First-principles study of KCoF$_3$: Jahn-Teller effect, dynamical magnetic charges, magnetoelectric multipoles and antimagnetoelectricity

TL;DR

This work uses first-principles DFT to elucidate the cubic-to-tetragonal transition in KCoF$_3$ as an electronic first-order Jahn-Teller instability at the R point, revealing a G-type AFM ground state and a substantial SOC-induced orbital moment. It goes beyond conventional analyses by computing dynamical magnetic charges (DMC) and magnetoelectric multipoles, finding Co DMC vanishes by symmetry while apical F sites exhibit large DMCs, driven by Jahn-Teller distortions and orbital physics, leading to a strong antimagnetoelectric response of about $210\mathrm{ps/m}$ per spin channel. The tetragonal ground state $I4/mcm$ arises from an R-point distortion with an energy gain of $23.1\mathrm{meV/f.u.}$, and the orbital moment decreases with distortion from $\approx 0.95\mu_B$ to $\approx 0.55\mu_B$ while the spin moment remains nearly constant. The results imply that large DMC and AM behavior can be generic in perovskites with Jahn-Teller activity and significant SOC, suggesting new routes to harness magnetoelectric effects in nonfunctional materials.

Abstract

We study from \textit{ab~initio} density functional theory calculations the structural and magnetic properties of the crystal KCoF$_3$. We found that the experimentally reported cubic to tetragonal phase transition is due to an electronic first-order Jahn-Teller effect from the R zone boundary point. We also obtain that the magnetic ground state is the G-type antiferromagnetic order, in agreement with the R-point Jahn-Teller distortion and that the magnetic moment of the Co atoms contains a strong orbital contribution ($m_L=0.95$ $μ_B$ in the cubic phase and 0.55 $μ_B$ in the tetragonal phase). Furthermore, we compute the dynamical magnetic effective charges and show that it is zero by symmetry for the Co and they can reach a value as large as 200 $10^{-2}μ_{\text{B}}/\text{Å}$ for the apical F anion. This large magnetic effective charge comes from the spin-orbit coupling (50\% of the response is from the orbital moment) contrary to the rare-earth manganites and ferrites with similar order of magnitude but originating from the exchange striction mechanism. The fact that the dynamical magnetic effective charges are non-zero also proves that the tetragonal phase of KCoF$_3$ is antimagnetoelectric with a large magnetic sublattice magnetoelectric response of 210 ps/m per spin-channel. We also discuss the generality of these magnetic effective charges.

Figures (7)

• Figure 1: (Left) Magnetic structure of KCoF$_3$ showing the ground state G-type antiferromagnetic ordering. The purple spheres represent K atoms, blue spheres represent Co atoms with alternating spin directions (indicated by red vectors), and light gray spheres represent F atoms forming octahedra around Co sites. The crystallographic axes are indicated in the bottom left corner. (Right) Calculated magnon dispersion along high-symmetry paths in the FM cubic Brillouin zone. The dispersion shows characteristic energy minima at the R point corresponding to the configuration shown in left panel. $\Gamma$= (0, 0, 0), X= (1/2, 0, 0), M = (1/2, 1/2, 0) and R= (1/2, 1/2, 1/2) in units of the cubic reciprocal lattice vectors.
• Figure 2: Phonon dispersion curves of KCoF$_3$ in the calculated (collinear DFT regime) ground state G-AFM $I4/mcm$ phase. $\Gamma$ = (0, 0, 0), X = ( 0, 0, 1/2), Y = ( -0.26, 0.26, 1/2), $\Sigma$ = ( -0.38, 0.38, 0.38), Z = ( 1/2, 1/2, -1/2), $\Sigma_1$ = (0.38, 0.62, -0.38), N = ( 0, 1/2, 0), and P = (1/4, 1/4, 1/4) in units of the cubic reciprocal lattice vectors.
• Figure 3: Visualization of the atomic displacements associated with the $R_3^-$ Jahn-Teller mode. (Left) Three-dimensional perspective of the crystal structure with two consecutive cobalt planes highlighted in cyan and red. (Center, Right) Top-view projections of the cobalt planes illustrating the in-plane atomic motion patterns.
• Figure 4: Energy evolution under the first-order type Jahn-Teller rigid distortion in KCoF$_3$ in the G-AFM magnetic state including SOC but at fixed cell parameter (the one of the high symmetry reference, see Table S.I). The zero energy is taken from the $P_I4/mm'm'$ high symmetry phase including SOC (Table S.I). Under the full cell relaxation, a total gain of 23.1 meV/f.u. is obtained, showing that the elastic contribution is important as at frozen cell parameter as shown in this figure the gain of energy is a bit less than 4 meV/f.u.
• Figure 5: Evolution of Co orbital magnetic moment of KCoF$_3$ with respect to the Jahn-Teller distortion amplitude in it G-AFM magnetic ground state. The relaxed Jahn-Teller distortion amplitude (0.01 Å) is reported by the vertical dashed line.