arXiv:cond-mat/0403165 · Physical Review B

Crossover to non-Fermi-liquid spin dynamics in cuprates

J. Bonča, Peter Prelovšek, Igor Sega

Published Dec 6, 2004• 4 citations

Abstract

The antiferromagnetic spin correlation function ${S}_{\mathbf{Q}}$, the staggered spin susceptibility ${\ensuremath{\chi}}_{\mathbf{Q}}$, and the energy scale ${\ensuremath{\omega}}_{FL}={S}_{\mathbf{Q}}∕{\ensuremath{\chi}}_{\mathbf{Q}}$ are studied numerically within the $t\text{\ensuremath{-}}J$ model and the Hubbard model, as relevant to cuprates. It is shown that ${\ensuremath{\omega}}_{FL}$, related to the onset of the non-Fermi-liquid spin response at $T>{\ensuremath{\omega}}_{FL}$, is very low in the regime below the ``optimum'' hole doping ${c}_{h}<{c}_{h}^{*}\ensuremath{\sim}0.16$, while it shows a steep increase in the overdoped regime. A quantitative analysis of the NMR spin-spin relaxation rate $1∕{T}_{2G}$ for various cuprates reveals a similar behavior, indicating a pronounced crossover between a Fermi-liquid and a non-Fermi-liquid behavior as a function of doping.

DOI: 10.1103/physrevb.70.224505

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arXiv:cond-mat/0403165 · Physical Review B

Crossover to non-Fermi-liquid spin dynamics in cuprates

J. Bonča, Peter Prelovšek, Igor Sega

Published Dec 6, 2004• 4 citations

arXiv HTML PDF

Abstract

The antiferromagnetic spin correlation function

{S}_{\mathbf{Q}}

, the staggered spin susceptibility

{\ensuremath{\chi}}_{\mathbf{Q}}

, and the energy scale

{\ensuremath{\omega}}_{FL}={S}_{\mathbf{Q}}∕{\ensuremath{\chi}}_{\mathbf{Q}}

are studied numerically within the

t\text{\ensuremath{-}}J

model and the Hubbard model, as relevant to cuprates. It is shown that

{\ensuremath{\omega}}_{FL}

, related to the onset of the non-Fermi-liquid spin response at

T>{\ensuremath{\omega}}_{FL}

, is very low in the regime below the ``optimum'' hole doping

{c}_{h}<{c}_{h}^{*}\ensuremath{\sim}0.16

, while it shows a steep increase in the overdoped regime. A quantitative analysis of the NMR spin-spin relaxation rate

1∕{T}_{2G}

for various cuprates reveals a similar behavior, indicating a pronounced crossover between a Fermi-liquid and a non-Fermi-liquid behavior as a function of doping.

