[Paper Review] Magnetoresistance driven by the magnetic Berezinskii-Kosterlitz-Thouless transition

Benedetta Flebus|arXiv (Cornell University)|Apr 25, 2021

Advanced Condensed Matter Physics47 references15 citations

TL;DR

This paper proposes that magnetoresistance in two-dimensional metallic ferromagnets arises from electron scattering off topological magnetic defects—merons and antimerons—above the Berezinskii-Kosterlitz-Thouless (BKT) transition temperature. Using a two-fluid model and Boltzmann transport theory, it demonstrates that the resistivity scales exponentially with the density of these defects, predicting a colossal, temperature-dependent magnetoresistance effect suppressed by in-plane magnetic fields.

ABSTRACT

While the Berezinskii-Kosterlitz-Thouless transition (BKT) has been under intense scrutiny for decades, unambiguous experimental signatures in magnetic systems remain elusive. Here, we investigate the interplay between electronic and magnetic degrees of freedom near the BKT transition. Focusing on a metal with easy-plane ferromagnetic order, we establish a framework that accounts both for the coupling between the charge current and the flow of topological magnetic defects and for electron scattering on their inhomogeneous spin texture. We show that electron scattering is responsible for a temperature-dependent magnetoresistance effect scaling as the density of the topological defects, which is expected to increase dramatically above the BKT transition temperature. Our findings call for further experimental investigations.

Motivation & Objective

• To establish a theoretical framework linking electronic transport to topological magnetic defects near the BKT transition.
• To investigate how electron scattering on inhomogeneous spin textures of merons and antimerons contributes to resistivity.
• To determine whether the proliferation of topological defects above TBKT leads to a measurable, temperature-dependent magnetoresistance.
• To explore the suppression of this effect by in-plane magnetic fields, offering a potential experimental signature.

Proposed method

• Models a 2D anisotropic easy-plane Heisenberg Hamiltonian in the continuum limit, describing ferromagnetic order with topological defects.
• Introduces a two-fluid model coupling electron fluid and magnetic defect fluid via collective coordinate dynamics.
• Applies Onsager reciprocity and Boltzmann transport theory to derive resistivity corrections from defect scattering and defect-current coupling.
• Uses the correlation length ξ(T) = a₀exp(b/√τ) to estimate defect density n(T) ≈ ξ(T)⁻² above TBKT.
• Derives the resistivity as ρₑ ∝ 1/τi + 1/τv, where τv is the defect-scattering relaxation time.
• Shows that defect scattering dominates resistivity, leading to ρₑ ∝ n(T) ∝ exp(2b/√τ) above TBKT.

Experimental results

Research questions

• RQ1 How does electron scattering on meron and antimeron spin textures affect electrical resistivity in a 2D metallic ferromagnet?
• RQ2 What is the temperature dependence of the resistivity correction due to topological defects above the BKT transition?
• RQ3 How does an in-plane magnetic field suppress the BKT transition and the resulting magnetoresistance?
• RQ4 Can the resistivity scaling with topological defect density serve as a detectable signature of the magnetic BKT transition?

Key findings

• The resistivity correction due to electron scattering on meron textures dominates over defect-current coupling, scaling as ρₑ ∝ n(T).
• The defect density n(T) increases exponentially above TBKT, following n(T) ≈ ξ(T)⁻² with ξ(T) = a₀exp(b/√τ).
• The resulting magnetoresistance scales as ρ(B=0,T) − ρ(B,T) ∝ n(T), exhibiting a colossal, temperature-dependent enhancement.
• An in-plane magnetic field suppresses the BKT transition and the proliferation of defects, thereby reducing the resistivity enhancement.
• The theory predicts a measurable, exponential rise in resistivity above TBKT, offering a clear experimental signature for the magnetic BKT transition.
• The framework is generalizable to other U(1)-symmetric spin systems with topological defects and can be extended to include spin waves and magnon drag.