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arXiv:1910.14621 · Physical review. B./Physical review. B

Ferromagnetic fluctuations in the Rashba-Hubbard model

A. Greco, Matías Bejas, Andreas P. Schnyder

Published May 14, 2020• 13 citations
arXivHTMLPDF

Abstract

We study the occurrence and the origin of ferromagnetic fluctuations in the longitudinal spin susceptibility of the $t\ensuremath{-}{t}^{\ensuremath{'}}$-Rashba-Hubbard model on the square lattice. The combined effect of the second-neighbor hopping ${t}^{\ensuremath{'}}$ and the spin-orbit coupling leads to ferromagnetic fluctuations in a broad filling region. The spin-orbit coupling splits the energy bands, leading to two Van Hove fillings, where the sheets of the Fermi surface change their topology. Between these two Van Hove fillings the model shows ferromagnetic fluctuations. We find that these ferromagnetic fluctuations originate from interband contributions to the spin susceptibility. These interband contributions only arise if there is one holelike and one electronlike Fermi surface, which is the case for fillings in between the two Van Hove fillings. We discuss implications for experimental systems and propose a test on how to identify these types of ferromagnetic fluctuations in experiments.

DOI
10.1103/physrevb.101.174420

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We study the occurrence and the origin of ferromagnetic fluctuations in the longitudinal spin susceptibility of the t\ensuremath−t\ensuremath′t\ensuremath{-}{t}^{\ensuremath{'}}t\ensuremath−t\ensuremath′-Rashba-Hubbard model on the square lattice. The combined effect of the second-neighbor hopping t\ensuremath′{t}^{\ensuremath{'}}t\ensuremath′ and the spin-orbit coupling leads to ferromagnetic fluctuations in a broad filling region. The spin-orbit coupling splits the energy bands, leading to two Van Hove fillings, where the sheets of the Fermi surface change their topology. Between these two Van Hove fillings the model shows ferromagnetic fluctuations. We find that these ferromagnetic fluctuations originate from interband contributions to the spin susceptibility. These interband contributions only arise if there is one holelike and one electronlike Fermi surface, which is the case for fillings in between the two Van Hove fillings. We discuss implications for experimental systems and propose a test on how to identify these types of ferromagnetic fluctuations in experiments.
We consider the electronic and magnetic properties of the Hubbard model on a square lattice with the Fermi level near van Hove singularity and the ratio of the next-nearest-neighbor and nearest-neighbor hoppings t′/t=−0.45t'/t=-0.45t′/t=−0.45, which favours the ferromagnetic instability. We find, that a self-consistent consideration of the ferromagnetic fluctuations within the D-TRILEX approach results in the splitting of the electronic spectral function at low temperatures. This splitting exhibits only a weak momentum dependence, and only one of the split bands crosses the Fermi level. As a result, the Fermi surface itself remains unsplit, but its area increases, reflecting the presence of non-Fermi-liquid electronic excitations. We show that both the self-consistent account of the non-local contributions to the electronic self-energy and the proper treatment of electron interaction vertices in D-TRILEX are important to obtain this behaviour.
We investigate magnetic and superconducting instabilities of the two-dimensional $t\ensuremath{-}{t}^{\ensuremath{'}}$ Hubbard model on a square lattice at van Hove densities from weak to intermediate coupling by means of the two-particle self-consistent approach. We find that as the next-nearest-neighbor hopping $|{t}^{\ensuremath{'}}|$ increases from zero, the leading instability is towards an incommensurate spin-density wave whose wave vector moves slowly away from $(\ensuremath{\pi},\ensuremath{\pi}).$ For intermediate values of $|{t}^{\ensuremath{'}}|,$ the leading instability is towards ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-wave superconductivity. For larger $|{t}^{\ensuremath{'}}|>0.33t,$ there are signs of a crossover to ferromagnetism at extremely low temperatures. The suppression of the crossover temperature is driven by Kanamori screening that strongly renormalizes the effective interaction and also causes the crossover temperature to depend only weakly on ${t}^{\ensuremath{'}}.$ Electronic self-energy effects for large $|{t}^{\ensuremath{'}}|$ lead to considerable reduction of the zero-energy single-particle spectral weight beginning at temperatures as high as $T\ensuremath{\lesssim}0.1t,$ an effect that may be detrimental to the existence of a ferromagnetic ground state at weak coupling.
We study the magnetic properties of the two-dimensional Hubbard model with nearest-neighbor (t) and next-nearest-neighbor (t2{t}_{2}t2​) hopping and on-site repulsion U. We first calculate the mean-field phase diagram as a function of band filling and U. Because of the Van Hove singularity in the density of states, we find a ferromagnetic phase extending to zero U for certain band filling. For the half-filled band case, antiferromagnetism sets in at a finite value of U if t2{t}_{2}t2​\ensuremath{\ne}0. We study the behavior of spin-spin correlation functions for small lattices of up to N=64 atoms using Monte Carlo simulations, as well as exact diagonalization for N=4. Our results show enhanced ferromagnetic correlations in some regions, but apparently no ferromagnetic long-range order. In the half-filled case, our numerical results are consistent with a nonzero critical U. For a non-half-filled band our results suggest that there is no long-range order.
Abstract We investigate magnetic correlation in the triangular lattice Hubbard model using determinant quantum Monte Carlo simulations. Focusing on the role of next-nearest-neighbor hopping t ′ and electron filling 〈 n 〉, we demonstrate that regions of high density of states, particularly near van Hove singularity (VHS) points, significantly enhance short-range ferromagnetic correlations as measured by the uniform spin susceptibility χ (Γ). Specifically, χ (Γ), quantifying ferromagnetic fluctuations, is amplified at fillings corresponding to the VHS for a given t ′ . Increasing the on-site Coulomb repulsion U further strengthens these ferromagnetic correlations, with a more pronounced effect at lower temperatures, and the observed ferromagnetic correlations are found to be short-ranged. Conversely, near half-filling 〈 n 〉 = 1.0, larger t ′ values promote antiferromagnetic (AFM) fluctuations, evidenced by an increase in χ ( K ). Our results reveal that t ′ and filling act as effective tuning parameters for manipulating the competition between ferromagnetic and AFM fluctuations in the triangular lattice.
We study the two-dimensional Hubbard model with the Rashba type spin-orbit coupling within and beyond the mean-field theory. The antiferromagnetic ground state for the model at half-filling and the Cooper pairing induced by antiferromagnetic spin fluctuations near half-filling are examined based on the random-phase approximation. We show that the antiferromagnetic order is suppressed and the magnetic susceptibility turns out to be anisotropic in the presence of the spin-orbit coupling. Energy spectrums of transverse spin fluctuations are obtained and the effective interactions between holes mediated by antiferromagnetic spin fluctuations are deduced in the case of low hole doping. It seems that the spin-orbit coupling tends to form s+p-wave Cooper pairs, while the s+d-wave pairing is dominant when the spin-orbit coupling is absent.
The Rashba-Hubbard model on the square lattice is the paradigmatic case for studying the effect of spin-orbit coupling, which breaks spin and inversion symmetry, in a correlated electron system. We employ a truncated-unity variant of the functional renormalization group which allows us to analyze magnetic and superconducting instabilities on equal footing. We derive phase diagrams depending on the strengths of Rasbha spin-orbit coupling, real second-neighbor hopping, and electron filling. We find commensurate and incommensurate magnetic phases which compete with ddd-wave superconductivity. Due to the breaking of inversion symmetry, singlet and triplet components mix; we quantify the mixing of ddd-wave singlet pairing with fff-wave triplet pairing.