BiFeO 3 thin ﬁlms - Thin ﬁlm multiferroics

6. Multiferroism and magnetoelectricity

6.4. Thin ﬁlm multiferroics

6.4.3. BiFeO 3 thin ﬁlms

No other single-phase multiferroic has experienced the same level of attention as BiFeO3 (BFO) in the last seven years and because of this we will discuss the evolution of this material in more length.

6.4.3.1. Historical perspective. The perovskite BFO was ﬁrst pro-duced in the late 1950s[338]and many of the early studies were focused on the same concepts important today—the potential for magnetoelectric coupling[339]. Throughout the 1960s and 1970s much controversy surrounded the true physical and structural properties of BFO, but as early as the 1960s BFO was suspected to be an antiferromagnetic, ferroelectric multiferroic[340,341]. The true ferroelectric nature of BFO, however, remained somewhat in question until ferroelectric measurements made at 77 K in 1970 [341]revealed a spontaneous polarization of 6.1

m

C/cm²along the 1 1 1-direction which was found to be consistent with the rhombohedral polar space group R3c determined from single crystal X-ray diffraction [342] and neutron diffraction studies [343]. These ﬁndings were at last conﬁrmed by detailed structural characterization of ferroelectric/ferroelastic monodomain single crystal samples of BFO in the late 1980s[339]. Chemical etching experiments on ferroelastic single domains later proved without a doubt that the BFO was indeed polar, putting to rest the hypothesis

Fig. 24. BiFeO3. (a) Structure of BiFeO3shown looking (a) down the pseudocubic-[1 1 0], (b) down the pseudocubic-[1 1 1] polarization direction, and (c) a general three-dimensional view of the structure. (d) The magnetic structure of BiFeO3is shown including G-type antiferromagnetic ordering and the formation of the weak ferromagnetic moment. (Adapted from Ref.[285].)

Fig. 23. BiMnO3. (a) Magnetization curve of a BiMnO3ﬁlm cooled under no applied magnetic ﬁeld. The inset shows the ferromagnetic hysteresis loop at 5 K. (Adapted from Ref.

[327].) (b) P–E hysteresis loop of a thin ﬁlm of BiMnO3on Si (1 0 0) above and below the ferromagnetic TC. (Adapted from Ref.[325].)

that BFO might be antiferroelectric, and proved that the ferro-electric/ferroelastic phase was stable from 4 to 1103 K[344]. The structure of BFO can be characterized by two distorted perovskite blocks connected along their body diagonal or the pseudocubic h1 1 1i, to build a rhombohedral unit cell (Fig. 24(a)). In this structure the two oxygen octahedra of the cells connected along the h1 1 1i are rotated clockwise and counterclockwise around theh1 1 1i by 13.8(3)8 and the Fe-ion is shifted by 0.135 A˚ along the same axis away from the oxygen octahedron center position. The ferroelectric state is realized by a large displacement of the Bi-ions relative to the FeO6octahedra (Fig. 24(a)–(c))[339,345].

During the 1980s, the magnetic nature of BFO was studied in detail. Early studies indicated that BFO was a G-type antiferro-magnet (G-type antiferroantiferro-magnetic order is shown schematically in Fig. 24(d)) with a Ne´el temperature of 673 K[346]and possessed a cycloidal spin structure with a period of 620 A˚[347]. This spin structure was found to be incommensurate with the structural lattice and was superimposed on the antiferromagnetic order. It was also noted that if the moments were oriented perpendicular to the h1 1 1i-polarization direction the symmetry also permits a small canting of the moments in the structure resulting in a weak ferromagnetic moment of the Dzyaloshinskii–Moriya type (Fig. 24(d))[348,349].

In 2003 a paper focusing on the growth and properties of thin ﬁlms of BFO spawned a hailstorm of research into thin ﬁlms of BFO that continues to the present day. The paper reported enhancements of polarization and related properties in heteroepitaxially con-strained thin ﬁlms of BFO[288]. Structural analysis of the ﬁlms suggested differences between ﬁlms (with a monoclinic structure) and bulk single crystals (with a rhombohedral structure) as well as enhancement of the polarization up to 90

m

C/cm² at room temperature and enhanced thickness-dependent magnetism com-pared to bulk samples. In reality, the high values of polarization observed actually represented the intrinsic polarization of BFO.

