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Relativistic Quantum Transport
Published in David K. Ferry, An Introduction to Quantum Transport in Semiconductors, 2017
The pre-factor of the last term in square brackets is the Bohr magneton, and this term is recognized as the Zeeman splitting of the two spin states in each band, which is normally added by hand in the semi-classical transport case. In MKS units, the value of the Bohr magneton is 9.274 × 10–24 J/T. But we see that the proper approach of the Dirac equation leads to the normal terms in kinetic energy with the addition of the Zeeman term.
Magnetic Nanoparticles for Neural Engineering
Published in Nguyễn T. K. Thanh, Clinical Applications of Magnetic Nanoparticles, 2018
Gerardo F. Goya, Vittoria Raffa
The choice of the material for the magnetic core of MNPs is related to the physical and magnetic properties of the corresponding bulk phase. However, below a given critical particle diameter d < dcrit (with 30 ≤ dcrit ≤ 100 nm, depending on the material’s nature) the magnetic structure of the particle’s core is different than the bulk material in the sense that domain walls collapse into a single magnetic domain. A deeper analysis of the concepts of magnetic domains, magnetic order in small particles and superparamagnetism is beyond the scope of this chapter, and the reader is referred to Ortega15 and the classic book by B.D. Cullity6 (Chapter 8). The value of dcrit is determined by the magnetic anisotropy (K) and the exchange stiffness coefficient (A) of the bulk material, and d < dcrit defines a size regime below which the magnetic cores are magnetically ordered in a single direction. Therefore, this spin alignment results in a net magnetic moment of several hundreds of Bohr magnetons (Bohr magneton is the elementary unit of magnetic moment, defined in SI units in terms of the electron charge e, and mass me, and the reduced Planck constant ℏ, by μB = eℏ/2me). The magnetostatic energy of a single-domain MNP (i.e. the magnetic energy in the presence of an externally applied magnetic field) is proportional to its volume V, and this energy competes with the thermal energy to keep the magnetic moment spatially fixed.16 Around room temperature (i.e. within the 25–45°C range), where most biomedical uses occur, the thermal energy can be of the same order than the magnetostatic energy for small applied fields. Therefore, the thermally induced magnetic relaxation impairs the magnetic alignment of m and B diminishing the magnetization at low fields. For MNPs with average size <30 nm thermal relaxation is predominant and thus affects the efficacy of those biomedical applications that require full magnetic saturation at room temperature. For these applications, the design of MNPs must consider average particle size and/or magnetic anisotropy large enough to prevent thermal relaxation.
Vibrational magnetism and the strength of magnetic dipole transition within the electric dipole forbidden v 2 + v 3 absorption band of carbon dioxide
Published in Molecular Physics, 2021
Any localised curvilinear movement of electrical charges is capable of giving rise to both magnetic and angular momenta. The ratio of these is generally called the gyromagnetic ratio ; is called the magneton (e.g. nuclear or electron (Bohr) magneton), g is the dimensionless g-factor, e is the elementary charge, m is the mass of a charged particle (respectively, for the proton (nucleon), for the electron); ℏ and c are the reduced Planck constant and the speed of light, respectively. A magnetic dipole in molecules is associated with both a positively charged nuclear frame and a negatively charged electronic cloud encompassing its molecular skeleton. Note that in this paper we refer only to closed-shell molecules with no net electronic spin magnetic moment. Both charge distributions are subject to variation in space and in time according to the vibrational and rotational motion of a molecule.
Local ordering and dynamics in anisotropic media by magnetic resonance: from liquid crystals to proteins
Published in Liquid Crystals, 2020
where is the Bohr magneton, the Planck constant, the electron gyromagnetic ratio, and the Hamiltonian is expressed in angular frequency units. The first term is the electron Zeeman interaction with . The second term describes the hyperfine interaction between the nuclear spin operator, , and the electron spin operator, . The g and A tensors depend on the coordinates . The nuclear Zeeman terms for nitrogen nuclei with spin equal to 1 are generally neglected in Equation (18).
Structural characterization, magnetic studies, and catecholase-like activities of Mn12 clusters
Published in Journal of Coordination Chemistry, 2018
Mo Ashafaq, Mukul Raizada, Mohd Khalid, M. Shahid, Musheer Ahmad, Zafar A. Siddiqi
The magnetic properties of 1 and 2 were investigated by solid state magnetic susceptibility measurements in dc fields at 0.1 T and in the 1.8–300 K temperature range. The magnetic moment for a particular Mn ion is associated to its spin through μi = −geSi, where is the Bohr magneton, ge = 2 is the electron g factor and Si is the total spin of individual manganese ion. The magnetic moment of a manganese ion can also expressed as μi= (in units of ).