Dynamic polarization of nuclear spins by optically-oriented electrons and holes in lead halide perovskite semiconductors

A theory of dynamic polarization of the nuclear spin system via optically-oriented charge carriers in lead halide perovskites is developed and compared with the experiments performed on a FA${0.9}$Cs${0.1}$PbI${2.8}$Br${0.2}$ crystal. The spin Hamiltonians of the electron and hole hyperfine interaction with the nuclear spins of lead and halogen are derived. The hyperfine interaction of the halogen spins with charge carriers is shown to be anisotropic and depending on the position of the halogen nucleus in the cubic elementary cell. The quadrupole splitting is absent for the lead spins, but plays an important role for the halogen spins and affects their dynamic polarization by charge carriers. The Overhauser fields of the dynamically polarized nuclei are calculated as functions of the tilting angle of an external magnetic field and compared with the experimentally measured angular dependence of the Hanle effect. The comparison of the theoretical model with the experimental data reveals an enhanced spin polarization of the lead nuclei, whose mean spin exceeds several times the mean spins of localized electrons and holes. This unexpectedly strong spin polarization is explained by the interaction of the lead nuclei with excitons having a high degree of spin orientation due to their short lifetime after excitation by circularly-polarized light. The dynamic polarization of the quadrupole-split halogen spins manifests itself via the magnetic field they produce at the lead nuclei. This field maintains the magnetization of the lead nuclei at zero external magnetic field. The dynamics of the nuclear spin polarization is measured under optical pumping and in the dark, yielding a nuclear spin-lattice relaxation time on the order of 10 seconds.

💡 Research Summary

This paper presents a comprehensive theoretical and experimental study of dynamic nuclear polarization (DNP) in the lead‑halide perovskite crystal FA0.9Cs0.1PbI2.8Br0.2. By optically orienting electrons and holes with circularly polarized light, the authors generate a non‑equilibrium spin polarization of charge carriers, which is transferred to the lattice nuclei via hyperfine interaction. The work is organized into several parts: (i) derivation of the spin Hamiltonians for electron‑nucleus and hole‑nucleus hyperfine coupling, (ii) analysis of the quadrupole interaction of halogen nuclei, (iii) calculation of the Overhauser fields produced by the polarized nuclei, (iv) experimental measurement of Hanle and polarization‑recovery curves as a function of the angle between the external magnetic field and the light propagation direction, and (v) comparison of theory with experiment to extract quantitative parameters such as hyperfine constants, quadrupole splittings, and nuclear spin‑lattice relaxation times.

Theoretical framework
The authors start from the crystal symmetry of the cubic perovskite phase. Lead nuclei (^207Pb, I = ½) experience no electric‑field gradient, so their quadrupole Hamiltonian vanishes. In contrast, halogen nuclei (Br, I, with I > ½) sit in a strong uniaxial electric‑field gradient aligned along the Pb‑X‑Pb bond. This produces a large quadrupole splitting (≈ 70 MHz for Br, ≈ 80 MHz for I) that separates the nuclear spin manifold into Kramers doublets (|±½⟩, |±3⁄2⟩, |±5⁄2⟩). Within each doublet the nucleus behaves as an effective spin‑½ with a highly anisotropic g‑tensor: the longitudinal component g∥ is of order unity, while the transverse components g⊥ are ≤ 0.04. Consequently, the Zeeman interaction for a given doublet is written as HZ = ½ħγN (g∥B∥σz + g⊥(B⊥xσx + B⊥yσy)).

Hyperfine interaction constants are derived from the orbital composition of the bands. The valence band is dominated by Pb‑s orbitals, giving a hole‑nucleus hyperfine constant A_h roughly five times larger than the electron‑nucleus constant A_e. Both constants are anisotropic for halogen nuclei because the carrier wavefunctions have different overlap with the halogen sites depending on the halogen position in the unit cell.

The nuclear dipole‑dipole interaction is treated in the usual mean‑field approximation, leading to a local “nuclear field” BL that scales with the sum over all neighboring nuclei (∝ ∑γ²/r³). The authors calculate BL for Pb and halogen sites in several perovskites; the dominant contribution comes from the halogen sublattice. When the halogen nuclei become polarized, their internal field adds to (or subtracts from) the external magnetic field, thereby generating an Overhauser field BOH that is felt by the electrons, holes, and the Pb nuclei themselves.

