Microscopic origin and causal role of the magnetic anomalies accompanying the disappearance of superconductivity in overdoped La$_{2-x}$Sr$_x$CuO$_4$

In La$_{2-x}$Sr$_x$CuO$_4$ (LSCO), superconductivity appears upon hole doping, peaks near $x\approx0.15$, and is lost again for $x\gtrsim0.26$. Torrance and co-workers [Phys. Rev. B 40, 8872 (1989)] showed that, across this overdoped region, the lattice constants and normal-state resistivity evolve monotonically while two magnetic anomalies occur near $x\approx0.25$: the spin susceptibility $\chi_{\rm spin}$ passes through a maximum as a function of doping, and the temperature $T_{\max}$ of the broad maximum of $\chi(T)$ falls to zero. The unresolved problem is to give a definitive microscopic account of this overdoped-side magnetism — the $\chi_{\rm spin}(x)$ peak, the collapse of $T_{\max}(x)$, and the Curie–Weiss-like low-temperature component of $\chi(T)$ — and to establish whether and how these magnetic changes are causally connected to the death of superconductivity, within a quantitative theory consistent with the smooth transport and lattice trends. Later neutron-scattering, nuclear magnetic/quadrupole resonance (NMR/NQR), muon-spin-relaxation, and magnetization work has sharpened the phenomenology (localized-moment loss with charge delocalization, an inhomogeneous shrinking volume fraction of antiferromagnetic correlations, dilute static moments and ferromagnetic fluctuations in the heavily overdoped nonsuperconducting material) and partial theories exist, but no accepted microscopic mechanism or causal verdict exists, so the problem remains open.

Background

La$_{2-x}$Sr$_x$CuO$_4$ is the archetypal single-layer cuprate superconductor: Sr$^{2+}$ substitution for La$^{3+}$ removes one electron per Cu site and injects holes $p$ (the $[\mathrm{CuO}_2]^{p-2}$ sheet charge) into the CuO$_2$ planes, whose parent compound La$_2$CuO$_4$ is a quasi-two-dimensional antiferromagnetic (AF) Mott insulator — an insulator whose gap arises from electron–electron repulsion rather than from filled bands — with an in-plane superexchange coupling $J\sim1000$–$1500$ K (the antiferromagnetic interaction between neighboring Cu spins, mediated by the intervening oxygen ions). With doping, three-dimensional antiferromagnetism gives way to a superconducting 'dome': the superconducting transition temperature $T_c$ rises to $\approx36$ K near $x\approx0.15$ and falls again, with bulk superconductivity absent for $x\gtrsim0.26$.

In a quasi-two-dimensional $S=1/2$ Heisenberg antiferromagnet, the uniform spin susceptibility $\chi(T)$ exhibits a broad maximum at a temperature $T_{\max}$ that scales with $J$ (Torrance et al. used $k_BT_{\max}\approx0.95J$). The 'spin susceptibility' $\chi_{\rm spin}$ quoted below is the measured molar susceptibility after subtracting core diamagnetism and other ionic contributions; a 'Curie–Weiss component' means a contribution of the form $C/(T-\theta)$ characteristic of localized moments with a Curie constant $C$ and Weiss temperature $\theta$.

Torrance, Bezinge, Nazzal, Huang, Parkin, Keane, LaPlaca, Horn, and Held [Phys. Rev. B 40, 8872 (1989)] prepared vacancy-free samples (annealed under 100-bar oxygen) up to $x\approx0.36$ and measured lattice constants, the tetragonal-to-orthorhombic transition temperature $T_s$ (the structural phase transition below which the crystal lattice distorts), resistivity, and $\chi(T)$. They found: (i) the in-plane lattice constant and room-temperature conductivity evolve monotonically with $x$, so no large-scale electronic restructuring accompanies the loss of superconductivity; (ii) $T_s$ vanishes near $x\approx0.19$ while superconductivity survives to $x\approx0.25$, so the structural transition is unrelated to the superconducting cutoff; (iii) $\chi_{\rm spin}$ rises with doping to a maximum near $x\sim0.25$ and then decreases, while $T_{\max}$ falls from $\approx390$ K at $x=0.15$ to $\approx0$ for $x\geq0.25$; (iv) an analysis of $\chi_{\rm spin}$ at high temperature within the two-dimensional Heisenberg model gives an effective $J\approx650$–$900$ K, weakened by roughly 40% from the undoped value. The paper noted that the vanishing of $T_{\max}$ could reflect either a true collapse of the in-plane exchange $J$ or a loss of localized Cu$^{2+}$ moments as the doped holes delocalize, and left open whether the coincidence of the magnetic changes with the superconducting cutoff is causal, consequential, or accidental.