Limitations in the quality of bulk crystals had kept researchers from observing such high polarization values until much later in bulk samples[350]. More importantly this report indicated a magneto-electric coupling coefﬁcient as high as 3 V/cm Oe at zero applied ﬁeld[288]. A series of detailed ﬁrst principles calculations utilizing the local spin-density approximation (LSDA) and LSDA + U methods helped shed light on the ﬁndings in this paper. Calculations of the spontaneous polarization in BFO suggested a value between 90 and 100

m

C/cm²(consistent with those measured in 2003)[351]which have since been conﬁrmed by many other experimental reports.

Other theoretical treatments attempted to understand the nature of magnetism and coupling between order parameters in BFO. Such calculations conﬁrmed the possibility of weak ferromagnetism arising from a canting of the antiferromagnetic moments in BFO. The canting angle was calculated to be 18 and would result in a small, but measurable, magnetization of 0.05

m

Bper unit cell[352]. It was also found that the magnetization should be conﬁned to an energetically degenerate easy {1 1 1} perpendicular to the polariza-tion direcpolariza-tion in BFO. These same calculapolariza-tions further discussed the connection of the weak ferromagnetism and the structure (and therefore ferroelectric nature) of BFO. This allowed the authors to extract three conditions necessary to achieve electric-ﬁeld-induced magnetization reversal: (i) the rotational and polar distortions must be coupled; (ii) the degeneracy between different conﬁgurations of polarization and magnetization alignment must be broken; (iii) there must be only one easy magnetization axis in the (1 1 1) which could be easily achieved by straining the material[352].

Nonetheless, the true nature of magnetism in thin ﬁlm BFO continues to be a contentious subject. The original work of Wang et al. presented an anomalously large value of magnetic moment (of the order of 70 emu/cm³)[288], which is signiﬁcantly higher than the expected canted moment of 8 emu/cm³. There have been

several studies aimed at clarifying the origins of this anomalous magnetism. Eerenstein et al. [353] proposed that the excess magnetism was associated with magnetic second phases (such as

g

-Fe2O3); this was supported by the studies of Be´a et al.[354]who showed that BFO ﬁlms, when grown under reducing conditions (for example under oxygen pressures lower than 1 10³Torr) showed enhanced magnetism as a consequence of the formation of magnetic second phases. It is, however, important to note that low oxygen pressure during growth is not the cause for the enhanced moment in the 2003 report by Wang et al. where ﬁlms were grown in oxygen pressures between 100 and 200 mTorr and cooled in 760 Torr rendering formation of such secondary magnetic phases thermo-dynamically unlikely and there was no evidence (despite extensive study of samples with X-ray diffraction and transmission electron microscopy techniques) for such second phases. Furthermore, subsequent X-ray magnetic circular dichroism studies supported the assertion that this magnetism is not from a magnetic

g

-Fe2O3

impurity phase[355]. To date, additional mixed reports—including reports of enhanced magnetism in nanoparticles of BFO[356]as well as the observation of samples exhibiting no such enhancement—

have been presented. It is thus fair to say that this one issue that remains unresolved in a rigorous sense.

6.4.3.2. Growth of BiFeO3 ﬁlms. Today, much progress has been made in understanding the structure, properties, and growth of thin ﬁlms of BFO. High quality epitaxial BFO ﬁlms have been grown via pulsed laser deposition [288,357], radio-frequency (RF) sputtering [358,359], metalorganic chemical vapor deposition (MOCVD)[360,361], and chemical solution deposition (CSD)[362]

on a wide range of substrates including traditional oxide substrates as well as Si[357,363]and GaN[364]. This work has shown that high quality ﬁlms, like those shown inFig. 25can be produced.

