Ferroelectricity

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Ferroelectricity is a characteristic of certain materials that have a spontaneous electric polarization that can be reversed by the application of an external electric field. [1] [2] All ferroelectrics are pyroelectric, with the additional property that their natural electrical polarization is reversible. The term is used in analogy to ferromagnetism, in which a material exhibits a permanent magnetic moment. Ferromagnetism was already known when ferroelectricity was discovered in 1920 in Rochelle salt by Valasek. [3] Thus, the prefix ferro, meaning iron, was used to describe the property despite the fact that most ferroelectric materials do not contain iron. Materials that are both ferroelectric and ferromagnetic are known as multiferroics.

A spontaneous process is the time-evolution of a system in which it releases free energy and it moves to a lower, more thermodynamically stable energy state. The sign convention for free energy follows the general convention for thermodynamic measurements, in which a release of free energy from the system corresponds to a negative change in the free energy of the system and a positive change in the free energy of the surroundings.

Polarization density physical quantity

In classical electromagnetism, polarization density is the vector field that expresses the density of permanent or induced electric dipole moments in a dielectric material. When a dielectric is placed in an external electric field, its molecules gain electric dipole moment and the dielectric is said to be polarized. The electric dipole moment induced per unit volume of the dielectric material is called the electric polarization of the dielectric.

Ferromagnetism physical phenomenon

Ferromagnetism is the basic mechanism by which certain materials form permanent magnets, or are attracted to magnets. In physics, several different types of magnetism are distinguished. Ferromagnetism is the strongest type and is responsible for the common phenomena of magnetism in magnets encountered in everyday life. Substances respond weakly to magnetic fields with three other types of magnetism, paramagnetism, diamagnetism, and antiferromagnetism, but the forces are usually so weak that they can only be detected by sensitive instruments in a laboratory. An everyday example of ferromagnetism is a refrigerator magnet used to hold notes on a refrigerator door. The attraction between a magnet and ferromagnetic material is "the quality of magnetism first apparent to the ancient world, and to us today".

Contents

Polarization

Dielectric polarization Dielectric polarisation.svg
Dielectric polarization
Paraelectric polarization Paraelectric polarisation.svg
Paraelectric polarization
Ferroelectric polarization Ferroelectric polarisation.svg
Ferroelectric polarization

When most materials are polarized, the polarization induced, P, is almost exactly proportional to the applied external electric field E; so the polarization is a linear function. This is called dielectric polarization (see figure). Some materials, known as paraelectric materials, [4] show a more enhanced nonlinear polarization (see figure). The electric permittivity, corresponding to the slope of the polarization curve, is not constant as in dielectrics but is a function of the external electric field.

Permittivity physical quantity, measure of the resistance to the electric field

In electromagnetism, absolute permittivity, often simply called permittivity, usually denoted by the Greek letter ε (epsilon), is the measure of capacitance that is encountered when forming an electric field in a particular medium. More specifically, permittivity describes the amount of charge needed to generate one unit of electric flux in a particular medium. Accordingly, a charge will yield more electric flux in a medium with low permittivity than in a medium with high permittivity. Permittivity is the measure of a material's ability to store an electric field in the polarization of the medium.

In addition to being nonlinear, ferroelectric materials demonstrate a spontaneous nonzero polarization (after entrainment, see figure) even when the applied field E is zero. The distinguishing feature of ferroelectrics is that the spontaneous polarization can be reversed by a suitably strong applied electric field in the opposite direction; the polarization is therefore dependent not only on the current electric field but also on its history, yielding a hysteresis loop. They are called ferroelectrics by analogy to ferromagnetic materials, which have spontaneous magnetization and exhibit similar hysteresis loops.

Hysteresis dependence of the state of a system on its history

Hysteresis is the dependence of the state of a system on its history. For example, a magnet may have more than one possible magnetic moment in a given magnetic field, depending on how the field changed in the past. Plots of a single component of the moment often form a loop or hysteresis curve, where there are different values of one variable depending on the direction of change of another variable. This history dependence is the basis of memory in a hard disk drive and the remanence that retains a record of the Earth's magnetic field magnitude in the past. Hysteresis occurs in ferromagnetic and ferroelectric materials, as well as in the deformation of rubber bands and shape-memory alloys and many other natural phenomena. In natural systems it is often associated with irreversible thermodynamic change such as phase transitions and with internal friction; and dissipation is a common side effect.

