Magnetoelectric Response of MultiferroicBiFeO3and Related Materials from First-Principles Calculations

Abstract

We present a first-principles scheme for computing the magnetoelectric response of multiferroics. We apply our method to BiFeO3 (BFO) and related compounds in which Fe is substituted by other magnetic species. We show that under certain relevant conditions -i.e., in absence of incommensurate spin modulation, as in BFO thin films and some BFO-based solid solutions -these materials display a large linear magnetoelectric response. Our calculations reveal the atomistic origin of the coupling and allow us to identify the most promising strategies to enhance it.PACS numbers: 75.80.+q, 71.15.Mb Magnetoelectric (ME) multiferroics present coupled electric and magnetic orders [1], which may allow the development of a variety of magnetic devices, from memories to spin filters, whose behavior would be switchable by application of a voltage. The experimental search for robust room-temperature (T room ) multiferroics is proving a major challenge. The first-principles contribution to this effort is quickly increasing, as shown by recent predictions of new materials [2,3,4] and novel ME coupling mechanisms [5,6,7]. Yet, many key issues remain to be addressed theoretically, as even the ME response of the most promising systems (e.g., thin films of BiFeO 3 [8]) still needs to be characterized and understood in detail. Here we describe a method for ab initio computations of the ME response of multiferroics, tackling the strainmediated contributions that typically exist in these materials. We apply our method to BiFeO 3 and related compounds.Methodology.-The response of a linear magnetoelectric that is not multiferroic -and is thus paraelectriccan be split in two contributions [9]: a purely electronic one and an ionic one. The ionic part accounts for the structural response to an electric (magnetic) field and the resulting change of magnetization (polarization). When the linear magnetoelectric is multiferroic -and thus ferroelectric -there is a third contribution associated to the piezoelectric response to the electric field. Indeed, it can be shown that all commensurate [11] multiferroics must be piezomagnetic, as the symmetries that preclude piezomagnetism are broken in such systems [12]. Hence, the combination of piezoelectricity and piezomagnetism in multiferroics results in a strain-mediated contribution to the linear ME response.In order to model such effects, we have generalized to the magnetoelectric case the formalism that Wu, Vanderbilt, and Hamann [13] (WVH in the following) introduced for a systematic ab initio treatment of dielectric and piezoelectric responses. Let us consider how the energy of a multiferroic crystal varies as a function of the following perturbations: displacements u m of atoms away from their equilibrium positions, homogeneous strains η j , and applied electric (E α ) and magnetic (H µ ) fields. Here, m is a composite label that runs over the atoms in the unit cell and displacement directions, j runs from 1 to 6 in Voigt notation, and α and µ are Cartesian directions.We write the energy per unde...

Induced Magnetoelectric Response inPnmaPerovskites

“…Electronic versus ionic contribution-Recently it has been shown by explicit calculation of the Zeeman electronic contribution to the ME response (α elec ) in Cr 2 O 3 and LiNiPO 4 , that α elec can be comparable in magnitude to the ionic contribution (α ionic ) [11]. It has also been suggested that in FE perovskites such as BiFeO 3 , the ME response is dominated by the FE soft mode (ionic contribution) [2,3,15]. To check how large are the electronic and ionic contributions to the ME response in strained CaMnO 3 , we computed these two contributions as in Ref.…”

“…In addition, although the magnitude of the response is in principle bounded by the product of the dielectric and magnetic permeabilities (α ≤ √ µ), in practice it tends to be much smaller than this value. One promising direction in the search for improved magnetoelectrics is the exploration of multiferroic materials, since the presence of multiple ferroic orders often presents the desired coupling properties for large ME responses [1][2][3]. Another route is the engineering of artificial heterostructures with specific chemistries and symmetries [4][5][6].…”

General microscopic model of magnetoelastic coupling from first principles

“…1) to the electric polarization due to the combined effect of spin-order induced stress and piezoelectricity [16,18] e  is the relaxed-ion piezoelectric tensor and jk S is the relaxed-ion elastic compliance tensor. Previously, Wojdel and Íñ iguez [17] investigated the linear magnetoelectric (ME) coupling by including the piezoelectricity and piezomagnetism in BiFeO3 and related materials. Their model can describe the overall linear ME coupling for the spin ground state.…”

Linear magnetoelectricity at room temperature in perovskite superlattices by design

“…We show from first-principles calculations that the magnitude of the linear ME tensor in these heterostructures is 2-3 times that of canonical ME materials such as Cr 2 O 3 [31][32][33][34][35][36] and BiFeO 3 . Moreover, the strength of linear ME coupling in (La/Ln)Fe 2 O 6 superlattices increases with the increase of the magnitude of the polarization.…”