Magnetoelectric Interfaces - Emerging Perspectives for Novel Functionalities

Magnetoelectric (ME) materials are those in which an external magnetic field affects the polarization, and an electric field influences the magnetization of the material.¹ A well-known example of the ME material is Cr₂O₃ where a rhombohedral unit cell and an antiferromagnetic order break the space inversion and time reversal symmetries that is required for the linear ME coupling to exist.

The ME coupling is typically stronger in multiferroic materials - materials which simultaneously exhibit two (or more) ferroic orders, e.g. ferroelectricity and antiferromagnetism. For example, BiFeO₃ is a room temperature multiferroic that has antiferromagnetic Neel temperature TN=643K and ferroelectric Curie temperature TC=1103K.²

Multiferroic materials have recently aroused considerable interest due to their potential for new device functions. Magnetoelectric multiferroics allow the possibility of switching the magnetization with electric field. This offers a wealth of opportunity for information storage applications. In particular, this property could remove the main hindrance in the miniaturization of magnetic random excess memories (MRAM) where the write operation requires magnetic fields or large currents. Another possibility is the development of memory bits with multiple stable states^3,4 or mixed memory and logic functions.⁵

The number of bulk multiferroic materials is however limited, especially those which maintain their ME properties at room temperature. Composite multiferroics, such as layered heterostructures of ferroelectric (FE) and ferromagnetic (FM) compounds, significantly broaden the class of multiferroic materials. The ME coupling in these heterostructures occurs across interfaces.

Two types of ME coupling can be expected: (i) direct due to electronic effects at the interface; (ii) indirect mediated by strain. Almost all practical structures to date use the elastic properties of the material to mediate ME coupling. A more interesting, however, both from the point of view of physics involved and device application is the coupling occurring through purely electronic mechanisms.

In the last few years a theoretical group at University of Nebraska-Lincoln and Materials Research Science and Engineering Center (MRSEC) has invested significant efforts to understand physical properties of magnetoelectric interfaces. Three types of phenomena were in focus of these studies: (i) affecting interface (surface) magnetization by electric field, in particular through a FE polarization of adjacent FE layer, (ii) effects on surface magnetocrystalline anisotropy; (iii) electron and spin transport across FM/FE interfaces in ferroelectric (multiferroic) tunnel junctions.

Interface Magnetization

When a metal film is exposed to an electric field, the induced surface charge σ = ε₀E screens the electric field over the screening length of the metal. In a FM metal the screening charge is spin-dependent due to the exchange splitting of the spin bands which induces a surface magnetization M_s, as demonstrated in Fig. 1. First principles calculations show however that the ME response is small for elemental FM metals, about the same order as for Cr₂O₃ but limited to the surface.⁶

Figure 1. Induced spin density on the Fe(001) surface due to an applied electric field.

The ME effect can be substantially enhanced at the interface between a ferromagnet and a dielectric, because the induced surface charge scales with the dielectric constant. For high-k dielectrics the dielectric constant can be as large as 100 and even larger, which increases the ME response by two or more orders of magnitude.⁷

The electronically-driven ME effects can be further enhanced by employing a FE material to produce a field effect. In this case the spin-dependent screening in a FM material occurs in response to the polarization charge at the FE/FM interface. The latter can be altered by switching the FE polarization. Such a ME effect was predicted for a SrRuO₃/BaTiO₃ interface where a magnetic moment change of 0.31µ_B on the interface Ru atom results from FE polarization reversal.⁸

The interface bonding mechanism may play an important role in the ME effect at the FM/FE interfaces.⁹ Change in atomic displacements at the interface alters orbital hybridizations, affecting the interface magnetic moments. First-principles calculations for the Fe/BaTiO₃(001) interface show a large change in the interface magnetic moment, 0.25µ_B per interface unit cell, when the electric polarization is switched by electric field.⁹ Similar effects were predicted for Fe₃O₄/BaTiO₃ interfaces.¹⁰ Interestingly, for the La_1-χA_χMnO₃/BaTiO₃ (001) interface, where A is a divalent cation, there is a possibility to switch an interface magnetic order from ferromagnetic to antiferromagnetic by reversing the FE polarization.¹¹

Surface Magnetocrystalline Anisotropy

Especially promising is to control the magnetocrystalline anisotropy (MCA) of a magnetic material by an applied electric field. Since the MCA determines stable orientations of magnetization, tailoring the anisotropy of a FM film by electric fields allows switching the magnetic moment.

