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arXiv:1201.5503 · Physical Review B

Impact of the Dzyaloshinskii-Moriya interaction in strongly correlated itinerant systems

Sergej Schuwalow, Christoph Piefke, Frank Lechermann

Published May 22, 2012• 6 citations
arXivHTMLPDF

Abstract

Spin-only approaches to anisotropic effects in strongly interacting materials are often insufficient for systems close to the Mott regime. Within a model context, here the consequences of the low-symmetry relevant Dzyaloshinskii-Moriya (DM) interaction are studied for strongly correlated, but overall itinerant, systems. Namely, we investigate the Hubbard bilayer model supplemented by a DM term at half filling and in the hole-doped regime. As an add-on, further results for the two-impurity Anderson model with DM interaction are also provided. The model Hamiltonians are treated by means of the rotational invariant slave boson technique at the saddle point within a (cellular) cluster approach. Already small values of the anisotropic interaction prove to have a strong influence on the phases and correlation functions with increasing $U$. An intriguing metallic spin-flop phase is found in the doped bilayer model, and a reduction of the Ruderman-Kittel-Kasuya-Yosida exchange is found in the two-impurity model.

DOI
10.1103/physrevb.85.205132

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Spin-only approaches to anisotropic effects in strongly interacting materials are often insufficient for systems close to the Mott regime. Within a model context, here the consequences of the low-symmetry relevant Dzyaloshinskii-Moriya (DM) interaction are studied for strongly correlated, but overall itinerant, systems. Namely, we investigate the Hubbard bilayer model supplemented by a DM term at half filling and in the hole-doped regime. As an add-on, further results for the two-impurity Anderson model with DM interaction are also provided. The model Hamiltonians are treated by means of the rotational invariant slave boson technique at the saddle point within a (cellular) cluster approach. Already small values of the anisotropic interaction prove to have a strong influence on the phases and correlation functions with increasing UUU. An intriguing metallic spin-flop phase is found in the doped bilayer model, and a reduction of the Ruderman-Kittel-Kasuya-Yosida exchange is found in the two-impurity model.
We examine the influence of an anisotropic interaction term of Dzyaloshinskii - Moriya (DM) type on the ground state ordering of the - spin- Heisenberg antiferromagnet on the square lattice. For the DM term we consider several symmetries corresponding to different crystal structures. For the pure - model there are strong indications for a quantum spin liquid in the region of . We find that a DM interaction influences the breakdown of the conventional antiferromagnetic order by (i) shifting the spin-liquid region, (ii) changing the isotropic character of the ground state towards anisotropic correlations and (iii) creating for certain symmetries a net ferromagnetic moment.
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We describe a new microscopic approach for analyzing interacting electron systems with local moments or, in principle, any local order parameter. We specialize attention to the doped Mott insulator phase of the Hubbard model, where standard weak-coupling perturbation methods fail. A rotationally invariant Stratonovich-Hubbard field is introduced to decouple the static spin components of the interaction at each site. Charge degrees of freedom are then treated by ``slave'' Hartree-Fock in the presence of a spatially varying random spin field. The effective action reduces to a classical Heisenberg model at half filling, insuring that the system has (i) finite-range order at T>0 with an exponentially diverging correlation length and (ii) a one-electron Mott-Hubbard gap in the presence of disorder. Away from half-filling properties are determined by strongly non-Gaussian fluctuations in the amplitude and orientation of the local spin fields. The saddle point equations of the theory at zero temperature reduce to inhomogeneous Hartree-Fock, so that disordering of domain walls at finite temperature is in principle included. We present preliminary small system results for the intermediate and large interaction regimes obtained by Monte Carlo simulation of random spin field configurations.
A one-dimensional model Hamiltonian that is motivated by the recent discovery of the heavy-fermion behavior in the cuprates of the Nd2{\mathrm{Nd}}_{2}Nd2​CuO4{\mathrm{O}}_{4}O4​ type is studied. It consists of $t\ensuremath{-}J$ interacting conduction electrons coupled to a lattice of localized spins through a Kondo exchange term JK{J}_{K}JK​. Exact diagonalization and density-matrix renormalization-group methods are used. The latter method is generalized to arbitrary densities. At half filling, a spin gap opens for all JK>0{J}_{K}>0JK​>0. Away from half filling it is shown that, at strong JK{J}_{K}JK​, the ground state is an unsaturated ferromagnet. At weak JK{J}_{K}JK​ the system is in a paramagnetic phase with enhanced Ruderman-Kittel-Kasuya-Yosida (RKKY) correlations. The importance of self-screening of the local moments in the depletion regime is discussed. We argue that these findings transcend the specifics of the model.
We derive the disorder vs doping phase diagram of the doped Hubbard model via dynamical mean-field theory combined with typical medium theory, which allows the description of both Mott (correlation driven) and Anderson (disorder driven) metal-insulator transitions. We observe a transition from a metal to an Anderson-Mott insulator for increasing disorder strength at all interactions. In the weak correlation regime and rather small doping, the Anderson-Mott insulator displays properties which are similar to the ones found at half filling. In particular, this phase is characterized by the presence of empty sites. If we further increase either the doping or the correlation, however, an Anderson-Mott phase of a different kind arises for sharply weaker disorder strength. This phase occupies the largest part of the phase diagram in the strong-correlation regime and is characterized by the absence of the empty sites.
The effects of the Dzyaloshinski—Moriya (DM) interaction on the ground-state properties of the anisotropic XY chain in a transverse field have been studied by means of correlation functions and entanglement. Different from the case without the DM interaction, the excitation spectra ∊ k of this model are not symmetrical in the momentum space and are not always positive. As a result, besides the ferromagnetic (FM) and the paramagnetic (PM) phases, a gapless chiral phase is induced. In the chiral phase, the von Neumann entropy is proportional to log 2 L ( L is the length of a subchain) with the coefficient A ≈ 1/3, which is the same as that of the XY chain in a transverse field without the DM interaction for γ = 0 and 0 < h ≤ 1. And in the vicinity of the critical point between the chiral phase and the FM (or PM) phase, the behaviors of the nearest-neighbor concurrence and its derivative are like those for the anisotropy transition.