Analogies and Differences Between Ferroelectrics and Ferromagnets

Analogies and Differences between Ferroelectrics and Ferromagnets Nicola A. Spaldin Materials Department, University of California, Santa Barbara, CA 93106-5050, USA [email protected] ferro Fer"ro A prefix, or combining form, indicating ferrous iron as an ingredient; as, ferrocyanide. [From Latin ferrum, iron.] Source: Webster’s Revised Unabridged Dictionary, (c) 1996, 1998 MICRA, Inc. Abstract. We describe the similarities and differences between ferromagnets – materials that have a spontaneous magnetization that is switchable by an applied magnetic field – and ferroelectrics, which have an analogous electric-field switchable electric polarization. After comparing the driving force for ion off-centering that causes the polarization in ferroelectrics with the physics of spin polarization that causes the magnetization of ferromagnets, we analyze the mechanisms of domain formation and resulting domain structures in both material classes. We describe the emerging technologies of ferroelectric and magnetoresistive random access memories, and discuss the behavior of magnetoelecric multiferroics, which combine ferromagnetism and ferroelectricity in the same phase. The “ferro” part in the name “ferroelectric” is something of a misnomer, since it does not refer to the presence of iron in ferroelectric materials. Rather it arises from the many similarities in behavior between ferroelectrics, with their spontaneous electric polarization, and ferromagnets, with their spontaneous magnetization. Indeed one of the earliest observations of ferroelectricity ([1]) describes the electric hysteresis in Rochelle salt as “analogous to the magnetic hysteresis in the case of iron.” A systematic comparison between the behavior of ferromagnets and ferroelectrics, does not, to our knowledge, exist in the literature. The purpose of this chapter is to outline the similarities in behavior between ferromagnets and ferroelectrics, and, perhaps more importantly, to point out the differences in their fundamental physics and consequent applications. We hope that the comparison will be useful both to readers with a background in ferroelectrics, who can benefit from the K. Rabe, C. H. Ahn, J.-M. Triscone (Eds.): Physics of Ferroelectrics: A Modern Perspective, Topics Appl. Physics 105, 175–218 (2007) © Springer-Verlag Berlin Heidelberg 2007 176 Nicola A. Spaldin Fig. 1. Comparison of hysteresis loops in (a)BaTiO3, a typical ferroelectric [2] (copyright (1950) by the American Physical Society), and (b) Fe, a typical ferromagnet [3]. Note that the forms of the hysteresis curves are rather similar in the two cases techniques, concepts and applications developed in the more mature field of ferromagnetism, as well as ferromagnetism researchers learning about ferroelectrics. We feel that such a discussion is particularly timely in light of the flurry of recent interest in so-called multiferroic materials, which are simul- taneously ferromagnetic and ferroelectric. Superficially there are indeed many similarities between ferroelectrics and ferromagnets. Let us start with the basic definition; a ferroelectric is defined to be a material with a spontaneous electric polarization that is switchable by an applied electric field. Likewise, a ferromagnet has a spontaneous magnetization that can be reoriented by an external magnetic field. (Note that in this chapter we will use “polarization” as a generic term to describe both magnetic and electric polarization.) Usually the switching process is associ- ated with a hysteresis, which can be very similar in form in the two cases (Fig. 1). And often a change in the polarization orientation is accompanied by a change in shape. In both cases the macroscopic polarization can be reduced to zero by the presence of domains; that is regions of oppositely oriented (and therefore canceling) polarization within the sample. Both ferromagnetic and ferroelectric polarization decrease with increasing temperature, with a phase transition to an unpolarized (paramagnetic or paraelectric) state often oc- curring at high temperature. Of course, the microscopic features that lead to ferromagnetism and ferroelectricity are quite distinct; ferroelectrics have an asymmetry in charge (either ionic or electronic or both), whereas ferromagnets have an asymmetry in electronic spin. On the applications front, the coupling between the polarization order parameter and the lattice strain leads to the properties of piezomagnetism in ferromagnets and piezoelectricity in ferroelectrics. Piezoelectric effects tend to be larger than piezomagnetic, and so ferroelectric piezoelectrics dominate in transducer and actuator technologies. In addition, the hysteresis that causes the spontaneous polarization to persist in the absence of an applied