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Journal of Applied Physics

Nontrivial magnetic order: Localized versus itinerant systems (invited) (abstract)

L. P. Gor’kov, Alexander Sokol

Published May 15, 1993• 0 citations
Publisher

Abstract

Recently the interest in non-Neel ground states for antiferromagnetically interacting localized spin systems has been revived. We discuss to what extent the generalization of such states is possible for itinerant electrons. Multiple spin correlation functions can be used to enumerate nontrivial order parameters for localized spins. This approach can be applied to itinerant systems without any modification. However, for the transition which breaks translational symmetry, electronic states far away from the Fermi surface are important and, hence, there is no distinct energetic mechanism for the nontrivial magnetic ordering. The only exception is the Fermi surface with the nesting property. As it is shown, among all phases known for localized spins only p-type spin nematic and chiral spin states can appear as a result of a Fermi liquid breakdown with respect to the electron-hole condensation near the Fermi surface. All other phases with zero local average spin known for localized systems, either are accompanied by the charge density wave or persistent orbital currents creating orbital magnetic moments, or can not appear as a result of a phase transition driven by such mechanism. Although two aforementioned phases are equivalent to their counterparts for localized spins from the symmetry viewpoint, the driving order parameter in an itinerant case is not a multiple spin average, but a wave function of the electron-hole condensate.