Later work built directly on this core. NQR (nuclear quadrupole resonance, a zero-field magnetic-resonance probe of the Cu site) showed AF correlations persisting into the overdoped superconductor [Ohsugi et al., Physica B 186-188, 1027 (1993)]. Nakano et al. [J. Low Temp. Phys. 105, 395 (1996)] found the effective Cu moment progressively suppressed for $x\gtrsim0.15$ from deteriorating localization of Cu $3d$ electrons, with a growing density of states at the Fermi level. Inelastic neutron scattering showed that the low-energy incommensurate spin excitations (peaks of the dissipative dynamic spin susceptibility $\chi''(\omega)$ shifted off the AF wavevector) weaken with overdoping and vanish at $x=0.30$ where bulk superconductivity is gone [Wakimoto et al., Phys. Rev. Lett. 92, 217004 (2004)], while intermediate-energy (20–100 meV) magnetic scattering also decreases with overdoping in a way that does not follow Fermi-surface nesting (the enhancement of magnetic response expected when parallel portions of the Fermi surface span the antiferromagnetic wavevector) but suggests a shrinking volume fraction of fluctuating AF 'bubbles' [Wakimoto et al., Phys. Rev. Lett. 98, 247003 (2007)]. Muon spin relaxation (muSR, which detects static or quasi-static local fields via implanted positive muons) found dilute static electronic moments appearing at low temperature in the heavily overdoped nonsuperconducting material, without long-range commensurate order [MacDougall et al., Physica B 374-375, 211 (2006); Sonier et al., PNAS 107, 17131 (2010)], and magnetization/high-field measurements together with resistivity power laws indicate ferromagnetic fluctuations in heavily overdoped LSCO [Adachi et al., Materials 16, 7048 (2023)]. On the theory side, a van Hove singularity (a peak in the electronic density of states caused by a saddle point of the energy dispersion) in the lower Hubbard band of the two-dimensional Hubbard model (the canonical lattice model of correlated electrons with on-site repulsion) has been proposed to explain the thermodynamic anomaly near $x\approx0.25$ [Avella et al., Solid State Commun. 108, 723 (1998)], and electronic-structure calculations find that the on-site Coulomb repulsion enhances ferromagnetic fluctuations at heavy overdoping [Teranishi et al., J. Phys. Soc. Jpn. 90, 094707 (2021)]. None of these constitutes a quantitative, unified microscopic account.

Problem Statement

Establish a definitive microscopic account of the overdoped-side magnetic anomalies of La$_{2-x}$Sr$_x$CuO$_4$ (LSCO, where $x$ is the Sr substitution fraction, i.e. the nominal hole-doping level) and of their relation to the disappearance of superconductivity. Specifically: (1) determine the microscopic origin of the observed behavior of the uniform spin susceptibility — the molar susceptibility $\chi_{\rm spin}$ measured after subtracting core-diamagnetic and other ionic contributions, whose doping dependence $\chi_{\rm spin}(x)$ is nonmonotonic with its maximum near $x\approx0.25$, the fall of the temperature $T_{\max}$ of the broad susceptibility maximum to zero near $x\approx0.25$ (which Torrance, Bezinge, Nazzal, Huang, Parkin, Keane, LaPlaca, Horn, and Held [Phys. Rev. B 40, 8872 (1989)] discussed either as a collapse of the in-plane exchange coupling $J$ or as a loss of localized Cu$^{2+}$ moments due to charge delocalization), and the Curie–Weiss-like low-temperature component and broadening/shifting of the $\chi(T)$ maximum; (2) establish whether the magnetic changes cause the loss of superconductivity for $x\gtrsim0.26$, are a consequence of the same underlying electronic evolution, or are independent — going beyond the compositional coincidence observed in the measurements of Torrance et al.; and (3) provide a quantitative microscopic theory consistent with the monotonic lattice-constant and normal-state resistivity trends across the same doping range, i.e. an account of the full overdoped phenomenology (nonmonotonic $T_c(x)$, smooth transport and structure, and the magnetic anomalies). These three items are jointly posed and concern a single account: item (1) is the magnetic content of the quantitative theory called for in (3), not an independent task. Chemical confounds noted by Torrance et al., such as oxygen nonstoichiometry (including nonstandard peroxide incorporation that contributes to the hole count $p$ inferred from iodometric chemical titration without actually doping the CuO$_2$ sheets) and nanoscale inhomogeneity, are part of the question to the extent that they must be excluded or incorporated in the answer.

References

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