Multiferroics—toward strong coupling between magnetization and polarization in a solid
Introduction
Highly efficient control of magnetism in terms of electric field or current in a solid may widen the bottle-neck of the state-of-art spin-electronics technology. Since the magnetoelectric (ME) effect, meaning magnetic (electric) induction of polarization P (magnetization M), was first confirmed in 1959–1960 theoretically by Dzyaloshinsky [1] and experimentally by Astrov [2], many magnetic materials have been demonstrated to show this effect [3]. Nevertheless, the magnitude of the observed ME effect has been too small to apply to any practical devices.
Multiferroics, the materials in which both ferromagnetism and ferroelectricity can coexist (Fig. 1), are the prospective candidates which can potentially host the gigantic ME effect. Strategy for exploring such multiferroics as showing strong M−P coupling and novel optical functions is argued in terms of the designed spin superstructure and tailor-made materials.
Section snippets
Toridal moment as the source of ME effect
To describe the genuinely electronic coupling between P and M in a solid, the toroidal moment, as defined byis the most fundamental quantity or order parameter [3], [4], [5]. The spin–orbit coupling term (λLS) in Hamiltonian as the quantum-mechanical source for the ME coupling can be converted to −λTp, where p is the electron momentum, and thereby the toroidal moment can be considered as built-in DC vector potential acting on the electrons. The macroscopic toroidal moment is
Bicritical-state phase control to enhance the ME effect
The multiferroic state or more generally the ferrotoroidic state is sure to show the liner ME effect, that is the linearly magnetic (electric) field induced polarization (magnetization). The ferrotoroidic GaFeO3 is one such example, in which the spin–orbit interaction converting the toroidic moment to the vector potential plays an essential role [5]. Therefore, the enhancement of the linear ME effect can be brought about by enlarging the spin–orbit interaction of the electrons which are
How to make magnetic ferroelectrics
To produce a ferroelectric state in a magnetically ordered state, the following cases may be considered:
- (1)
Bi3+ or Pb2+ (on the A-site) based perovskites with magnetic transition-metal ions on the B-site;
- (2)
FM tricolor superlattices;
- (3)
Charge ordering on a specific chemical lattice; and
- (4)
transverse-spiral (cycloidal) spin order.
As for (1), in literature it has been known that some polar (with build-in P) crystals can also show spontaneous M (FM), in particular, the perovskite structure involving the Bi3+
Toward electric control of magnetism
To realize the real multiferroics, namely the concurrent FM and ferroelectric state, with use of spiral (cycloidal) spin configuration, one may consider the conical spin state (Fig. 7(a)), that can be viewed as the sum of the FM component and transverse-spiral one. A remarkable characteristic expected for this kind of multiferroics is the electric (magnetic) reversal of the M (P) vector, as schematically shown in Fig. 1. Namely, the multiferroics of all spin origin may show the clamping of the
Acknowledgments
The author would like to thank T. Arima, Y. Shimada, and Y. Yamasaki for their help in preparing the manuscript.
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