Magnetization physical quantity

In classical electromagnetism, magnetization or magnetic polarization is the vector field that expresses the density of permanent or induced magnetic dipole moments in a magnetic material. The origin of the magnetic moments responsible for magnetization can be either microscopic electric currents resulting from the motion of electrons in atoms, or the spin of the electrons or the nuclei. Net magnetization results from the response of a material to an external magnetic field, together with any unbalanced magnetic dipole moments that may be inherent in the material itself; for example, in ferromagnets. Magnetization is not always uniform within a body, but rather varies between different points. Magnetization also describes how a material responds to an applied magnetic field as well as the way the material changes the magnetic field, and can be used to calculate the forces that result from those interactions. It can be compared to electric polarization, which is the measure of the corresponding response of a material to an electric field in electrostatics. Physicists and engineers usually define magnetization as the quantity of magnetic moment per unit volume. It is represented by a pseudovector M.

Typically, materials demonstrate ferroelectricity only below a certain phase transition temperature, called the Curie temperature (TC) and are paraelectric above this temperature: the spontaneous polarization vanishes, and the ferroelectric crystal transforms into the paraelectric state. Many ferroelectrics lose their piezoelectric properties above Tc completely, because their paraelectric phase has a centrosymmetric crystal structure. [5]

Applications

The nonlinear nature of ferroelectric materials can be used to make capacitors with tunable capacitance. Typically, a ferroelectric capacitor simply consists of a pair of electrodes sandwiching a layer of ferroelectric material. The permittivity of ferroelectrics is not only tunable but commonly also very high in absolute value, especially when close to the phase transition temperature. Because of this, ferroelectric capacitors are small in physical size compared to dielectric (non-tunable) capacitors of similar capacitance.

Ferroelectric capacitor

Ferroelectric capacitor is a capacitor based on a ferroelectric material. In contrast, traditional capacitors are based on dielectric materials. Ferroelectric devices are used in digital electronics as part of ferroelectric RAM, or in analog electronics as tunable capacitors (varactors).

The spontaneous polarization of ferroelectric materials implies a hysteresis effect which can be used as a memory function, and ferroelectric capacitors are indeed used to make ferroelectric RAM [6] for computers and RFID cards. In these applications thin films of ferroelectric materials are typically used, as this allows the field required to switch the polarization to be achieved with a moderate voltage. However, when using thin films a great deal of attention needs to be paid to the interfaces, electrodes and sample quality for devices to work reliably. [7]

Ferroelectric RAM

Ferroelectric RAM is a random-access memory similar in construction to DRAM but using a ferroelectric layer instead of a dielectric layer to achieve non-volatility. FeRAM is one of a growing number of alternative non-volatile random-access memory technologies that offer the same functionality as flash memory.

Ferroelectric materials are required by symmetry considerations to be also piezoelectric and pyroelectric. The combined properties of memory, piezoelectricity, and pyroelectricity make ferroelectric capacitors very useful, e.g. for sensor applications. Ferroelectric capacitors are used in medical ultrasound machines (the capacitors generate and then listen for the ultrasound ping used to image the internal organs of a body), high quality infrared cameras (the infrared image is projected onto a two dimensional array of ferroelectric capacitors capable of detecting temperature differences as small as millionths of a degree Celsius), fire sensors, sonar, vibration sensors, and even fuel injectors on diesel engines.

Another idea of recent interest is the ferroelectric tunnel junction (FTJ) in which a contact is made up by nanometer-thick ferroelectric film placed between metal electrodes. [8] The thickness of the ferroelectric layer is small enough to allow tunneling of electrons. The piezoelectric and interface effects as well as the depolarization field may lead to a giant electroresistance (GER) switching effect.

