[Paper Review] Metallization and Spin Fluctuations in Cu-doped Lead Apatite

Yang Sun, Kai‐Ming Ho+1 more|arXiv (Cornell University)|Aug 7, 2023

Theoretical and Computational Physics4 citations

TL;DR

This study uses first-principles DFT and RPA calculations to investigate Cu-doped lead apatite (LK99), revealing that Cu substitution at Pb2 sites induces a semiconducting state with localized, rigidly ferromagnetic Cu-O clusters, while Pb1 substitution leads to metallization. The system exhibits spin-glass-like behavior due to disordered magnetic clusters with no long-range order, and quantum spin fluctuations stabilize local moments, suggesting a competition between metallic and insulating phases with no long-range magnetic order.

ABSTRACT

An electronic structure and magnetic properties analysis of the recently proposed Cu-doped lead apatite is performed. We show that electronic structures of differently Cu-substituted structures are characterized by localized molecular Cu-O bands at or near the Fermi level. The Cu substitutions can happen at both Pb1 and Pb2 sites, leading to metallic and semiconducting states differently. The electronic states in these bands are highly unstable magnetically and form clusters of rigidly ferromagnetically coupled magnetic moments on Cu and neighboring oxygen atoms with a total moment of about 1 $μ_B$. The ground state of uniformly Cu-doped lead apatite appears to be magnetic and semiconducting. The non-uniform distribution of two Cu atoms at the nearest Pb2 sites leads to an antiferromagnetic semiconducting state with formation energy close to uniformly distributed Cu configurations. The inclusion of quantum spin fluctuations confirms the stability of magnetic Cu-O clusters. Our calculations revealed the absence of the long-range magnetic order between uniformly distributed Cu-O clusters, creating the spin glass type of system.

Motivation & Objective

• To clarify the electronic and magnetic origin of metallization and semiconducting behavior in Cu-doped lead apatite (LK99).
• To determine the stability and electronic structure of different Cu-doping configurations at Pb1 and Pb2 sites.
• To investigate the role of local magnetic moments and spin fluctuations in stabilizing or destabilizing superconducting or magnetic phases.
• To assess the possibility of long-range magnetic order and the nature of magnetic interactions between Cu-O clusters.
• To evaluate the competition between metallic and semiconducting ground states in the presence of spin fluctuations.

Proposed method

• First-principles density functional theory (DFT) with PBE, LDA, and LDA+U functionals using the projector augmented wave (PAW) method in VASP.
• Structure relaxation and electronic structure calculations performed with a 520 eV kinetic energy cutoff and fine k-point sampling (2π×0.017 Å⁻¹).
• Spin susceptibility and exchange coupling parameters computed using an in-house FLAPW code with mixed product basis sets.
• Random-phase approximation (RPA) used to include quantum spin fluctuations and assess their effect on magnetic stability.
• Stoner model applied to estimate Curie temperature and assess the localized vs. itinerant nature of magnetic moments.
• Formation energy calculations compared for different Cu-doping configurations to assess thermodynamic stability and ordering tendencies.

Experimental results

Research questions

• RQ1 What is the electronic structure and stability of Cu-doped lead apatite when Cu substitutes at Pb1 versus Pb2 sites?
• RQ2 How do local magnetic moments on Cu and neighboring O atoms form, and what is their magnetic coupling behavior?
• RQ3 What is the role of spin fluctuations in stabilizing or suppressing local magnetic moments in Cu-doped apatite?
• RQ4 Does the system exhibit long-range magnetic order, or does it display spin-glass-like behavior at zero temperature?
• RQ5 How do different Cu-doping configurations influence the coexistence of metallic and semiconducting phases?

Key findings

• Cu substitution at Pb2 sites leads to a semiconducting ground state with a band gap of approximately 0.4 eV, while Pb1 substitution results in metallization.
• Localized molecular-like Cu-O bands near the Fermi level form rigid, ferromagnetically coupled CuO3 clusters with a total magnetic moment of about 1 μB.
• The system exhibits spin-glass-like behavior at T=0K due to the absence of long-range magnetic order between CuO3 clusters, despite strong local moments.
• RPA calculations confirm that quantum spin fluctuations do not destroy the local magnetic moments on CuO3 clusters, indicating their stability.
• The Stoner temperature is estimated at 2500–3000 K, supporting the localized nature of the Cu magnetic moment and the robustness of ferromagnetic clusters.
• Non-uniform Cu distribution at nearest Pb2 sites leads to an antiferromagnetic semiconducting state with formation energy nearly equal to uniformly distributed configurations, indicating no strong preference for ordering.