For metallic ferromagnets the electronically-driven ME effect is confined to the interface and consequently the electric field affects only the surface (interface) MCA.⁶ For 3d ferromagnets the effect originates from the change in the relative population of the 3d-orbitals (see Fig. 1) which contribute differently to the MCA energy. Recently, a strong effect of applied electric field on the interface MCA was demonstrated experimentally for the Fe/MgO (001) interfaces.¹²

A change in the interface MCA energy can be used for switching the magnetization by applied electric field.⁶ Recently this prediction was confirmed experimentally for a MgO/FeCo interface exhibiting perpendicular MCA.¹³ Using a FeCo film thickness for which the MCA and shape anisotropy energies are equal, voltage-assisted magnetization switching between in-plane and out-of-plane states was achieved.

Even more efficiently the MCA may be controlled at the FE/FM interface. First-principles calculations of Fe/BaTiO₃ bilayer have shown that a reversal of the electric polarization of BaTiO₃ produces a sizeable change in the surface MCA energy of the Fe film.¹⁴

Ferroelectric and Multiferroic Tunnel Junctions

Multiferroic tunnel junctions (MFTJs) involve a new concept for a multifunctional device and have recently attracted significant interest.¹⁵ MFTJs exploit the capability to control electron and spin tunneling via FM and FE polarizations of the MFTJ constituents.

Figure 2. Schematic view of the different types of tunnel junctions: (a) magnetic tunnel junction (MTJ); (b) ferroelectric tunnel junction (FTJ); and (c, d) multiferroic tunnel junction (MFTJ) with ferroelectric barrier in MTJ (c) and a multiferroic barrier (d). The ferromagnetic (FM), ferroelectric (FE), normal metal (NM), insulating (I) and multiferroic (MF) layers are indicated where appropriate.

Ferroelectric Tunnel Junctions

MFTJ is a particular type of a ferroelectric tunnel junction (FTJ). In a FTJ a FE thin film serves as a barrier between two metal electrodes (Fig. 2b).¹⁵ The key property of a FTJ is tunneling electroresistance (TER) that is the change in resistance of a FTJ with reversal of FE polarization. The origin of the TER effect is illustrated in Fig. 3. Polarization switching affects the interface transmission function by changing (a) the electrostatic potential at the interface; (b) interface bonding strength; and/or (c) strain associated with the piezoelectric response.¹⁵

(a) The electrostatic effect results from incomplete screening of the polarization charges at the interface of FTJs.¹⁶ This creates finite size charge depletion (accumulation) regions at the interfaces and hence an asymmetric potential profile in FTJs with different electrodes. The predicted TER effect becomes especially strong if an additional thin dielectric layer is placed at the FTJ interface.¹⁷ (b) The interface bonding effect on TER becomes apparent in atomistic calculations.¹⁸ The presence of interfaces imposes restrictions on the atomic displacements responsible for spontenious polarization since the atoms at the boundary of the ferroelectric are bonded to the electrodes. (c) The piezoelectric effect is important because most ferroelectrics are piezoelectric. In particular, atomic displacements influence the decay rate in the barrier and consequently the transmission through it.¹⁸

Figure 3. Mechanisms affecting tunneling in ferroelectric tunnel junctions: (a) electrostatic potential at the interface, (b) interface bonding, (c) strain. After ref. #15.

Experimentally, the key problem is to reveal the correlation between the FE polarization and tunneling conductance. This has been achieved very recently when three experimental groups reported independently experimental observations of the TER effect associated with the switching of FE polarization of BaTiO₃ or Pb_1-χZr_χTiO₃ FE films.^19,20,21 As predicted,^16,17 the observed effects are really giant, showing the resistance change by two-three orders in magnitude.

Multiferroic Tunnel Junctions

MFTJ is a FTJ with FM electrodes or equivalently a magnetic tunnel junction (MTJ) with a FE barrier (see Figs. 2a and 2c).¹⁵ Electron tunneling from a FM metal electrode through a thin insulating barrier layer is spin-polarized. As a consequence, in a MTJ the tunneling current depends on the relative magnetization orientation of the two FM electrodes, a phenomenon known as tunneling magnetoresistance (TMR). In MFTJ the TER and TMR effects coexist.²² Therefore, MFTJ represents a four-state resistance device where resistance can be switched both by electric and magnetic fields.

First-principles transport calculations of SrRuO₃/BaTiO₃/SrRuO₃ MFTJs show that FE displacements affect differently the interface transmission for parallel and antiparallel magnetization orientation of the electrodes, resulting in TMR.⁴ The asymmetric interface termination (RuO₂/BaO versus TiO₂/SrO) creates a different polarization profile when the FE polarization is switched, producing TER. The same principles should apply to any MFTJ with asymmetric interfaces. Another type of MFTJ is feasible in which a single-phase multiferroic is used as barrier (Fig. 2d).³

In conclusion, the emerging field of research related to magnetoelectric interfaces and ferroelectric (multiferroic) tunnel junctions involves interesting fundamental physics and offer exciting opportunities for technological applications. New functionalities not available in conventional devices may open new directions for nanoelectronics, spintronics, and information storage.

References

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