# Partial order induced superconductivity in $Fe^{2+}$ iron

## TL;DR

This paper proposes a novel mechanism for superconductivity in iron-based materials, where a quantum partial order state induced by an external magnetic field leads to spin triplet superconductivity.

## Contribution

It introduces a new quantum partial order state in $Fe^{2+}$ iron, showing how external magnetic fields can induce superconductivity with a specific triplet pairing symmetry.

## Key findings

- The $F^{2+}$ state of iron has a well-defined Fermi surface, indicating metallic behavior.
- Applying an external magnetic field can induce a quantum partial order state that suppresses magnetism from the sixth electron.
- The induced state exhibits spin triplet superconductivity with $T_{1u}$ symmetry.

## Abstract

In this letter, we address a novel mechanism for iron based superconductors. We study $F^{2+}$ state of iron with six 3d electrons. Five of them are localized with ferromagnetic order, while the sixth one is itinerant antiparallel with the localized ones. We consider spin-fermion model of 3d electrons and show that one can fix the parameters in the theory so that the calculated magnetization to match the experimentally measured one. With these parameters in mind we show that the sixth 3d electrons have well defined Fermi surfaces, therefore the material is metal. Further on we consider an iron prepared by means of applied external magnetic field upon a cooling. We assume that the applied magnetic field is along the magnetic order of localized 3d electrons and antiparallel to the magnetic order of the itinerant sixth electron. Therefore the applied field decreases the Zeeman splitting of spin-up and spin-down sixth electrons. We focus on quantum partial order (QPO) state which is obtained when the applied field compensates the Zeeman splitting so that the sixth 3d electrons do not contribute the magnetism of iron and magnetic order is formed by means of localized 3d electrons. We obtain an effective Hamiltonian for iron in (QPO) state and show that it posses a spin triplet superconductivity with $T_{1u}$ configuration.