field leads to storage applications in which the direction of either electric or magnetic Ferroelectrics and Ferromagnets 177 polarization represents the “1” or “0” of the data bit. Here, magnetic materials have the largest market share, for example in computer hard disks, and magnetic tape, although ferroelectrics are an upcoming technology for information storage. This contribution is organized as follows: In Sect. 1 (Fundamentals) we compare the fundamental driving force for ion offcentering that causes the electric polarization in ferroelectrics with the physics of spin-polarization that results in the magnetization of ferromagnets. In addition, we compare the domain structures, and mechanisms of domain formation in ferromagnets and ferroelectrics. In Sect. 2 (Applications) we focus on the use of ferromagnets and ferroelectrics in random access memory (RAM) devices, and compare the emerging technologies of ferroelectric RAM and magnetoresistive RAM. Finally, in Sect. 3 (Multiferroics) we discuss the rather limited class of materials known as magnetoelectric multiferroics that are both ferromagnetic and ferroelectric. 1 Fundamentals 1.1 Understanding the Origin of Spontaneous Polarization In this section we outline the mechanisms that cause some materials to be either magnetically or electrically polarized, while most are not. We will see that, in spite of the similarities in the macroscopic phenomena described as ferromagnetism or ferroelectricity, the electron-level details that lead to electric or magnetic polarization arise from quite different origins. 1.1.1 What Causes Ferroelectricity? In order for a material to exhibit a spontaneous electric polarization it must have a noncentrosymmetric arrangement of the constituent ions and their corresponding electrons. To be classified as a ferroelectric, the electric polarization must in addition be switchable, and so a nonreconstructive transition between two stable states of opposite polarization must be accessible at known experimental fields. In this section we review the origins of ionic offcentering in known ferroelectrics, and show that, in most cases, the polar phase is stabilized by energy-lowering chemical-bond formation. Note that a permanent noncentrosymmetric arrangement of the ions is insufficient; some noncentrosymmetric structures, such as the wurtzite structure (Fig. 2), do not permit ferroelectricity since they can not be switched at known experimental electric fields. Second-Order Jahn–Teller Ferroelectrics Many ferroelectric structures can be considered to be derivatives of a nonpolar, centrosymmetric prototype phase, of which the most widely studied 178 Nicola A. Spaldin Fig. 2. Materials such as ZnO and GaN, which adopt the noncentrosymmetric wurtzite structure shown here, have spontaneous electric polarization but are not ferroelectric since they do not switch in response to an applied electric field Fig. 3. The centrosymmetric cubic perovskite structure. The small B cation (in black)isat thecenterofanoctahedronofoxygenanions (in gray). The large A cations (white) occupy the unit-cell corners example is the perovskite structure shown in Fig. 3. The noncentrosymmetric structure is reached by shifting either the A or B cations (or both) offcenter relative to the oxygen anions, and the spontaneous polarization derives largely from the electric dipole moment created by this shift. If the bonding in an ideal cubic perovskite were entirely ionic, and the ionic radii were of the correct size to ensure ideal packing, then the structure would remain centrosymmetric, and therefore not ferroelectric. This is be- cause, although long-range Coulomb forces favor the ferroelectric state, the short-range repulsions between the electron clouds of adjacent ions are mini- mized for nonpolar, cubic structures [4, 5]. The existence or absence of ferroelectricity is determined by a balance between these short-range repulsions, that favor the nonferroelectric symmetric structure, and additional bonding considerations which act to stabilize the distortions necessary for the ferroelectric phase [6]. The changes in chemical bonding that stabilize distorted structures have long been recognized in the field of coordination chemistry, and are classified as second-order Jahn–Teller effects [7–9], or sometimes pseudo-Jahn–Teller effects [10], in the chemistry literature. Ferroelectrics and Ferromagnets 179 The origin of the second-order, or pseudo-, Jahn–Teller effect can be seen by writing down a perturbative expansion of the energy of the electronic ground state, E(Q), as a function of the coordinate of the distortion, Q [11]: E(Q)=E(0) + 0|(δH/δQ) |0Q 0 | | | |2 1 | 2 2 | − 0 (δH/δQ)0 n 2 + 0 (δ H/δQ )0 0 2 n Q 2 En − E(0) + ··· . (1) Here, E(0) is the energy of the

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