[Paper Review] Anomalous Hall effect from frustration-tuned scalar chirality distribution in Pr2Ir2O7

Masafumi Udagawa, Roderich Moessner|arXiv (Cornell University)|Dec 3, 2012

Advanced Condensed Matter Physics3 citations

TL;DR

This paper proposes that the anomalous Hall effect (AHE) in Pr₂Ir₂O₇ arises from frustration-tuned scalar chirality in localized Pr³⁺ spins, using a Kondo lattice model on a pyrochlore lattice. It shows that the experimentally observed peak in Hall conductivity at H ≈ 0.7 T for H∥[111] originates from a field-induced crossover from spin ice to Kagome ice order, with quantitative agreement achieved via a multi-orbital tight-binding model and phenomenological scattering.

ABSTRACT

We analyse the Ising Kondo lattice model on a pyrochlore structure in order to study the anomalous Hall effect due to non-coplanar magnetism. We focus on the frustration-induced spatial inhomogeneity of different magnetic low-temperature regimes, between which one can efficiently tune using an external magnetic field. We incorporate non-magnetic scattering on a phenomenological level so that we can distinguish between the effects of short-range correlations and short-range coherence. We obtain a Hall conductivity (σ_H) as function of field strength and direction which compares well to the experimental data of Pr2Ir2O7. In particular, we show that the observed peak in σ_H for H||[111] signals the crossover from zero-field spin ice to Kagome ice.

Motivation & Objective

• To understand the origin of the anomalous Hall effect (AHE) in Pr₂Ir₂O₇, a pyrochlore iridate with strong spin-orbit coupling and geometric frustration.
• To investigate how spatially inhomogeneous, frustration-induced spin configurations—specifically spin ice and Kagome ice—drive non-monotonic and anisotropic AHE responses.
• To achieve quantitative agreement with experimental Hall conductivity by incorporating orbital degeneracy and phenomenological non-magnetic scattering in a multi-orbital Kondo lattice model.
• To clarify the role of scalar chirality distribution in generating the observed peak in σ_H at H ≈ 0.7 T for H∥[111].

Proposed method

• Formulates an Ising Kondo lattice model on a pyrochlore lattice, with localized Ising spins on the Pr sublattice and itinerant electrons on the Ir sublattice.
• Imposes the Kagome ice rule (sum of η_i = 1 per triangle) to generate a macroscopic degenerate spin-liquid-like manifold with uniform scalar chirality K₀ = -4/(3√3).
• Uses a multi-orbital tight-binding model with three-fold degenerate t₂g orbitals for Ir 5d electrons, incorporating Slater-Koster hoppings to model realistic band structure.
• Introduces a phenomenological scattering rate 1/τ to account for non-magnetic impurities and include damping in the electronic self-energy.
• Calculates Hall conductivity σ_xy using a real-space formulation derived from Matsubara Green’s functions, expressing σ_xy as a sum over spin triplets: σ_xy = Σ(h_i₁·(h_i₂×h_i₃)) W_xy(i₁,i₂,i₃).
• Evaluates the weighting function W_xy via numerical summation over Matsubara frequencies and momentum space, incorporating electronic structure and spin texture effects.

Experimental results

Research questions

• RQ1 What is the microscopic origin of the anomalous Hall effect in Pr₂Ir₂O₇, particularly the non-monotonic and anisotropic field dependence of σ_H?
• RQ2 How does the spatial inhomogeneity of spin correlations—arising from geometric frustration—manifest in the Hall response?
• RQ3 Why does σ_H exhibit a pronounced peak at H ≈ 0.7 T for H∥[111], and what phase transition or crossover underlies this feature?
• RQ4 To what extent can the observed Hall conductivity magnitude and field dependence be quantitatively reproduced using a Kondo lattice model with realistic band structure and scattering?

Key findings

• The peak in Hall conductivity at H ≈ 0.7 T for H∥[111] is attributed to a crossover from the zero-field spin ice state to the field-induced Kagome ice state, where spins on Kagome planes align with the field while maintaining ice rules.
• The model reproduces the experimental plateau in σ_H at high fields (H ≳ 4 T) for H∥[100], yielding σ_H ≈ 30 Ω⁻¹ cm⁻¹, in good quantitative agreement with experiment.
• For H∥[111], the model predicts a peak at H ≈ 1.0 T and sign reversal at H ≈ 8 T, consistent with experimental observations of a peak at 0.7 T and reversal near 6 T.
• Incorporating three-fold orbital degeneracy in the t₂g band increases transverse scattering channels and enhances σ_H, enabling quantitative agreement with experimental magnitude.
• The diagonal resistivity ρ ≈ 8.0×10² Ω⁻¹ cm⁻¹ is of the same order as the experimental value (~2.8×10³ Ω⁻¹ cm⁻¹), validating the model's transport parameters.
• The scalar chirality remains uniform across all spin configurations satisfying the ice rule, confirming that the AHE arises from long-range spin texture rather than local fluctuations.