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arXiv:1101.5301 · Physical Review B

Magnetic excitations in one-dimensional spin-orbital models

Alexander Herzog, Peter Horsch, Andrzej M. Oleś, Jesko Sirker

Published Jun 28, 2011• 16 citations
arXivHTMLPDF

Abstract

We study the dynamics and thermodynamics of one-dimensional spin-orbital models relevant for transition-metal oxides. We show that collective spin, orbital, and combined spin-orbital excitations with infinite lifetime can exist, if the ground state of both sectors is ferromagnetic. Our main focus is the case of effectively ferromagnetic (antiferromagnetic) exchange for the spin (orbital) sector, and we investigate the renormalization of spin excitations via spin-orbital fluctuations using a boson-fermion representation. We contrast a mean-field decoupling approach with results obtained by treating the spin-orbital coupling perturbatively. Within the latter self-consistent approach we find a significant increase of the linewidth and additional structures in the dynamical spin structure factor as well as Kohn anomalies in the spin-wave dispersion caused by the scattering of spin excitations from orbital fluctuations. Finally, we analyze the specific heat $c(T)$ by comparing a numerical solution of the model obtained by the density-matrix renormalization group with perturbative results. At low temperatures $T$ we find numerically $c(T)~T$ pointing to a low-energy effective theory with dynamical critical exponent $z=1$.