DOI
10.1063/1.353721

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Recently the interest in non-Neel ground states for antiferromagnetically interacting localized spin systems has been revived. We discuss to what extent the generalization of such states is possible for itinerant electrons. Multiple spin correlation functions can be used to enumerate nontrivial order parameters for localized spins. This approach can be applied to itinerant systems without any modification. However, for the transition which breaks translational symmetry, electronic states far away from the Fermi surface are important and, hence, there is no distinct energetic mechanism for the nontrivial magnetic ordering. The only exception is the Fermi surface with the nesting property. As it is shown, among all phases known for localized spins only p-type spin nematic and chiral spin states can appear as a result of a Fermi liquid breakdown with respect to the electron-hole condensation near the Fermi surface. All other phases with zero local average spin known for localized systems, either are accompanied by the charge density wave or persistent orbital currents creating orbital magnetic moments, or can not appear as a result of a phase transition driven by such mechanism. Although two aforementioned phases are equivalent to their counterparts for localized spins from the symmetry viewpoint, the driving order parameter in an itinerant case is not a multiple spin average, but a wave function of the electron-hole condensate.
Magnetic phenomena in itinerant electron systems have been at the forefront of materials science. Here we show that the Weyl spin-orbit coupling (SOC) in three-dimensional repulsively interacting itinerant Fermi systems opens up a platform to host new itinerant magnetic phases, excitations, and phase transitions. A putative ferromagnetic state (FM) is always unstable against a stripe spiral spin density wave (S-SDW) or a stripe longitudinal SDW (LSDW) at small or large SOC strengths, respectively. The stripe-ordering wave vector is given by the nesting momentum of the two SOC-split Fermi surfaces with the same or opposite helicities at small or large SOC strengths, respectively. The LSDW is accompanied by a charge density wave (CDW) with half of its pitch. The transition from the paramagnet to the SSDW or LSDW+CDW is described by quantum Lifshitz-type actions, in sharp contrast to the Hertz-Millis types for itinerant electron systems without SOC. The collective excitations and Fermi surface reconstructions inside the SSDW and LSDW+CDW are also studied. The effects of a harmonic trap in cold-atom experiments are briefly discussed. In view of recent ground-breaking experimental advances in generating two-dimensional SOC in cold atoms, these phenomena can be observed in current or near-future cold-atom experiments even at very weak interactions. They may also be relevant to some itinerant magnetic materials with a strong SOC.
The microscopic mechanism of itinerant ferromagnetism is a long-standing problem due to the lack of non-perturbative methods to handle strong magnetic fluctuations of itinerant electrons. We have non-pertubatively studied thermodynamic properties and magnetic phase transitions of a two-dimensional multi-orbital Hubbard model exhibiting ferromagnetic ground states. Quantum Monte-Carlo simulations are employed, which are proved in a wide density region free of the sign problem usually suffered by simulations for fermions. Both Hund's coupling and electron itinerancy are essential for establishing the ferromagnetic coherence. No local magnetic moments exist in the system as a priori, nevertheless, the spin channel remains incoherent showing the Curie-Weiss type spin magnetic susceptibility down to very low temperatures at which the charge channel is already coherent exhibiting a weakly temperature-dependent compressibility. For the SU(2) invariant systems, the spin susceptibility further grows exponentially as approaching zero temperature in two dimensions. In the paramagnetic phase close to the Curie temperature, the momentum space Fermi distributions exhibit strong resemblance to those in the fully polarized state. The long-range ferromagnetic ordering appears when the symmetry is reduced to the Ising class, and the Curie temperature is accurately determined. These simulations provide helpful guidance to searching for novel ferromagnetic materials in both strongly correlated ddd-orbital transition metal oxide layers and the ppp-orbital ultra-cold atom optical lattice systems.
We investigate the magnetic order of a one-dimensional spin-1/2 fermion dynamical lattice, where itinerant fermions are coupled to bond-centered localized spins via an Ising-like spin dependent hopping. The model provides an anisotropic dynamical extension of conventional spin-1/2 fermion systems, in which the motion of itinerant fermions is directly modulated by the configuration of localized spins. Using density matrix renormalization group simulations, we map out the ground state phase diagram in various parameter spaces. Depending on the interplay among the hopping dependent on localized spins, the longitudinal field, and the external Zeeman field, two distinct phases are obtained: a paramagnetic phase and a spin-density-wave phase. Most notably, in the partially spin-polarized fermion phase, the spin-density wave ordering wave vector exhibits two distinct phenomena, corresponding respectively to the nesting vectors 2kF↑2k_{F\uparrow}2kF↑​ and 2kF↓2k_{F\downarrow}2kF↓​ of the spin-resolved Fermi surfaces. We further demonstrate that the two spin-density wave phases are robust against the repulsive Hubbard interaction between itinerant fermions. Our results reveal a novel route for tuning magnetic modulations in one-dimensional correlated systems and enrich the microscopic understanding of dynamical lattice magnetism.
The Landau theory of phase and phase transition, which describes the state of matter by the spontaneous symmetry breaking, and the Fermi liquid theory of interacting Fermi systems are the two corner stones of contemporary condensed matter physics. They act as our starting points to understand the structure, excitations and phase transitions of any condensed matter system. According to such a Landau paradigm, an interacting Fermi system will behave just as non-interacting Fermi gas system at sufficient low energy, if the interaction is not strong enough to induce a symmetry breaking phase transition in the system. In such a case, the perturbation expansion in the interaction strength is assumed to converge and the low energy excitation can be connected to that of a Fermi gas system adiabatically. In strongly correlated electron systems, such as the high temperature superconductors and quantum antiferromagnets, a pertubative picture on the interaction effect usually fails. The correlation effect between the electrons can induce new forms of order that are beyond the Landau symmetry breaking paradigm. Non-Fermi liquid behavior can emerge in the fully symmetric correlated phases. The Mott insulating phase and the quantum spin liquid phase are the most prominent example of such exotic state of matter. After about three decades of intensive studies, people find that the quantum non-locality effect is at the heart of such new forms of order. The quantum non-locality effect manifests itself in the emergence of gauge degree of freedom in the low energy physics of such strongly correlated system. Such emergent gauge filed is not only important for the characterization and classification of the ground state structure, but is also directly responsible for the non-Fermi liquid behavior of the system. The Landau paradigm should be extended to accommodate such new forms of order and the related new form of excitations and new universal class of phase transitions. Such an extension will elevate our understanding of the structure of matter to the level of quantum wave function. Unlike the conventional symmetry breaking order, which is characterized by the correlation functions between local physical observables, the new form of orders, which are commonly called quantum order (with the topological order as one of its typical example), can be better characterized by the entanglement property in the quantum wave function. From a mathematical point of view, the new form of order is closely related to the projective representation theory of the symmetry group, while the conventional symmetry breaking order is well described by the linear representation theory of the symmetry group.
Strongly interacting systems are known to often spontaneously develop exotic ground states under certain conditions. For instance, spin nematic phases have been discovered in various magnetic models. Such phases, which break spin symmetry but have no net local magnetization, have also been proposed by Nersesyan et al. [J. Phys.: Condens. Matter 3, 3353 (1991)] in the context of electronic models. We introduce a NNN-flavor microscopic model that interpolates from the large-NNN limit, where mean field is valid and such a nematic phase occurs, to the more realistic N=1N=1N=1 case. By using a sign-free quantum Monte Carlo, we show the existence of a spin nematic phase (analogous to a spin flux phase) for finite NNN; when NNN decreases, quantum fluctuations increase and this phase ultimately disappears in favor of an sss-wave superconducting state. We also show that this nematic phase extends up to a finite critical charge doping. Dynamical studies allow us to clarify the Fermi surface property: in the nematic phase at half-filling, it consists of four points and the low-energy structure has a Dirac conelike shape. Under doping, we observe clear signatures of Fermi pockets around these points. This is one of the few examples where numerical simulations show how quantum fluctuations can destroy a large-NNN phase.
We investigate the magnetic order and related strongly correlated effects in a one-dimensional Ising-Kondo lattice with transverse field. This model is the anisotropic limit of the conventional isotropic Kondo lattice model, in the sense that the itinerant electrons interact with the localized magnetic moments via only longitudinal Kondo exchange. Adopting the numerical density-matrix renormalization group method, we map out the ground-state phase diagram in various parameter spaces. Depending on the Kondo coupling and filling number, three distinct phases, including a metallic paramagnetic, a metallic ferromagnetic, and a gapped spin-density wave phase, are obtained. The spin-density wave is characterized by an ordering wave vector, which coincides with the nesting wave vector of the Fermi surface. This makes the corresponding magnetic transition a spin analog of the Peierls transition occurring in the one-dimensional metal. Moreover, by analyzing the momentum distribution function and charge correlation function, the conduction electrons are shown to behave like free spinless fermions in the ferromagnetic phase. We finally discuss the effect of the repulsive Hubbard interaction between conduction electrons. Our paper enriches the Kondo physics and deepens the current understanding of the heavy fermion compounds.