# Effect of Frustrated Exchange Interactions and Spin-half Impurity on the Electronic Structure of Strongly Correlated NiFe$_{2}$O$_{4}$

## TL;DR

This study investigates how frustrated exchange interactions and a spin-half impurity (Yb) influence the electronic and magnetic properties of strongly correlated NiFe₂O₄, revealing complex magnetic behavior and impurity effects through combined computational and experimental methods.

## Contribution

It provides new insights into the magnetic exchange interactions and impurity effects in Yb-substituted NiFe₂O₄ using density functional calculations and neutron diffraction.

## Key findings

- Both octahedral-octahedral and octahedral-tetrahedral interactions are antiferromagnetic.
- Yb acts as a spin-half impurity in +3 charge state.
- Yb substitution reduces the Curie temperature.

## Abstract

Spin-polarized density functional calculations, magnetization, and neutron diffraction measurements are carried out to investigate the magnetic exchange interactions and strong correlation effects in Yb substituted inverse spinel nickel ferrite. In the pristine form, the compound is found to be a mixed insulator under the Zaanen-Sawtazsky-Allen classification scheme as it features both charge transfer and Mott insulator mechanism. Estimation of magnetic exchange couplings reveals that both octahedral-octahedral and octahedral-tetrahedral spin-spin interactions are antiferromagnetic which is typical of a spin-frustrated triangular lattice. However, the latter is dominant compared to the former leading to a forced parallel alignment of the spins at the octahedral site which is in agreement with the results of neutron diffraction measurements. The substituent Yb is found to be settled in +3 charge state, as confirmed from the XPS measurements, to behave like a spin-half impurity carried by the localized $f_{z(x^2-y^2)}$ orbital. The impurity $f$ spin significantly weakens the antiferromagnetic coupling with the spins at the tetrahedral site, which explains the experimental observation of fall in Curie temperature with Yb substitution.