Typical XRD

u

measurements (Fig. 25(a)) show the ability of researchers to produce high quality, fully epitaxial, single phase ﬁlms of BFO (data here is for a BFO/SRO/STO (0 0 1) hetero-structure). Detailed XRD analysis has shown that ﬁlms possess a monoclinic distortion of the bulk rhombohedral structure over a wide range of thicknesses, but the true structure of very thin ﬁlms (<15 nm) remains unclear [365]. The quality of such hetero-structures as produced by pulsed laser deposition can be probed further by transmission electron microscopy (TEM) (Fig. 25(b)).

TEM imaging reveals ﬁlms that are uniform over large areas and with the use of high resolution TEM we can examine the atomically abrupt, smooth, and coherent interface between BFO and a commonly used bottom electrode material SRO.

In Section4.3.4, we discussed the advances that have been made in controlling ferroelectric domain structures of thin ﬁlms of BFO.

This work, in turn, has enabled signiﬁcant progress in the under-standing of this complex multiferroic material. In addition to being of great interest for photonic devices, nanolithography, and more, ﬁne control of the domain structures and the ability to create extremely high quality thin ﬁlms of these materials make it possible to probe a number of important questions related to this material.

This includes, the evolution of magnetism in thin ﬁlms (i.e., variations from the bulk picture and the mechanism of enhanced magnetism in thin ﬁlms), the role of domain walls in determining macroscopic properties, doping effects in BFO, the nature of magnetoelectric coupling in these materials, and more. In the next few sections, we will address these different questions in detail.

6.4.3.3. Evolution of antiferromagnetism in BiFeO3thin ﬁlms. As was discussed in Section6.4.3.1, the structure of BFO can be character-ized by two distorted perovskite blocks connected along their body diagonal or the pseudocubic h1 1 1i to build a rhombohedral unit cell, possesses G-type antiferromagnet order with the moments conﬁned to a plane perpendicular to the h1 1 1i-polarization

directions, and possesses symmetry that permits a small canting of the moments in the structure resulting in a weak ferromagnetic moment of the Dzyaloshinskii–Moriya type[348,349]. Also recall that Ederer and Spaldin suggested that only one easy magnetization axis in the energetically degenerate 1 1 1-plane might be selected when one was to strain the material[352]. Thus, one critical question concerning magnetism in multiferroics such as BFO that is of both fundamental and technological importance is how this order parameter develops with strain and size effects?

Using angle and temperature dependent dichroic measure-ments and photoemission spectromicroscopy, Holcomb et al.[366]

have discovered that the antiferromagnetic order in BFO evolves and changes systematically as a function of thickness and strain.

Lattice mismatch induced strain is found to break the easy-plane magnetic symmetry of the bulk and leads to an easy axis of magnetization which can be controlled via the sign of the strain—

1 1 0-type for tensile strain and 1 1 2-type for compressive strain.

This understanding of the evolution of magnetic structure and the ability to manipulate the magnetism in this model multiferroic has signiﬁcant implications for eventual utilization of such magneto-electric materials in applications.

6.4.3.4. Role of domain walls in BiFeO3. A number of recent ﬁndings are poised to deﬁnitively answer the questions surrounding the wide array of magnetic properties observed in BFO thin ﬁlms.

There is now a growing consensus that epitaxial ﬁlms (with a thickness less than 100 nm) are highly strained and thus the crystal structure is more akin to a monoclinic phase rather than the bulk rhombohedral structure. Furthermore, a systematic depen-dence of the ferroelectric domain structure in the ﬁlm as a function of the growth rate has been observed [367]. Films grown very slowly (for example by MBE, laser-MBE, or off-axis sputtering) exhibit a classical stripe-like domain structure that is similar to ferroelastic domains in tetragonal Pb(Zrx,Ti1x)O3 ﬁlms. Due to symmetry considerations, two sets of such twins are observed.

These twins are made up of 718 ferroelastic walls, that form on the {1 0 1}-type planes (which is a symmetry plane). In contrast, if the ﬁlms are grown rapidly (as was done in the original work of Wang et al.[288]) the domain structure is dramatically different. It now resembles a mosaic-like ensemble that consists of a dense distribution of 718, 1098, and 1808 domain walls. It should be noted that 1098 domain walls form on {0 0 1}-type planes (which is not a symmetry plane for this structure). Preliminary measure-ments reveal a systematic difference in magnetic moment between samples possessing different types and distributions of domain

walls. The work of Martin et al.[367]suggests that such domain walls could play a key role in the many observations of enhanced magnetic moment in BFO thin ﬁlms.

