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Magnetic Anisotropy
In condensed matter physics, magnetic anisotropy describes how an object's magnetic properties can be different depending on direction. In the simplest case, there is no preferential direction for an object's magnetic moment. It will respond to an applied magnetic field in the same way, regardless of which direction the field is applied. This is known as magnetic isotropy. In contrast, magnetically anisotropic materials will be easier or harder to magnetize depending on which way the object is rotated. For most magnetically anisotropic materials, there are two easiest directions to magnetize the material, which are a 180° rotation apart. The line parallel to these directions is called the easy axis. In other words, the easy axis is an energetically favorable direction of spontaneous magnetization. Because the two opposite directions along an easy axis are usually equivalently easy to magnetize along, the actual direction of magnetization can just as easily settle into either di ...
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Condensed Matter Physics
Condensed matter physics is the field of physics that deals with the macroscopic and microscopic physical properties of matter, especially the solid and liquid phases which arise from electromagnetic forces between atoms. More generally, the subject deals with "condensed" phases of matter: systems of many constituents with strong interactions between them. More exotic condensed phases include the superconducting phase exhibited by certain materials at low temperature, the ferromagnetic and antiferromagnetic phases of spins on crystal lattices of atoms, and the Bose–Einstein condensate found in ultracold atomic systems. Condensed matter physicists seek to understand the behavior of these phases by experiments to measure various material properties, and by applying the physical laws of quantum mechanics, electromagnetism, statistical mechanics, and other theories to develop mathematical models. The diversity of systems and phenomena available for study makes condensed matter phy ...
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Exchange Bias
Exchange bias or exchange anisotropy occurs in bilayers (or multilayers) of magnetic materials where the hard magnetization behavior of an antiferromagnetic thin film causes a shift in the soft magnetization curve of a ferromagnetic film. The exchange bias phenomenon is of tremendous utility in magnetic recording, where it is used to pin the state of the readback heads of hard disk drives at exactly their point of maximum sensitivity; hence the term "bias." Fundamental science The essential physics underlying the phenomenon is the exchange interaction between the antiferromagnet and ferromagnet at their interface. Since antiferromagnets have a small or no net magnetization, their spin orientation is only weakly influenced by an externally applied magnetic field. A soft ferromagnetic film which is strongly exchange-coupled to the antiferromagnet will have its interfacial spins pinned. Reversal of the ferromagnet's moment will have an added energetic cost corresponding to the ...
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Unit Vector
In mathematics, a unit vector in a normed vector space is a vector (often a spatial vector) of length 1. A unit vector is often denoted by a lowercase letter with a circumflex, or "hat", as in \hat (pronounced "v-hat"). The term ''direction vector'', commonly denoted as d, is used to describe a unit vector being used to represent spatial direction and relative direction. 2D spatial directions are numerically equivalent to points on the unit circle and spatial directions in 3D are equivalent to a point on the unit sphere. The normalized vector û of a non-zero vector u is the unit vector in the direction of u, i.e., :\mathbf = \frac where , u, is the norm (or length) of u. The term ''normalized vector'' is sometimes used as a synonym for ''unit vector''. Unit vectors are often chosen to form the basis of a vector space, and every vector in the space may be written as a linear combination of unit vectors. Orthogonal coordinates Cartesian coordinates Unit vectors may be us ...
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Direction Cosines
In analytic geometry, the direction cosines (or directional cosines) of a vector are the cosines of the angles between the vector and the three positive coordinate axes. Equivalently, they are the contributions of each component of the basis to a unit vector in that direction. Three-dimensional Cartesian coordinates If v is a Euclidean vector in three-dimensional Euclidean space, R3, :\mathbf v = v_x \mathbf e_x + v_y \mathbf e_y + v_z \mathbf e_z, where e''x'', e''y'', e''z'' are the standard basis in Cartesian notation, then the direction cosines are :\begin \alpha &= \cos a = \frac &&= \frac,\\ \beta &= \cos b = \frac &&= \frac,\\ \gamma &= \cos c = \frac &&= \frac. \end It follows that by squaring each equation and adding the results : \cos^2 a + \cos^2 b + \cos^2 c = \alpha^ + \beta^ + \gamma^ = 1. Here ''α'', ''β'' and ''γ'' are the direction cosines and the Cartesian coordinates of the unit vector v/, v, , and ''a'', ''b'' and ''c'' are the direction angl ...
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Saturation Magnetization
Seen in some magnetic materials, saturation is the state reached when an increase in applied external magnetic field ''H'' cannot increase the magnetization of the material further, so the total magnetic flux density ''B'' more or less levels off. (Though, magnetization continues to increase very slowly with the field due to paramagnetism.) Saturation is a characteristic of ferromagnetic and ferrimagnetic materials, such as iron, nickel, cobalt and their alloys. Different ferromagnetic materials have different saturation levels. Description Saturation is most clearly seen in the ''magnetization curve'' (also called ''BH'' curve or hysteresis curve) of a substance, as a bending to the right of the curve (see graph at right). As the ''H'' field increases, the ''B'' field approaches a maximum value asymptotically, the saturation level for the substance. Technically, above saturation, the ''B'' field continues increasing, but at the paramagnetic rate, which is several orders of m ...
