Comment on 'Distorted perovskite with $e_g^1$ configuration as a frustrated spin system'

TL;DR

This paper critiques a previous study on manganite magnetic structures, correcting the phase diagram and energy minimization method, and clarifies the conditions for the E-phase to occur.

Contribution

It provides the corrected phase diagram and energy minimization approach for the magnetic structure in manganites, challenging prior assumptions.

Findings

The E-phase does not occur at the previously suggested exchange ratios.

The original energy minimization method was incorrect.

The finite temperature phase diagram in the original study is also incorrect.

Abstract

Interesting magnetic structure found experimentally in a series of manganites RMnO$_3$, where R is a rare earth, was explained, ostensibly, by Kimura et al, in terms of a classical Heisenberg model with an assumed set of exchange parameters, nearest-neighbor and next-nearest-neighbor interactions, $J_n$. They calculated a phase diagram as a function of these parameters for the ground state, in which the important "up-up-down-down" or E-phase occurs for finite ratios of the $J_n$. In this Comment we show that this state does not occur for such ratios; the error is traced to an incorrect method for minimizing the energy. The correct phase diagram is given. We also point out that the finite temperature phase diagram presented there is incorrect.