This suggestion builds off of the work of Prˇı´vratska´ and Janovec [368,369], where detailed symmetry analyzes were used to make the conclusion that magnetoelectric coupling could lead to the appearance of a net magnetization in the middle of antiferromag-netic domain walls. Speciﬁcally, they showed that this effect is allowed for materials with the R3c space group (i.e., that observed for BFO). Although such analysis raises the possibility of such an effect, the group-symmetry arguments do not allow for any quantitative estimate of that moment. The idea that novel properties could occur at domain walls in materials presented by Prˇı´vratska´ and Janovec is part of a larger ﬁeld of study of the morphology and properties of domains and their walls that has taken place over the last 50 years with increasing recent attention given to the study novel functionality at domain walls[370–372].

For instance, recent work has demonstrated that spin rotations across ferromagnetic domain walls in insulating ferromagnets can induce a local polarization in the walls of otherwise non-polar materials[372,373], preferential doping along domain walls has been reported to induce 2D superconductivity in WO3x[374]and enhanced resistivity in phosphates[375], while in paraelectric (non-polar) SrTiO3the ferroelastic domain walls appear to be ferroelec-trically polarized [376]. Taking this idea one step further, Daraktchiev et al. [377,378] have proposed a thermodynamic (Landau-type) model with the aim of quantitatively estimating whether the walls of BFO can be magnetic and, if so, to what extent they might contribute to the observed enhancement of magnetiza-tion in ultrathin ﬁlms. One can develop a simple thermodynamic potential incorporating two order parameters expanded up to P⁶and M⁶terms (the transitions in BFO are found experimentally to be ﬁrst order, and the low-symmetry (P₀, 0) phase is described here) with biquadratic coupling between the two order parameters (biquadratic coupling is always allowed by symmetry, and therefore always present in any system with two order parameters). Because biquadratic free energy terms such as P²M²are scalars in any symmetry group, this potential can be written thusly:

GMP¼ G0þ

k

2ðrPÞ²þ

l

2ðrMÞ²þ LMPðP; MÞ

¼ G0þ

k

2ðrPÞ²þ

l

2ðrMÞ²þ

a

2P²þ

b

4P⁴þ

h

6P⁶þa 2M² þb

4M⁴þn 6M⁶þ

g

2P²M² (9)

Fig. 25. . Thin ﬁlms of BiFeO3. (a) X-ray diffraction results from a fully epitaxial, single phase BFO/SRO/STO(0 0 1) heterostructure. (b) Low (top) and high (bottom) resolution transmission electron microscopy images of BFO/SRO/STO(0 0 1) heterostructure. (Adapted from Ref.[285].)

When one goes from +P to P, it is energetically more favorable for the domain wall energy trajectory not to go through the centre of the landscape (P = 0, M = 0), but to take a diversion through the saddle points at M06¼ 0, thus giving rise to a ﬁnite magnetization (Fig. 26). The absolute values of the magnetic moment at the domain wall will depend on the values of the Landau coefﬁcients as well as the boundary conditions imposed on the system, namely whether the material is magnetically ordered or not. Analysis of the phase space of this thermodynamic potential shows that it is possible for net magnetization to appear in the middle of ferroelectric walls even when the domains themselves are not ferromagnetic (Fig. 26(b)). The authors of this model note, however, that it is presently only a ‘‘toy model’’ which does not take into account the exact symmetry of BFO, so it cannot yet quantitatively estimate how much domain walls can contribute to the magnetization. The exact theory of magnetoelectric coupling at the domain walls of BFO also remains to be formulated.

Recently, a holistic picture of the connection between proces-sing, structure, and properties has brought to light the role of magnetism at ferroelectric domain walls in determining the magnetic properties in BFO thin ﬁlms. By controlling domain structures through epitaxial growth constraints and probing these domain walls with exchange bias studies, X-ray magnetic dichroism based spectromicroscopy, and high resolution transmis-sion electron microscopy He et al.[379]have demonstrated that the formation of certain types of ferroelectric domain walls (i.e., 1098 walls) can lead to enhanced magnetic moments in BFO.

