In the high-T_c cuprate superconductivity, the relationship between antiferromagnetic (AF) spin fluctuations and superconductivity has been extensively studied. It has been suggested that low-energy AF fluctuations disappear concomitant with the suppression of superconductivity in the overdoped regime.¹⁾ On the other hand, resonant inelastic X-ray scattering has revealed robust AF fluctuations in the non-superconducting heavily overdoped (HOD) regime.²⁾

 It has been proposed that ferromagnetic (FM) fluctuations exist and are related to the suppression of superconductivity in the HOD regime of high-T_c cuprates.^3,4) There are two candidates for the origin of FM fluctuations. One is itinerant electron ferromagnetism due to enhanced spin susceptibility at q ~ (0, 0) and large density of states at the Fermi level.^5,6) The other is the double exchange interaction due to the multiband nature of the Cu3d_x2-y2 and Cu3d_3z2-r2 orbitals suggested by the Compton scattering.⁷⁾

 Our former studies of the overdoped and HOD Bi-2201 cuprates revealed that FM fluctuations exist and were enhanced by the Fe-substitution.^8,9) To further understand the details of FM fluctuations, we performed muon-spin-relaxation (μSR) measurements of Fe-substituted Bi-2201.

 Figure (a) shows zero-field μSR time spectra of 9.6% Fe-substituted Bi_1.74Pb_0.38Sr_1.88Cu_1-yFe_yO_6+δ with y = 0.096 in the HOD regime. It is found that fast relaxation and muon-spin precession are observed at 4.1 K, suggesting the formation of a long-range magnetic order. Figure (b) shows the temperatures dependence of the relaxation rate of muon spins λ in HOD Bi_1.74Pb_0.38Sr_1.88Cu_1-yFe_yO_6+δ with y = 0, 0.05, 0.096. It is found that λ is enhanced and exhibits a peak at low temperatures for the Fe-substituted samples. The peak temperature below which the spin-glass state is formed increases with Fe substitution.

 For y = 0.096, the internal magnetic field at the muon site is comparable to that reported in the overdoped regime of Bi-2201 in which the AF order is formed around Fe.¹⁰⁾ We propose the formation of a cluster spin-glass at low temperatures, in which a short-range magnetic order is formed in a cluster around each Fe and a spin-glass state is formed between clusters in the CuO₂ plane. In the clusters, an AF order might be formed according to the overdoped regime.¹⁰⁾ On the other hand, based on our results, a FM order might be formed in the cluster.

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Figure: (a) Zero-field μSR time spectrum of HOD Bi_1.74Pb_0.38Sr_1.88Cu_1-yFe_yO_6+δ with y = 0.096. (b) Temperature dependence of the relaxation rate of muon spins λ in HOD Bi_1.74Pb_0.38Sr_1.88Cu_1-yFe_yO_6+δ with y = 0, 0.05, 0.096.

Keywords: Ferromagnetic fluctuations, Bi-2201, Heavily overdoped regime, Muon spin relaxation