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Single-domain (magnetic)
Single domain, in magnetism, refers to the state of a ferromagnet in which the magnetization does not vary across the magnet. A magnetic particle that stays in a single domain state for all magnetic fields is called a single domain particle (but other definitions are possible; see below). Such particles are very small (generally below a micrometre in diameter). They are also very important in a lot of applications because they have a high coercivity. They are the main source of hardness in hard magnets, the carriers of magnetic storage in tape drives, and the best recorders of the ancient Earth's magnetic field (see paleomagnetism). History Early theories of magnetization in ferromagnets assumed that ferromagnets are divided into magnetic domains and that the magnetization changed by the movement of domain walls. However, as early as 1930, Frenkel and Dorfman predicted that sufficiently small particles could only hold one domain, although they greatly overestimated the upper size ...
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Nuclear Overhauser Effect
The nuclear Overhauser effect (NOE) is the transfer of nuclear spin polarization from one population of spin-active nuclei (e.g. 1H, 13C, 15N etc.) to another via cross-relaxation. A phenomenological definition of the NOE in nuclear magnetic resonance spectroscopy (NMR) is the change in the integrated intensity (positive or negative) of one NMR resonance that occurs when another is saturated by irradiation with an RF field. The change in resonance intensity of a nucleus is a consequence of the nucleus being close in space to those directly affected by the RF perturbation. The NOE is particularly important in the assignment of NMR resonances, and the elucidation and confirmation of the structures or configurations of organic and biological molecules. The 1H two-dimensional NOE SpectroscopY (NOESY) experiment and its extensions are important tools to identify stereochemistry of proteins and other biomolecules in solution, whereas in solid form crystal x-ray diffraction typicall ...
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Chemical Shift
In nuclear magnetic resonance (NMR) spectroscopy, the chemical shift is the resonant frequency of an atomic nucleus relative to a standard in a magnetic field. Often the position and number of chemical shifts are diagnostic of the structure of a molecule. Chemical shifts are also used to describe signals in other forms of spectroscopy such as photoemission spectroscopy. Some atomic nuclei possess a magnetic moment ( nuclear spin), which gives rise to different energy levels and resonance frequencies in a magnetic field. The total magnetic field experienced by a nucleus includes local magnetic fields induced by currents of electrons in the molecular orbitals (note that electrons have a magnetic moment themselves). The electron distribution of the same type of nucleus (e.g. ) usually varies according to the local geometry (binding partners, bond lengths, angles between bonds, and so on), and with it the local magnetic field at each nucleus. This is reflected in the spin energy le ...
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Carbonyl Group
In organic chemistry, a carbonyl group is a functional group composed of a carbon atom double-bonded to an oxygen atom: C=O. It is common to several classes of organic compounds, as part of many larger functional groups. A compound containing a carbonyl group is often referred to as a carbonyl compound. The term carbonyl can also refer to carbon monoxide as a ligand in an inorganic or organometallic complex (a metal carbonyl, e.g. nickel carbonyl). The remainder of this article concerns itself with the organic chemistry definition of carbonyl, where carbon and oxygen share a double bond. Carbonyl compounds In organic chemistry, a carbonyl group characterizes the following types of compounds: Other organic carbonyls are urea and the carbamates, the derivatives of acyl chlorides chloroformates and phosgene, carbonate esters, thioesters, lactones, lactams, hydroxamates, and isocyanates. Examples of inorganic carbonyl compounds are carbon dioxide and carbonyl sulfide. A ...
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Alkene
In organic chemistry, an alkene is a hydrocarbon containing a carbon–carbon double bond. Alkene is often used as synonym of olefin, that is, any hydrocarbon containing one or more double bonds.H. Stephen Stoker (2015): General, Organic, and Biological Chemistry'. 1232 pages. Two general types of monoalkenes are distinguished: terminal and internal. Also called α-olefins, terminal alkenes are more useful. However, the International Union of Pure and Applied Chemistry (IUPAC) recommends using the name "alkene" only for acyclic hydrocarbons with just one double bond; alkadiene, alkatriene, etc., or polyene for acyclic hydrocarbons with two or more double bonds; cycloalkene, cycloalkadiene, etc. for cyclic ones; and "olefin" for the general class – cyclic or acyclic, with one or more double bonds. Acyclic alkenes, with only one double bond and no other functional groups (also known as mono-enes) form a homologous series of hydrocarbons with the general formula with '' ...
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Benzene
Benzene is an organic chemical compound with the molecular formula C6H6. The benzene molecule is composed of six carbon atoms joined in a planar ring with one hydrogen atom attached to each. Because it contains only carbon and hydrogen atoms, benzene is classed as a hydrocarbon. Benzene is a natural constituent of petroleum and is one of the elementary petrochemicals. Due to the cyclic continuous pi bonds between the carbon atoms, benzene is classed as an aromatic hydrocarbon. Benzene is a colorless and highly flammable liquid with a sweet smell, and is partially responsible for the aroma of gasoline. It is used primarily as a precursor to the manufacture of chemicals with more complex structure, such as ethylbenzene and cumene, of which billions of kilograms are produced annually. Although benzene is a major industrial chemical, it finds limited use in consumer items because of its toxicity. History Discovery The word "''benzene''" derives from "''gum benzoin''" (benzoin res ...
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