DOI: 10.1103/physrevb.70.224505

Related papers

Non-Fermi-liquid regime of a doped Mott insulator

Olivier Parcollet, Antoine Georges

We study the doping of a Mott insulator in the presence of quenched frustrating disorder in the magnitude and sign of the magnetic exchange. Two quite different doping regimes $\ensuremath{\delta}<{\ensuremath{\delta}}^{*}$ and $\ensuremath{\delta}>{\ensuremath{\delta}}^{*}$ are found, with ${\ensuremath{\delta}}^{*}\ensuremath{\simeq}J/t (J$ is the characteristic magnitude of the exchange, and t the hopping amplitude). In the high-doping regime, a (Brinkman-Rice) Fermi-liquid description applies with a coherence scale of order $\ensuremath{\delta}t.$ In the low-doping regime, local magnetic correlations strongly affect the formation of quasiparticles, resulting in a very low coherence scale ${\ensuremath{\epsilon}}_{F}^{*}\ensuremath{\simeq}J(\ensuremath{\delta}/{\ensuremath{\delta}}^{*}{)}^{2}.$ Fermi-liquid behavior does apply below ${\ensuremath{\epsilon}}_{F}^{*},$ but a ``quantum-critical regime'' ${\ensuremath{\epsilon}}_{F}^{*}<T<J$ holds, in which marginal Fermi-liquid behavior of several physical properties is found: NMR relaxation time ${1/T}_{1}\ensuremath{\sim}\mathrm{const},$ resistivity ${\ensuremath{\rho}}_{\mathrm{dc}}(T)\ensuremath{\propto}T,$ optical lifetime ${\ensuremath{\tau}}_{\mathrm{opt}}^{\ensuremath{-}1}\ensuremath{\propto}\ensuremath{\omega}/\mathrm{ln}(\ensuremath{\omega}/{\ensuremath{\epsilon}}_{F}^{*})$ together with $\ensuremath{\omega}/T$ scaling of response functions, e.g., $J{\ensuremath{\sum}}_{\stackrel{\ensuremath{\rightarrow}}{q}}{\ensuremath{\chi}}^{\ensuremath{''}}(\stackrel{\ensuremath{\rightarrow}}{q},\ensuremath{\omega})\ensuremath{\propto}\mathrm{tanh}(\ensuremath{\omega}/2T).$ In contrast, single-electron properties display stronger deviations from Fermi-liquid theory in this regime with a $\sqrt{\ensuremath{\omega}}$ dependence of the inverse single-particle lifetime and a $1/\sqrt{\ensuremath{\omega}}$ decay of the photoemission intensity. 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arXiv:2605.15059May 14, 20260 citations

The antiferromagnetic spin correlation function

{S}_{\mathbf{Q}}

, the staggered spin susceptibility

{\ensuremath{\chi}}_{\mathbf{Q}}

, and the energy scale

{\ensuremath{\omega}}_{FL}={S}_{\mathbf{Q}}∕{\ensuremath{\chi}}_{\mathbf{Q}}

are studied numerically within the

t\text{\ensuremath{-}}J

model and the Hubbard model, as relevant to cuprates. It is shown that

{\ensuremath{\omega}}_{FL}

, related to the onset of the non-Fermi-liquid spin response at

T>{\ensuremath{\omega}}_{FL}

, is very low in the regime below the ``optimum'' hole doping

{c}_{h}<{c}_{h}^{*}\ensuremath{\sim}0.16

, while it shows a steep increase in the overdoped regime. A quantitative analysis of the NMR spin-spin relaxation rate

1∕{T}_{2G}

for various cuprates reveals a similar behavior, indicating a pronounced crossover between a Fermi-liquid and a non-Fermi-liquid behavior as a function of doping.

T<J

, low-frequency and static susceptibilities show a pronounced

T

dependence, supporting a scenario related to the marginal Fermi liquid one, for the explanation of neutron-scattering and NMR relaxation experiments in cuprates. Calculated NMR relaxation rates reasonably reproduce experimental ones.

{\mathit{T}}_{2\mathrm{G}}

, in

{\mathrm{La}}_{2}

{\mathrm{CuO}}_{4}

, and provide qualitative understanding of both 1/

{\mathit{T}}_{1}

and 1/

{\mathit{T}}_{2\mathrm{G}}

nuclear relaxation rates in doped cuprates.

q

-vector and bosonic frequency contributions in the spin channel. Within this framework we find that the key contributions to the single-particle self-energy that give non-Fermi-liquid character show complicated dependence on zero, positive, and negative frequency bosonic modes. We find that for a nominal choice of ${t}^{\ensuremath{'}}$ that electron- and hole-doped systems with similar Fermi-liquid character have distinct spin and charge susceptibility and distinct spin-fluctuation diagnostics spectra.

U=7t

and

t'=-0.3t

, we find a critical doping

p^{\ast}

that marks a continuous quantum phase transition between a pseudogap metal and a normal Fermi liquid. The transition is identified by a continuous collapse, from both sides, of the Fermi-liquid scale extracted from charge, spin, and

d_{x^2-y^2}

-wave pairing susceptibilities. This collapse produces a non-Fermi-liquid regime at intermediate energy scales, which appears to extend to arbitrarily low scales at

p^{\ast}

. As

p^{\ast}

is crossed from the normal Fermi liquid at

p>p^{\ast}

into the pseudogap metal at $p