[Paper Review] Quasiclassical theory of $C_4$-symmetric magnetic order in disordered multiband metals

Maxim Dzero, Maxim Khodas|arXiv (Cornell University)|Mar 26, 2020

Iron-based superconductors researchMaterials Science43 references3 citations

TL;DR

This paper develops a quasiclassical theory to study C4-symmetric (tetragonal) magnetic order in disordered, multiband iron-based superconductors, focusing on a three-band model with anisotropic Fermi surfaces. It demonstrates that intraband disorder promotes the double-⃗Q spin density wave state over the C2-symmetric single-⃗Q state, providing a mechanism for the experimentally observed tetragonal magnetic phase in iron pnictides.

ABSTRACT

Recent experimental studies performed in the normal state of iron-based superconductors have discovered the existence of the $C_4$-symmetric (tetragonal) itinerant magnetic state. This state can be described as a spin density wave with two distinct magnetic vectors ${\vec Q}_1$ and ${\vec Q}_2$. Given an itinerant nature of magnetism in iron-pnictides, we develop a quasiclassical theory of tetragonal magnetic order in disordered three-band metal with anisotropic band structure. Within our model we find that the $C_4$-symmetric magnetism competes with the $C_2$-symmetric state with a single ${\vec Q}$ magnetic structure vector. Our main results is that disorder promotes tetragonal magnetic state which is in agreement with earlier theoretical studies.

Motivation & Objective

• To understand the origin of C4-symmetric magnetic order in iron-based superconductors, particularly the double-⃗Q spin density wave state observed in experiments.
• To investigate how disorder influences the stability of competing magnetic states—specifically, the competition between C2-symmetric (single-⃗Q) and C4-symmetric (double-⃗Q) magnetic order.
• To develop a quasiclassical framework applicable to disordered, multiband metals with anisotropic band structures, relevant to iron-pnictide systems.
• To clarify the role of intraband versus interband disorder in stabilizing the tetragonal magnetic phase.

Proposed method

• Formulates a three-band Hamiltonian with hole-like (Γ-point) and electron-like (X and Y points) bands, incorporating anisotropic Fermi surface nesting via parameters δ0 and δ2.
• Introduces a spin-density wave term with two distinct magnetic vectors ⃗Q1 and ⃗Q2, modeled via Ising-like magnetization fields mX and mY.
• Applies the quasiclassical approximation by integrating over single-particle energies, deriving effective equations for the quasiclassical propagator and self-energy.
• Imposes intraband disorder via a self-energy term, neglecting interband scattering to isolate the effect of intraband scattering on magnetic order.
• Performs a Landau expansion of the free energy to determine the stability of the C2- and C4-symmetric magnetic states.
• Solves the resulting self-consistent equations numerically to compare the free energy contributions of the two magnetic states under varying disorder strength.

Experimental results

Research questions

• RQ1 Does intraband disorder favor the emergence of a C4-symmetric double-⃗Q magnetic state over a C2-symmetric single-⃗Q state in a multiband metal?
• RQ2 How does the anisotropy of the Fermi surface (controlled by δ0 and δ2) influence the competition between different magnetic orders?
• RQ3 What is the role of intraband scattering in stabilizing the tetragonal magnetic phase, relative to interband scattering?
• RQ4 How does the quasiclassical formalism capture the interplay between disorder and itinerant magnetism in multiband systems?
• RQ5 Can the observed experimental suppression of the single-⃗Q state in iron-based superconductors be explained by intraband disorder alone?

Key findings

• Intraband disorder promotes the C4-symmetric double-⃗Q magnetic state over the C2-symmetric single-⃗Q state, consistent with experimental observations in iron-based superconductors.
• The stabilization of the double-⃗Q state occurs even when interband disorder is neglected, indicating that intraband scattering alone is sufficient to favor tetragonal symmetry.
• The Landau free energy expansion shows that the double-⃗Q state becomes energetically favorable as disorder strength increases, particularly in the presence of anisotropic band structure.
• The model reproduces the experimentally observed suppression of the single-⃗Q state and enhancement of the double-⃗Q state under disorder, supporting a mechanism for the tetragonal magnetic phase.
• The results are in agreement with earlier theoretical studies showing that disorder favors C4-symmetric magnetic order, providing a quasiclassical foundation for this phenomenon.
• The quasiclassical approach successfully captures the competition between magnetic states in a disordered, multiband system, offering a framework for studying similar phenomena in iron-based materials.