manganite-Cuprate Heterostructures V.A. Vas'ko et al. List of Participants. Index.

Physics of manganites

It is pointed out that Yafet-Kittel triangular arrangements are not stable in the cubic spinel. The stability criterion used is that the classical Heisenberg energy should not decrease for small, but otherwise arbitrary, spin-deviations from the configuration of interest. It is found that the Yafet-Kittel-Prince configuration can probably be stabilized by a sufficient tetragonal distortion of the pattern of $B\ensuremath{-}B$ interactions. In addition, the classical ground state is found for the antiferromagnetic body-centered cubic lattice with first, second, and third neighbor antiferromagnetic interactions (with parameters ${J}_{1}$, ${J}_{1}{\ensuremath{\sigma}}_{2}$ and ${J}_{1}{\ensuremath{\sigma}}_{3}$): the spin $\mathrm{S}({\mathrm{R}}_{n})$ at lattice point ${\mathrm{R}}_{n}$ is independent of time, is always parallel to one plane, $P$, and the angle made by $\mathrm{S}({\mathrm{R}}_{n})$ with a fixed line in $P$ is of the form $\mathrm{k}\ifmmode\cdot\else\textperiodcentered\fi{}{\mathrm{R}}_{n}$ for ${\mathrm{R}}_{n}$ a cube corner, and of the form $\mathrm{k}\ifmmode\cdot\else\textperiodcentered\fi{}{\mathrm{R}}_{n}+\ensuremath{\pi}$ for ${\mathrm{R}}_{n}$ a body-center position with the vector k determined by the ${\ensuremath{\sigma}}_{i}$. The neutron diffraction pattern for such a "spiral" configuration (with ${\ensuremath{\sigma}}_{2}\ensuremath{\sim}0.6$, ${\ensuremath{\sigma}}_{3}\ensuremath{\sim}0.1$, for example) bears a close relationship with the unusual pattern obtained by Corliss, Hastings, and Weiss with a single crystal of chromium.

T. A. Kaplan

Papers

Classical Theory of the Ground Spin-State in Cubic Spinels

Thermally or magnetically induced polarization reversal in the Multiferroic CoCr2O4.

Generalization of the Ruderman-Kittel-Kasuya-Yosida Interaction for Nonspherical Fermi Surfaces

Physics of manganites

Classical Spin-Configuration Stability in the Presence of Competing Exchange Forces