Dynamic equations
The time evolution of the average nuclear spin ⟨I⟩ is described by a rate equation of the form

d⟨I⟩/dt = W (⟨S⟩ − ⟨I⟩/Imax) − ⟨I⟩/T1,

where ⟨S⟩ is the average carrier spin, W is the flip‑flop rate proportional to the hyperfine constants and carrier density, Imax is the maximal nuclear spin (½ for Pb, 3⁄2 or 5⁄2 for halogens), and T1 is the nuclear spin‑lattice relaxation time. The Overhauser field is BOH = A ⟨I⟩/(gμB). Because the quadrupole splitting isolates each Kramers doublet, the effective W for the halogen doublets depends on the orientation of the external field relative to the EFG axis, leading to a characteristic angular dependence of BOH.

Experimental methodology
The crystal is cooled to 4 K and excited with a continuous‑wave laser (≈ 750 nm) of fixed helicity (σ⁺ or σ⁻). The external magnetic field Bext is applied at a variable tilt angle θ with respect to the light wavevector k. Two measurement geometries are used: (a) Hanle configuration (B ⟂ k) where the PL polarization decreases with increasing B due to dephasing in random nuclear fields, and (b) polarization‑recovery (Faraday) configuration (B ∥ k) where PL polarization increases because the external field suppresses nuclear‑field‑induced dephasing. By alternating the helicity of the pump (helicity‑modulated excitation) the authors obtain a reference curve with no nuclear polarization.

Key observations

1. In the presence of a constant helicity pump, the Hanle curves are shifted horizontally, indicating a non‑zero Overhauser field. The shift magnitude depends on θ and follows a cos θ law, consistent with the theoretical prediction for BOH.
2. The polarization‑recovery curves are similarly displaced, confirming that the same Overhauser field adds to the external field in the Faraday geometry.
3. By fitting the angular dependence, the authors extract an effective Overhauser field of up to ~30 mT for the Pb nuclei.
4. The inferred average Pb nuclear spin ⟨IPb⟩ is 3–5 times larger than the average carrier spin ⟨S⟩, a surprising result because nuclear polarization is usually limited by the carrier polarization. The authors attribute this amplification to the short exciton lifetime (sub‑nanosecond) combined with a high degree of exciton spin orientation; each exciton can transfer its spin to many Pb nuclei before recombination.
5. The halogen nuclei, despite being strongly quadrupole‑split, contribute indirectly: their polarized doublets generate a static magnetic field at the Pb sites, which sustains the Pb nuclear magnetization even when Bext = 0. This explains the observed “zero‑field nuclear magnetization”.
6. After switching off the pump, the decay of the PL polarization (monitored in the dark) yields a nuclear spin‑lattice relaxation time T1 ≈ 10 s. This value is intermediate between the long T1’s reported for II‑VI and III‑V semiconductors and the much shorter times observed in some organic systems.

Discussion and implications
The work demonstrates that lead‑halide perovskites provide a fertile platform for DNP because (i) both electrons and holes possess spin‑½ and can be efficiently oriented optically, (ii) the hole hyperfine coupling is unusually strong, and (iii) the halogen sublattice introduces large quadrupole effects that create anisotropic nuclear dynamics. The combination of a strong Overhauser field and a relatively long T1 makes these materials attractive for spin‑based memory and for low‑field nuclear magnetic resonance techniques such as optically detected NMR (ODNMR). Moreover, the ability to maintain nuclear polarization without an external field could be exploited in zero‑field quantum information protocols.

Future directions suggested include temperature‑dependent studies to map the evolution of quadrupole splitting across phase transitions, exploration of mixed‑halide compositions to tune hyperfine constants, and extension to two‑dimensional perovskite layers where confinement may further enhance carrier‑nucleus spin transfer.

In summary, the authors have built a quantitative theory of hyperfine‑mediated DNP in cubic lead‑halide perovskites, validated it with angle‑resolved Hanle and polarization‑recovery measurements, and uncovered an unexpectedly large Pb nuclear polarization sustained by exciton‑mediated spin transfer and halogen‑induced internal fields. This advances our understanding of spin physics in perovskites and opens pathways toward perovskite‑based spintronic and quantum‑coherent devices.