# Nature of the spiral state, electric polarisation and magnetic transitions in Sr-doped YBaCuFeO$_5$: A first-principles study

## TL;DR

This study uses first-principles calculations to clarify the magnetic and ferroelectric properties of Sr-doped YBaCuFeO$_5$, revealing the absence of electric polarization in the helical spiral state and analyzing doping effects on magnetic transitions.

## Contribution

It provides a detailed first-principles analysis of the magnetic spiral state and ferroelectric response in YBaCuFeO$_5$, clarifying previous ambiguities and exploring doping effects with QMC simulations.

## Key findings

- Helical spiral is stable below the transition temperature with spins in the ab plane.
- No electric polarization is found in the helical spiral state due to absence of DM interaction.
- Doping influences the magnetic transition temperature, increasing up to x=0.5 then decreasing.

## Abstract

Contradictory results on the ferroelectric response of type II multiferroic YBaCuFeO$_{5}$, in its incommensurate phase, has of late, opened up a lively debate. There are ambiguous reports on the nature of the spiral magnetic state. Using first-principles DFT calculations for the parent compound within LSDA+U+SO approximation, the multiferroic response and the nature of spiral state is revealed. The helical spiral is found to be more stable below the transition temperature as spins prefer to lie in ab plane. The Dzyaloshinskii-Moriya (DM) interaction and the spin current mechanism were earlier invoked to account for the electric polarisation in this system. However, the DM interaction is found to be absent, spin current mechanism is not valid in the helical spiral state and there is no electric polarisation thereof. These results are in good agreement with the recent single-crystal data. We also investigate the magnetic transitions in YBa$_{1-x}$Sr$_x$CuFeO$_5$ for the entire range $0\le x\le 1$ of doping. The exchange interactions are estimated as a function of doping and a quantum Monte Carlo (QMC) calculation on an effective spin Hamiltonian shows that the paramagnetic to commensurate phase transition temperature increases with doping till $x=0.5$ and decreases beyond. Our observations are consistent with experimental findings.