DOI
10.1103/physrevb.83.245130

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We study the dynamics and thermodynamics of one-dimensional spin-orbital models relevant for transition-metal oxides. We show that collective spin, orbital, and combined spin-orbital excitations with infinite lifetime can exist, if the ground state of both sectors is ferromagnetic. Our main focus is the case of effectively ferromagnetic (antiferromagnetic) exchange for the spin (orbital) sector, and we investigate the renormalization of spin excitations via spin-orbital fluctuations using a boson-fermion representation. We contrast a mean-field decoupling approach with results obtained by treating the spin-orbital coupling perturbatively. Within the latter self-consistent approach we find a significant increase of the linewidth and additional structures in the dynamical spin structure factor as well as Kohn anomalies in the spin-wave dispersion caused by the scattering of spin excitations from orbital fluctuations. Finally, we analyze the specific heat c(T)c(T)c(T) by comparing a numerical solution of the model obtained by the density-matrix renormalization group with perturbative results. At low temperatures TTT we find numerically c(T) Tc(T)~Tc(T) T pointing to a low-energy effective theory with dynamical critical exponent z=1z=1z=1.
We investigate the spin and orbital correlations of a superexchange model with spin S=1S=1S=1 and orbital L=1L=1L=1 relevant for 5d45{d}^{4}5d4 transition-metal Mott insulators [O. N. Meetei et al., Phys. Rev. B 91, 054412 (2015)], using exact diagonalization and density matrix renormalization group (DMRG). For spin-orbit coupling $\ensuremath{\lambda}=0$, the orbitals are in an entangled state that is decoupled from the spins. We find two phases with increasing $\ensuremath{\lambda}$: (I) the S2S2S2 phase with two peaks in the structure factor for $\ensuremath{\lambda}\ensuremath{\le}{\ensuremath{\lambda}}_{c1}\ensuremath{\approx}0.34J$ where JJJ is the ferromagnetic exchange; and, (II) the S1S1S1 phase for ${\ensuremath{\lambda}}_{c1}<\ensuremath{\lambda}\ensuremath{\le}{\ensuremath{\lambda}}_{c2}\ensuremath{\approx}1.2J$ with emergent antiferromagnetic correlations. Both S1S1S1 and S2S2S2 phases are shown to exhibit power-law correlations, indicative of a gapless spectrum. Upon increasing $\ensuremath{\lambda}>{\ensuremath{\lambda}}_{c2}$ leads to a product state of local spin-orbital singlets that exhibit exponential decay of correlations, indicative of a gapped phase. We obtain insights into the phases from the well-known Uimin-Lai-Sutherland model in an external field that provides an approximate description of our model within mean-field theory.
We present a comprehensive study of the spin excitations---as measured by the dynamical spin structure factor $S(q,\ensuremath{\omega})$---of the so-called block-magnetic state of low-dimensional orbital-selective Mott insulators. We realize this state via both a multi-orbital Hubbard model and a generalized Kondo-Heisenberg Hamiltonian. Due to various competing energy scales present in the models, the system develops periodic ferromagnetic islands of various shapes and sizes, which are antiferromagnetically coupled. The $2\ifmmode\times\else\texttimes\fi{}2$ particular case was already found experimentally in the ladder material BaFe2Se3\mathrm{Ba}{\mathrm{Fe}}_{2}{\mathrm{Se}}_{3}BaFe2​Se3​ that becomes superconducting under pressure. Here we discuss the electronic density as well as Hubbard and Hund coupling dependence of $S(q,\ensuremath{\omega})$ using density matrix renormalization group method. Several interesting features were identified: (1) An acoustic (dispersive spin-wave) mode develops. (2) The spin-wave bandwidth establishes a new energy scale that is strongly dependent on the size of the magnetic island and becomes abnormally small for large clusters. (3) Optical (dispersionless spin excitation) modes are present for all block states studied here. In addition, a variety of phenomenological spin Hamiltonians have been investigated but none matches entirely our results that were obtained primarily at intermediate Hubbard UUU strengths. Our comprehensive analysis provides theoretical guidance and motivation to crystal growers to search for appropriate candidate materials to realize the block states, and to neutron scattering experimentalists to confirm the exotic dynamical magnetic properties unveiled here, with a rich mixture of acoustic and optical features.
This work deals with the calculation of magnetic properties for strongly correlated electron systems. One of most important model in this field of physics is the Hubbard model. It describes the situation of, for example, transition metal oxides. This particular class of materials is known for magnetic order at low temperatures. The reason for this and at the same time the difficulty for theoretically describing them are strong electron-electron-interactions. For calculating the magnetic properties I used the dynamical mean field theory (DMFT), which relates the lattice model to an impurity model. Even this simplified model is highly non trivial. For solving it I used two different renormalization group approaches. I used the numerical renormalization group (NRG) and the density matrix renormalization group (DMRG) and also compared both methods with each other. These modern non-perturbative techniques are able to solve the impurity model, which then can be used for calculating the magnetic phases of the lattice models. In this work I mainly focused on the frustrated one-orbital Hubbard model and the two-orbital Hubbard model. Frustration represents a situation where the aimed magnetic solution cannot be stabilized for the used lattice. Frustration can, for example, be generated by long range hopping of the electrons. This can lead to a situation where new magnetic phases are stable. For systematically analyzing the effects of frustration, I performed calculations for a Bethe lattice with nearest and next nearest neighbor hopping, for which I varied the strength of the interaction and the next nearest neighbor hopping. Another very important aspect for describing transition metal oxides are orbital degrees of freedom. For analyzing the influence of these degrees of freedom I used the two-orbital Hubbard model, which shows new effects.
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This thesis describes the neutron scattering measurements of magnetic excitations in \nspin-chains and ladders. The first part discusses an experimental investigation of the copper oxide family Srâ â Cuâ â Oâ â composed of edge-sharing chains and spin-ladders. \nThe study of Laâ Srâ â Cuâ â Oâ â comprises a slightly hole-doped chain and an undoped ladder structure where the chain can be modeled by a ferromagnetic nearest and an \nantiferromagnetic next-nearest neighbor coupling. The hole effects are apparent in gaps in the dispersion relation and can be described by a charge-density wave agreeing with the commensuration of the dispersion. Investigating the undoped ladder establishes \nthe exchange constants including a cyclic exchange manifested by the two-magnon \ncontinuum and the suppression of the S = 1 bound mode. An orbital consideration \nprovides an explanation for the exchanges including the different sizes of rung and \nleg coupling. The excitation spectrum of the doped ladder in Caâ .â Srâ â .â Cuâ â Oâ â can be \ndescribed by a direct comparison with the undoped ladder and the differences consisting \nof a higher energy mode and subgap scattering can be successfully modeled by the charge spectrum of the ladder calculated from the free electron model. The second part of the thesis investigates the alternating chain material Cu(NOâ )â · 2.5D2O and establishes the gapped one-magnon dispersion, the two-magnon continuum and for the first time the S =1 bound mode. Applying magnetic field drives the system through two critical field transitions, condensation of magnons into the ground state and saturation. The modes beyond saturation can be modeled by spin wave theory and the excitations at the first critical field follow Luttinger Liquid behavior. Additionally investigated are the temperature effects with the excitations being of a different nature but containing the signature of a strong correlated system. For an outlook the measurements including temperature and field are provided with further theoretical descriptions necessary.
We investigate ground-state properties of a one-dimensional S=1 spin-orbital model with or without uniaxial single-ion anisotropy. By means of the density matrix renormalization group method, we compute the ground-state energy, the magnetization curves and the correlation functions. We discuss how the ground-state properties depend on the two exchange couplings for orbital and spin sectors. The phase diagram obtained is compared with that for the S=1/2 model. We also address the effect of uniaxial single-ion anisotropy.