Moment magnetic dipole

The microscopic magnetic dipole moment, m, is expressed in ampere square meters (A.m ), or in J.T , and characterizes the magnetic properties of microscopic entities such as elementary particles (e.g., neutron, proton, electron), nuchdes, atoms, or molecules having a spin angular momentum value different from zero. 

The torque, t, in N.m, exerted on a magnetic dipole of momemt m put in a magnetic induction B is then given by the following equation  

10 ELECTRIC AND MAGNETIC MOMENTS 2.10.1 Magnetic Dipole Moment 

The magnetic moments of nuclei are measures of the distribution of electric currents in the nucleus while the electric moments are measures of the distribution of electric charges. Because the magnetic moment may not be a familiar concept, we will begin 

Remember that the angular momentum of the electron moving in a circle, /, is niovr. Thus, 

In quantum mechanics, the projection of the angular momentum l is mfi. We, therefore, expect the magnetic dipole moment due to the orbital motion of the electron to be given by 

Extending these ideas to nucleons, we can define the nuclear magneton, pN as (eh /2mp), which has the numerical value of 3.15 x 10-8 eV/tesla or 

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The interaction of the electron spin s magnetic dipole moment with the magnetic dipole moments of nearby nuclear spins provides another contribution to the state energies and the number of energy levels, between which transitions may occur. This gives rise to the hyperfme structure in the EPR spectrum. The so-called hyperfme interaction (HFI) is described by the Hamiltonian... 

Magnetic dipole moment of a molecule m, fJL Molar (decadic) absorption coefficient e... 

All elements possessing an isotope with a suitable magnetic dipole moment (about half the elements in the periodic table)... 

Here (r - Rc) (r - Rq) is the dot product times a unit matrix (i.e. (r — Rg) (r — Rg)I) and (r - RG)(r — Rg) is a 3x3 matrix containing the products of the x,y,z components, analogous to the quadrupole moment, eq. (10.4). Note that both the L and P operators are gauge dependent. When field-independent basis functions are used the first-order property, the HF magnetic dipole moment, is given as the expectation value over the unperturbed wave funetion (for a singlet state) eqs. (10.18)/(10.23). 

A nucleus in a state with spin quantum number 7 > 0 will interact with a magnetic field by means of its magnetic dipole moment p. This magnetic dipole interaction or nuclear Zeeman effect may be described by the Hamiltonian... 

Nuclear magnetic dipole moment of ground (g) and excited (e) state (in nuclear magnetons, n.m.)... 

Fig. 7.3 Effect of magnetic dipole interaction (7/m), electric quadmpole interaction (Hq), and combined interaction// = Hu + //q, Em> q on the Mossbauernuclear levels of Ni. The larger spacings between the sublevels of the ground state are due to the somewhat larger magnetic dipole moment of the nuclear ground state as compared to the excited state. The relative transition probabilities for a powder sample as well as the relative positions of the transition lines are indicated by the stick spectra below...

The ground state as well as the 6.2 keV excited state of Ta possesses sizeable electric quadrupole and magnetic dipole moments (cf. Table 7.1 at the end of the book) which, in cooperation with the extremely narrow line width, generally yield well-resolved Mossbauer spectra even in cases with relatively weak interactions. 

The magnetic field seen by the probe neutron is solely due to the magnetic dipole moment density of the unpaired electrons. In other words, the magnetisation density is simply related to the electron spin density by a multiplicative factor, and there is no ambiguity in its definition. 

In Equation (6) ge is the electronic g tensor, yn is the nuclear g factor (dimensionless), fln is the nuclear magneton in erg/G (or J/T), In is the nuclear spin angular momentum operator, An is the electron-nuclear hyperfine tensor in Hz, and Qn (non-zero for fn > 1) is the quadrupole interaction tensor in Hz. The first two terms in the Hamiltonian are the electron and nuclear Zeeman interactions, respectively the third term is the electron-nuclear hyperfine interaction and the last term is the nuclear quadrupole interaction. For the usual systems with an odd number of unpaired electrons, the transition moment is finite only for a magnetic dipole moment operator oriented perpendicular to the static magnetic field direction. In an ESR resonator in which the sample is placed, the microwave magnetic field must be therefore perpendicular to the external static magnetic field. The selection rules for the electron spin transitions are given in Equation (7)... 

As shown in the Appendix (in Section V), in the C2h point group, the 1Ag - 1Bll (i.e. the monoelectronic r - jr excitation) possesses only an electric dipole moment, while in the C2V structure the electric and magnetic dipole moments, both non-vanishing, are orthogonal. In both cases the product in equation 1 leads to zero rotational strength. 

There are two contributions to the magnetic dipole moment of an electron bound to an atomic nucleus, which, in semiclassical models, are attributed to orbital motion, represented by quantum number l, and spin, represented by quantum number, v. The orbital and spin components are linked, or coupled, on isolated atoms or ions to give an overall magnetic dipole moment for the atom. The total magnetic dipole moment of the atom is given by... 

Equation (S6.1) is applicable to the salts of lanthanide ions. These have a partly filled 4f shell, and the 4f orbitals are well shielded from any interaction with the surrounding atoms by filled 5.9, 5p, and 6.9 orbitals, so that, with the notable exceptions, Eu3+ and Sm3+, they behave like isolated ions. For the transition metals, especially those of the 3d series, interaction with the surroundings is considerable. Because of this, the 3d transition-metal ions often have magnetic dipole moments corresponding only to the electron spin contribution. The orbital moment is said to be quenched. In such materials Eq. (S6.1) can then be replaced by a spin-only formula ... 

The magnetic hyperfine splitting, the Zeeman effect, arises from the interaction between the nuclear magnetic dipole moment and the magnetic field H at the nucleus. This interaction gives rise to six transitions the separation between the peaks in the spectrum is proportional to the magnetic field at the nucleus. 

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