A ferroelectric crystal exhibits a stable and switchable electrical polarization that is manifested in the form of cooperative atomic displacements. A ferromagnetic crystal exhibits a stable and switchable magnetization that arises through the quantum mechanical phenomenon of exchange. There are very few 'multiferroic' materials that exhibit both of these properties, but the 'magnetoelectric' coupling of magnetic and electrical properties is a more general and widespread phenomenon. Although work in this area can be traced back to pioneering research in the 1950s and 1960s, there has been a recent resurgence of interest driven by long-term technological aspirations.

/pdf/multiferroic-and-magnetoelectric-materials-2fpof7uzog.pdf

Multiferroic and magnetoelectric materials

The Becker-Kersten treatment of domain boundary movements is widely applicable in the interpretation of magnetization curves, but it does not account satisfactorily for the higher coercivities obtained, for example, in permanent magnet alloys. It is suggested that in many ferromagnetic materials there may occur ‘particles’ (this term including atomic segregates or ‘islands’ in alloys), distinct in magnetic character from the general matrix, and below the critical size, depending on shape, for which domain boundary formation is energetically possible. For such single-domain particles, change of magnetization can take place only by rotation of the magnetization vector, I O . As the field changes continuously, the resolved magnetization, I H , may change discontinuously at critical values, H O , of the field. The character of the magnetization curves depends on the degree of magnetic anisotropy of the particle, and on the orientation of ‘easy axes’ with respect to the field. The magnetic anisotropy may arise from the shape of the particle, from magneto-crystalline effects, and from strain. A detailed quantitative treatment is given of the effect of shape anisotropy when the particles have the form of ellipsoids of revolution (§§ 2, 3, 4), and a less detailed treatment for the general ellipsoidal form (§ 5). For the first it is convenient to use the non-dimensional parameter such that h = H /(| N a - N b |) I O , N a and N b being the demagnetization coefficients along the polar and equatorial axes. The results are presented in tables and diagrams giving the variation with h of I H / I O . For the special limiting form of the oblate spheroid there is no hysteresis. For the prolate spheroid, as the orientation angle, θ , varies from 0 to 90°, the cyclic magnetization curves change from a rectangular form with | h O | = 1, to a linear non-hysteretic form, with an interesting sequence of intermediate forms. Exact expressions are obtained for the dependence of h θ on θ , and curves for random distribution are computed. All the numerical results are applicable when the anisotropy is due to longitudinal stress, when h = HI 0 /3λδ, where λ is the saturation magnetostriction coefficient, and δ the stress. The results also apply to magneto-crystalline anisotropy in the important and representative case in which there is a unique axis of easy magnetization as for hexagonal cobalt. Estimates are made of the magnitude of the effect of the various types of anisotropy. For iron the maximum coercivities, for the most favourable orientation, due to the magneto-crystalline and strain effects are about 400 and 600 respectively. These values are exceeded by those due to the shape effect in prolate spheroids if the dimensional ratio, m , is greater than 1·1; for m = 10, the corresponding value would be about 10,000 (§7). A fairly precise estimate is made of the lower limit for the equatorial diameter of a particle in the form of a prolate spheroid below which boundary formation cannot occur. As m varies from 1 (the sphere) to 10, this varies from 1·5 to 6·1 x 10 -6 for iron, and from 6·2 to 25 x 10 -6 for nickel (§ 6). A discussion is given (§ 7) of the application of these results to ( a ) non-ferromagnetic metals and alloys containing ferromagnetic ‘impurities’, ( b ) powder magnets, ( e ) high coeravity alloys of the dispersion hardening type. In connexion with ( c ) the possible bearing on the effects of cooling in a magnetic field is indicated.

A Mechanism of Magnetic Hysteresis in Heterogeneous Alloys

BiFeO3 is perhaps the only material that is both magnetic and a strong ferroelectric at room temperature. As a result, it has had an impact on the field of multiferroics that is comparable to that of yttrium barium copper oxide (YBCO) on superconductors, with hundreds of publications devoted to it in the past few years. In this Review, we try to summarize both the basic physics and unresolved aspects of BiFeO3 (which are still being discovered with several new phase transitions reported in the past few months) and device applications, which center on spintronics and memory devices that can be addressed both electrically and magnetically.

Physics and Applications of Bismuth Ferrite

Long viewed as a topic in classical physics, ferroelectricity can be described by a quantum mechanical ab initio theory. Thin-film nanoscale device structures integrated onto Si chips have made inroads into the semiconductor industry. Recent prototype applications include ultrafast switching, cheap room-temperature magnetic-field detectors, piezoelectric nanotubes for microfluidic systems, electrocaloric coolers for computers, phased-array radar, and three-dimensional trenched capacitors for dynamic random access memories. Terabit-per-square-inch ferroelectric arrays of lead zirconate titanate have been reported on Pt nanowire interconnects and nanorings with 5-nanometer diameters. Finally, electron emission from ferroelectrics yields cheap, high-power microwave devices and miniature x-ray and neutron sources.

http://science.sciencemag.org/content/sci/315/5814/954.full.pdf

Applications of Modern Ferroelectrics

http://files.janapv.webnode.cz/200000097-8a03f8afdf/ex_bias_nano.pdf

Exchange bias in nanostructures

"Reprinted from the Physical review, vol. 70, nos. 11 and 12, 965-971, Dec. 1 and 15, 1946."

Theory of the structure of ferromagnetic domains in films and small particles

Interpretation of Anomalous Larmor Frequencies in Ferromagnetic Resonance Experiment

A theoretical discussion is given of the application of microwave-absorption measurements to the determination of energy levels in single crystals of paramagnetic salts. Selection rules are given for magnetic-dipole transitions between sublevels in the presence of crystalline electric fields of cubic, tetragonal, trigonal, and rhombic symmetry. The Zeeman effect in the presence of crystalline electric fields is discussed in some detail for three special cases: (a)$J=\frac{5}{2}$, cubic field; (b) $J=\frac{7}{2}$, cubic field; (c) $J=\frac{3}{2}$, trigonal field. These examples may correspond approximately to certain magnetically dilute salts containing ${\mathrm{Fe}}^{+++}$, ${\mathrm{Gd}}^{+++}$, and ${\mathrm{Cr}}^{+++}$ ions, respectively, provided that exchange interactions do not play an important role and that the assumed symmetries are approximately correct. Numerical values are tabulated for the relative frequencies and line strengths associated with magnetic-dipole transitions in the cases discussed. The character of the spectra may change radically between the limit where the Zeeman splitting is small in comparison with the Stark splitting, and the opposite limit where the Stark splitting may be neglected.

Crystalline stark splitting and microwave resonance absorption in paramagnetic salts

http://science.sciencemag.org/content/sci/105/2719/150.full.pdf

The Nature and Development of Operations Research

A discussion is given of the long period changes in magnetization in a mild steel specimen subjected to alternating stresses while in a weak magnetic field. The magnetization changes appear to occur with two time constants, of the order of three months and five years. A formal treatment of the phenomena is given along the lines of the time-dependent barrier potential used by Snoek in discussing other magnetic relaxation processes. The increase in the potential barrier is pictured as caused by the mechanical relaxation of local strains.

Charles Kittel

Papers

Theory of the structure of ferromagnetic domains in films and small particles

Interpretation of Anomalous Larmor Frequencies in Ferromagnetic Resonance Experiment

Crystalline stark splitting and microwave resonance absorption in paramagnetic salts

The Nature and Development of Operations Research

Theory of Long Period Magnetic Relaxation