Ferroelectric Materials List
Magdalena Liendo
In physics and materials science, the Curie temperature (TC), or Curie point, is the temperature above which certain materials lose their permanent magnetic properties, which can (in most cases) be replaced by induced magnetism. The Curie temperature is named after Pierre Curie, who showed that magnetism was lost at a critical temperature.[1]
The force of magnetism is determined by the magnetic moment, a dipole moment within an atom that originates from the angular momentum and spin of electrons. Materials have different structures of intrinsic magnetic moments that depend on temperature; the Curie temperature is the critical point at which a material's intrinsic magnetic moments change direction.
In analogy to ferromagnetic and paramagnetic materials, the Curie temperature can also be used to describe the phase transition between ferroelectricity and paraelectricity. In this context, the order parameter is the electric polarization that goes from a finite value to zero when the temperature is increased above the Curie temperature.
Iron filings, after being heated for a long time, are attracted by a loadstone, yet not so strongly or from so great a distance as when not heated. A loadstone loses some of its virtue by too great a heat; for its humour is set free, whence its peculiar nature is marred. (Book 2, Chapter 23).
At the atomic level, there are two contributors to the magnetic moment, the electron magnetic moment and the nuclear magnetic moment. Of these two terms, the electron magnetic moment dominates, and the nuclear magnetic moment is insignificant. At higher temperatures, electrons have higher thermal energy. This has a randomizing effect on aligned magnetic domains, leading to the disruption of order, and the phenomena of the Curie point.[5][6]
Ferromagnetic, paramagnetic, ferrimagnetic, and antiferromagnetic materials have different intrinsic magnetic moment structures. At a material's specific Curie temperature (TC), these properties change. The transition from antiferromagnetic to paramagnetic (or vice versa) occurs at the Nel temperature (TN), which is analogous to Curie temperature.
Ferromagnetic, paramagnetic, ferrimagnetic, and antiferromagnetic structures are made up of intrinsic magnetic moments. If all the electrons within the structure are paired, these moments cancel out due to their opposite spins and angular momenta. Thus, even with an applied magnetic field, these materials have different properties and no Curie temperature.[7][8]
A material is paramagnetic only above its Curie temperature. Paramagnetic materials are non-magnetic when a magnetic field is absent and magnetic when a magnetic field is applied. When a magnetic field is absent, the material has disordered magnetic moments; that is, the magnetic moments are asymmetrical and not aligned. When a magnetic field is present, the magnetic moments are temporarily realigned parallel to the applied field;[9][10] the magnetic moments are symmetrical and aligned.[11] The magnetic moments being aligned in the same direction are what causes an induced magnetic field.[11][12]
For paramagnetism, this response to an applied magnetic field is positive and is known as magnetic susceptibility.[7] The magnetic susceptibility only applies above the Curie temperature for disordered states.[13]
Above the Curie temperature, the atoms are excited, and the spin orientations become randomized[8] but can be realigned by an applied field, i.e., the material becomes paramagnetic. Below the Curie temperature, the intrinsic structure has undergone a phase transition,[15] the atoms are ordered, and the material is ferromagnetic.[11] The paramagnetic materials' induced magnetic fields are very weak compared with ferromagnetic materials' magnetic fields.[15]
When a magnetic field is absent the material has spontaneous magnetization which is a result of the ordered magnetic moments; that is, for ferromagnetism, the atoms are symmetrical and aligned in the same direction creating a permanent magnetic field.