Yet another hot topic is multiferroics, where researchers are looking for ways to couple magnetic and ferroelectric ordering within a material or heterostructure; there are several recent reviews on this topic. [9]

Materials

The internal electric dipoles of a ferroelectric material are coupled to the material lattice so anything that changes the lattice will change the strength of the dipoles (in other words, a change in the spontaneous polarization). The change in the spontaneous polarization results in a change in the surface charge. This can cause current flow in the case of a ferroelectric capacitor even without the presence of an external voltage across the capacitor. Two stimuli that will change the lattice dimensions of a material are force and temperature. The generation of a surface charge in response to the application of an external stress to a material is called piezoelectricity. A change in the spontaneous polarization of a material in response to a change in temperature is called pyroelectricity.

Generally, there are 230 space groups among which 32 crystalline classes can be found in crystals. There are 21 non-centrosymmetric classes, within which 20 are piezoelectric. Among the piezoelectric classes, 10 have a spontaneous electric polarization, that varies with the temperature, therefore they are pyroelectric. Among pyroelectric materials, some of them are ferroelectric.[ citation needed ]

32 Crystalline classes
21 noncentrosymmetric11 centrosymmetric
20 classes piezoelectric non piezoelectric
10 classes pyroelectric non pyroelectric
ferroelectricnon ferroelectric
e.g. : PbZr/TiO3, BaTiO 3, PbTiO 3e.g. : Tourmaline, ZnO, AlN e.g. : Quartz, Langasite

Ferroelectric phase transitions are often characterized as either displacive (such as BaTiO3) or order-disorder (such as NaNO2), though often phase transitions will demonstrate elements of both behaviors. In barium titanate, a typical ferroelectric of the displacive type, the transition can be understood in terms of a polarization catastrophe, in which, if an ion is displaced from equilibrium slightly, the force from the local electric fields due to the ions in the crystal increases faster than the elastic-restoring forces. This leads to an asymmetrical shift in the equilibrium ion positions and hence to a permanent dipole moment. The ionic displacement in barium titanate concerns the relative position of the titanium ion within the oxygen octahedral cage. In lead titanate, another key ferroelectric material, although the structure is rather similar to barium titanate the driving force for ferroelectricity is more complex with interactions between the lead and oxygen ions also playing an important role. In an order-disorder ferroelectric, there is a dipole moment in each unit cell, but at high temperatures they are pointing in random directions. Upon lowering the temperature and going through the phase transition, the dipoles order, all pointing in the same direction within a domain.

An important ferroelectric material for applications is lead zirconate titanate (PZT), which is part of the solid solution formed between ferroelectric lead titanate and anti-ferroelectric lead zirconate. Different compositions are used for different applications; for memory applications, PZT closer in composition to lead titanate is preferred, whereas piezoelectric applications make use of the diverging piezoelectric coefficients associated with the morphotropic phase boundary that is found close to the 50/50 composition.

Ferroelectric crystals often show several transition temperatures and domain structure hysteresis, much as do ferromagnetic crystals. The nature of the phase transition in some ferroelectric crystals is still not well understood.

In 1974 R.B. Meyer used symmetry arguments to predict ferroelectric liquid crystals, [10] and the prediction could immediately be verified by several observations of behavior connected to ferroelectricity in smectic liquid-crystal phases that are chiral and tilted. The technology allows the building of flat-screen monitors. Mass production between 1994 and 1999 was carried out by Canon. Ferroelectric liquid crystals are used in production of reflective LCoS.

In 2010 David Field found that prosaic films of chemicals such as nitrous oxide or propane exhibited ferroelectric properties.[ citation needed ] This new class of ferroelectric materials exhibit "spontelectric" properties, and may have wide-ranging applications in device and nano-technology and also influence the electrical nature of dust in the interstellar medium.

Other ferroelectric materials used include triglycine sulfate, polyvinylidene fluoride (PVDF) and lithium tantalate. [11]


Two-Dimensional Ferroelectric Materials: Electric Conductors

It should be possible to produce materials which combine both ferroelectric and metallic properties simultaneously, at room temperature. [12] . According to research published in 2018 in Nature Communications [13] , scientists were able to produce a "two-dimensional" sheet of material which was both "ferroelectric" (had a polar crystal structure) and which conducted electricity.