Building off the work of Martin et al.[367], the authors of this study were able to demonstrate that samples possessing 1098 domain walls show signiﬁcantly enhanced circular dichroism that is consistent with collective magnetic correlations, while samples with only 718 domain walls show no circular dichroism. In summary, it appears certain domain walls can give rise to enhanced magnetic behavior in BFO thin ﬁlms.

It is also important to note that Seidel et al.[380], motivated by the desire to understand similar magnetic properties at domain walls in BFO, undertook a detailed scanning probe-based study of these materials and discovered a new and previously unantici-pated ﬁnding: the observation of room temperature electronic conductivity at certain ferroelectric domain walls. The origin of the observed conductivity was explored using high-resolution trans-mission electron microscopy and ﬁrst-principles density func-tional computations. The results showed that domain walls in a multiferroic ferroelectric such as BFO, can exhibit unusual

electronic transport behavior on a local scale that is quite different from that in the bulk of the material. Using a model (1 1 0)-oriented BFO/SRO/STO heterostructure with a smooth surface (Fig. 27(a)), the researchers were able to switch the BFO material in such a way that enabled them to create all the different types of domain walls possible in BFO (i.e., 718, 1098, and 1808 domain walls) in a local region (Fig. 27(b) and (c)). Conducting-atomic force microscopy (c-AFM) measurements (Fig. 27(d)) revealed conduc-tion at 1098 and 1808 domain walls. Detailed high-resoluconduc-tion transmission electron microscopy studies (Fig. 27(e)) revealed this conductivity was, in part, structurally induced and can be activated and controlled on the scale of the domain wall width—about 2 nm in BFO. From the combined study of conductivity measurements, electron microscopy analysis, and density functional theory calculations, two possible mechanisms for the observed conduc-tivity at the domain walls have been suggested: (1) an increased carrier density as a consequence of the formation of an electrostatic potential step at the wall; and/or (2) a decrease in the band gap within the wall and corresponding reduction in band offset with the c-AFM tip. It was noted that both possibilities are the result of structural changes at the wall and both may, in principle, be acting simultaneously, since they are not mutually exclusive.

6.4.3.5. Magnetoelectric coupling in BiFeO₃. Although many researchers anticipated strong magnetoelectric coupling in BFO, until the ﬁrst evidence for this coupling in 2003 there was no deﬁnitive proof. Two years after this ﬁrst evidence, a detailed report was published in which researchers observed the ﬁrst visual evidence for electrical control of antiferromagnetic domain structures in a single phase multiferroic at room temperature.

By combining X-ray photoemission electron microscopy (PEEM) imaging of antiferromagnetic domains (Fig. 28(a) and (b)) and piezoresponse force microscopy (PFM) imaging of ferroelectric domains (Fig. 28(c) and (d)) the researchers were able to observe direct changes in the nature of the antiferromagnetic domain structure in BFO with application of an applied electric ﬁeld (Fig. 28(e)) [381]. This research showed that the ferroelastic switching events (i.e., 718 and 1098) resulted in a corresponding rotation of the magnetization plane in BFO (Fig. 28(f)) and has paved the way for further study of this material in attempts to gain room temperature control of ferromagnetism (to be discussed in detail later). This work has since been conﬁrmed by neutron diffraction experiments in bulk BFO as well[382].

Fig. 26. Shape of ferroelectric polarization and magnetism across a domain wall in BiFeO3. (a) Ferroelectric polarization goes to zero at the center of the domain wall. (b) A net magnetization appears at the center of the domain wall even though the domains themselves do not possess a net moment. (Adapted from Refs.[377,378].)

6.4.3.6. Doped BiFeO3thin ﬁlms. In the last few years, attention has also been given to studying doped BFO thin ﬁlms (both A-site and B-site doping) in an attempt to reduce leakage currents and alter the magnetic properties[383]. Doping the B-site of BFO with Ti⁴⁺

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