The magnetic interactions are held together by exchange interactions; otherwise thermal disorder would overcome the weak interactions of magnetic moments. The exchange interaction has a zero probability of parallel electrons occupying the same point in time, implying a preferred parallel alignment in the material.[16] The Boltzmann factor contributes heavily as it prefers interacting particles to be aligned in the same direction.[17] This causes ferromagnets to have strong magnetic fields and high Curie temperatures of around 1,000 K (730 C).[18]
Below the Curie temperature, the atoms are aligned and parallel, causing spontaneous magnetism; the material is ferromagnetic. Above the Curie temperature the material is paramagnetic, as the atoms lose their ordered magnetic moments when the material undergoes a phase transition.[15]
Materials are only ferrimagnetic below their corresponding Curie temperature. Ferrimagnetic materials are magnetic in the absence of an applied magnetic field and are made up of two different ions.[19]
When a magnetic field is absent the material has a spontaneous magnetism which is the result of ordered magnetic moments; that is, for ferrimagnetism one ion's[clarification needed] magnetic moments are aligned facing in one direction with certain magnitude and the other ion's magnetic moments are aligned facing in the opposite direction with a different magnitude. As the magnetic moments are of different magnitudes in opposite directions there is still a spontaneous magnetism and a magnetic field is present.[19]
Similar to ferromagnetic materials the magnetic interactions are held together by exchange interactions. The orientations of moments however are anti-parallel which results in a net momentum by subtracting their momentum from one another.[19]
Below the Curie temperature the atoms of each ion are aligned anti-parallel with different momentums causing a spontaneous magnetism; the material is ferrimagnetic. Above the Curie temperature the material is paramagnetic as the atoms lose their ordered magnetic moments as the material undergoes a phase transition.[19]
The material has equal magnetic moments aligned in opposite directions resulting in a zero magnetic moment and a net magnetism of zero at all temperatures below the Nel temperature. Antiferromagnetic materials are weakly magnetic in the absence or presence of an applied magnetic field.
Similar to ferromagnetic materials the magnetic interactions are held together by exchange interactions preventing thermal disorder from overcoming the weak interactions of magnetic moments.[16][21] When disorder occurs it is at the Nel temperature.[21]
As temperature is inversely proportional to magnetic susceptibility, when T approaches TC the denominator tends to zero and the magnetic susceptibility approaches infinity allowing magnetism to occur. This is a spontaneous magnetism which is a property of ferromagnetic and ferrimagnetic materials.[30][31]
The spontaneous magnetism, occurring in ferromagnetic, ferrimagnetic, and antiferromagnetic materials, approaches zero as the temperature increases towards the material's Curie temperature. Spontaneous magnetism is at its maximum as the temperature approaches 0 K.[32] That is, the magnetic moments are completely aligned and at their strongest magnitude of magnetism due to lack of thermal disturbance.
In paramagnetic materials thermal energy is sufficient to overcome the ordered alignments. As the temperature approaches 0 K, the entropy decreases to zero, that is, the disorder decreases and the material becomes ordered. This occurs without the presence of an applied magnetic field and obeys the third law of thermodynamics.[16]
This model is important for solving and understanding the concepts of phase transitions and hence solving the Curie temperature. As a result, many different dependencies that affect the Curie temperature can be analysed.
One should note, in 1D the Curie (critical) temperature for a magnetic order phase transition is found to be at zero temperature, i.e. the magnetic order takes over only at T = 0. In 2D, the critical temperature, e.g. a finite magnetization, can be calculated by solving the inequality:
Materials structures consist of intrinsic magnetic moments which are separated into domains called Weiss domains.[37] This can result in ferromagnetic materials having no spontaneous magnetism as domains could potentially balance each other out.[37] The position of particles can therefore have different orientations around the surface than the main part (bulk) of the material. This property directly affects the Curie temperature as there can be a bulk Curie temperature TB and a different surface Curie temperature TS for a material.[38]
The surface and bulk properties can be predicted by the Ising model and electron capture spectroscopy can be used to detect the electron spins and hence the magnetic moments on the surface of the material. An average total magnetism is taken from the bulk and surface temperatures to calculate the Curie temperature from the material, noting the bulk contributes more.[35][39]
For terbium which is a rare-earth metal and has a high orbital angular momentum the magnetic moment is strong enough to affect the order above its bulk temperatures. It is said to have a high anisotropy on the surface, that is it is highly directed in one orientation. It remains ferromagnetic on its surface above its Curie temperature (219K) while its bulk becomes antiferromagnetic and then at higher temperatures its surface remains antiferromagnetic above its bulk Nel Temperature (230K) before becoming completely disordered and paramagnetic with increasing temperature. The anisotropy in the bulk is different from its surface anisotropy just above these phase changes as the magnetic moments will be ordered differently or ordered in paramagnetic materials.[38][42]
Composite materials, that is, materials composed from other materials with different properties, can change the Curie temperature. For example, a composite which has silver in it can create spaces for oxygen molecules in bonding which decreases the Curie temperature[43] as the crystal lattice will not be as compact.
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