Theory

An introduction to Landau theory can be found here. [14] Based on Ginzburg–Landau theory, the free energy of a ferroelectric material, in the absence of an electric field and applied stress may be written as a Taylor expansion in terms of the order parameter, P. If a sixth order expansion is used (i.e. 8th order and higher terms truncated), the free energy is given by:

where Px, Py, and Pz are the components of the polarization vector in the x, y, and z directions respectively, and the coefficients, must be consistent with the crystal symmetry. To investigate domain formation and other phenomena in ferroelectrics, these equations are often used in the context of a phase field model. Typically, this involves adding a gradient term, an electrostatic term and an elastic term to the free energy. The equations are then discretized onto a grid using the finite difference method and solved subject to the constraints of Gauss's law and Linear elasticity.

In all known ferroelectrics, and . These coefficients may be obtained experimentally or from ab-initio simulations. For ferroelectrics with a first order phase transition, , whereas for a second order phase transition.

The spontaneous polarization, Ps of a ferroelectric for a cubic to tetragonal phase transition may be obtained by considering the 1D expression of the free energy which is:

This free energy has the shape of a double well potential with two free energy minima at , where Ps is the spontaneous polarization. At these two minima, the derivative of the free energy is zero, i.e.:

Since Px = 0 corresponds to a free energy maxima in the ferroelectric phase, the spontaneous polarization, Ps, is obtained from the solution of the equation:

which is:

and elimination of solutions yielding a negative square root (for either the first or second order phase transitions) gives:

If , using the same approach as above, the spontaneous polarization may be obtained as:

The hysteresis loop (Px versus Ex) may be obtained from the free energy expansion by adding another electrostatic term, Ex Px, as follows:

Plotting Ex as a function of Px and reflecting the graph about the 45 degree line gives an 'S' shaped curve. The central part of the 'S' corresponds to a free energy local maximum (since ). Elimination of this region, and connection of the top and bottom portions of the 'S' curve by vertical lines at the discontinuities gives the hysteresis loop.

See also

Related Research Articles

Piezoelectricity the electric charge that accumulates in certain solid materials in response to applied mechanical stress

Piezoelectricity is the electric charge that accumulates in certain solid materials in response to applied mechanical stress. The word piezoelectricity means electricity resulting from pressure and latent heat. It is derived from the Greek word πιέζειν; piezein, which means to squeeze or press, and ἤλεκτρον ēlektron, which means amber, an ancient source of electric charge. French physicists Jacques and Pierre Curie discovered piezoelectricity in 1880.

Dielectric electrically poorly conducting or non-conducting, non-metallic substance of which charge carriers are generally not free to move

A dielectric is an electrical insulator that can be polarized by an applied electric field. When a dielectric is placed in an electric field, electric charges do not flow through the material as they do in an electrical conductor but only slightly shift from their average equilibrium positions causing dielectric polarization. Because of dielectric polarization, positive charges are displaced in the direction of the field and negative charges shift in the opposite direction. This creates an internal electric field that reduces the overall field within the dielectric itself. If a dielectric is composed of weakly bonded molecules, those molecules not only become polarized, but also reorient so that their symmetry axes align to the field.

In electrodynamics, elliptical polarization is the polarization of electromagnetic radiation such that the tip of the electric field vector describes an ellipse in any fixed plane intersecting, and normal to, the direction of propagation. An elliptically polarized wave may be resolved into two linearly polarized waves in phase quadrature, with their polarization planes at right angles to each other. Since the electric field can rotate clockwise or counterclockwise as it propagates, elliptically polarized waves exhibit chirality.

In electrodynamics, linear polarization or plane polarization of electromagnetic radiation is a confinement of the electric field vector or magnetic field vector to a given plane along the direction of propagation. See polarization and plane of polarization for more information.

Crystal structure Ordered arrangement of atoms, ions, or molecules in a crystalline material

In crystallography, crystal structure is a description of the ordered arrangement of atoms, ions or molecules in a crystalline material. Ordered structures occur from the intrinsic nature of the constituent particles to form symmetric patterns that repeat along the principal directions of three-dimensional space in matter.

Pyroelectricity property of certain crystals which are naturally electrically polarized and contain large electric fields

Pyroelectricity is a property of certain crystals which are naturally electrically polarized and as a result contain large electric fields. Pyroelectricity can be described as the ability of certain materials to generate a temporary voltage when they are heated or cooled. The change in temperature modifies the positions of the atoms slightly within the crystal structure, such that the polarization of the material changes. This polarization change gives rise to a voltage across the crystal. If the temperature stays constant at its new value, the pyroelectric voltage gradually disappears due to leakage current.

The Rayleigh law describes the behavior of ferromagnetic materials at low fields.

Polarizability is the ability to form instantaneous dipoles. It is a property of matter. Polarizabilities determine the dynamical response of a bound system to external fields, and provide insight into a molecule's internal structure. In a solid, polarizability is defined as dipole moment per unit volume of the crystal cell.

Electrostriction is a property of all electrical non-conductors, or dielectrics, that causes them to change their shape under the application of an electric field.

Energy harvesting is the process by which energy is derived from external sources, captured, and stored for small, wireless autonomous devices, like those used in wearable electronics and wireless sensor networks.

Duffing equation Non-linear second order differential equation and its attractor

The Duffing equation, named after Georg Duffing (1861–1944), is a non-linear second-order differential equation used to model certain damped and driven oscillators. The equation is given by

Barium titanate chemical compound

Barium titanate is an inorganic compound with chemical formula BaTiO3. Barium titanate appears white as a powder and is transparent when prepared as large crystals. It is a ferroelectric ceramic material that exhibits the photorefractive effect and piezoelectric properties. It is used in capacitors, electromechanical transducers and nonlinear optics.

Ferroics is the generic name given to the study of ferromagnets, ferroelectrics, and ferroelastics.

Covariant formulation of classical electromagnetism

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Photon polarization is the quantum mechanical description of the classical polarized sinusoidal plane electromagnetic wave. An individual photon can be described as having right or left circular polarization, or a superposition of the two. Equivalently, a photon can be described as having horizontal or vertical linear polarization, or a superposition of the two.

The electrogyration effect is the spatial dispersion phenomenon, that consists in the change of optical activity (gyration) of crystals by a constant or time-varying electric field. Being a spatial dispersion effect, the induced optical activity exhibit different behavior under the operation of wave vector reversal, when compared with the Faraday effect: the optical activity increment associated with the electrogyration effect changes its sign under that operation, contrary to the Faraday effect. Formally, it is a special case of gyroelectromagnetism obtained when the magnetic permeability tensor is diagonal.

Piezoresponse force microscopy

Piezoresponse force microscopy (PFM) is a variant of atomic force microscopy (AFM) that allows imaging and manipulation of piezoelectric/ferroelectric materials domains. This is achieved by bringing a sharp conductive probe into contact with a ferroelectric surface and applying an alternating current (AC) bias to the probe tip in order to excite deformation of the sample through the converse piezoelectric effect (CPE). The resulting deflection of the probe cantilever is detected through standard split photodiode detector methods and then demodulated by use of a lock-in amplifier (LiA). In this way topography and ferroelectric domains can be imaged simultaneously with high resolution.

In its most general form, the magnetoelectric effect (ME) denotes any coupling between the magnetic and the electric properties of a material. The first example of such an effect was described by Wilhelm Röntgen in 1888, who found that a dielectric material moving through an electric field would become magnetized. A material where such a coupling is intrinsically present is called a magnetoelectric.

Frequency selective surface

A frequency-selective surface (FSS) is any thin, repetitive surface designed to reflect, transmit or absorb electromagnetic fields based on the frequency of the field. In this sense, an FSS is a type of optical filter or metal-mesh optical filters in which the filtering is accomplished by virtue of the regular, periodic pattern on the surface of the FSS. Though not explicitly mentioned in the name, FSS's also have properties which vary with incidence angle and polarization as well - these are unavoidable consequences of the way in which FSS's are constructed. Frequency-selective surfaces have been most commonly used in the radio frequency region of the electromagnetic spectrum and find use in applications as diverse as the aforementioned microwave oven, antenna radomes and modern metamaterials. Sometimes frequency selective surfaces are referred to simply as periodic surfaces and are a 2-dimensional analog of the new periodic volumes known as photonic crystals.

References

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Further reading