Magnetism: quantum spins

The negative sign in equation (b 1.15.26) implies that, unlike the case for electron spins, states with larger magnetic quantum number have smaller energy for g O. In contrast to the g-value in EPR experiments, g is an inlierent property of the nucleus. NMR resonances are not easily detected in paramagnetic systems because of sensitivity problems and increased linewidths caused by the presence of unpaired electron spins. 

The spins of two electrons are said to be paired if one is T and the other 1 (Fig. 1.43). Paired spins are denoted Tl, and electrons with paired spins have spin magnetic quantum numbers of opposite sign. Because an atomic orbital is designated by three quantum numbers (n, /, and mt) and the two spin states are specified by a fourth quantum number, ms, another way of expressing the Pauli exclusion principle for atoms is... 

C07-0075. List the values for the quantum numbers for a 3d electron that has spin up and the largest possible value for its magnetic quantum number. 

Quantum numbers The four quantum numbers—principal, angular momentum, magnetic, and spin—arise from solutions to the wave equation and govern the electron configuration of atoms. 

The Hamiltonian operator for the electric quadrupole interaction, 7/q, given in (4.29), coimects the spin of the nucleus with quantum number I with the EFG. In the simplest case, when the EFG is axial (y = Vyy, i.e. rf = 0), the Schrddinger equation can be solved on the basis of the spin functions I,mi), with magnetic quantum numbers m/ = 7, 7—1,. .., —7. The Hamilton matrix is diagonal, because... 

Magnetic dipole interaction Hm (4.47) and electric quadmpole interaction //q (4.29) both depend on the magnetic quantum numbers of the nuclear spin. Therefore, their combined Hamiltonian may be difficult to evaluate. There are closed-form solutions of the problem [64], but relatively simple expressions exist only for a few special cases [65]. In Sect. 4.5.1 it will be shown which kind of information can be obtained from a perturbation treatment if one interaction of the two is much weaker than the other and will be shown below. In general, however, if the interactions are of the same order of magnitude, eQV Jl, and... 

In addition to the magnetism due to the electron spin, the magnetism of the orbital motion has to be considered. For this purpose the magnetic quantum numbers of the electrons are added to a resultant orbital quantum number L = beginning with the highest magnetic quantum number. For example ... 

The valence electron for the cesium atom is in the 6s orbital. In assigning quantum numbers, n = principal energy level = 6. The quantum number l represents the angular momentum (type of orbital) with s orbitals = 0, p orbitals = 1, d orbitals = 2, and so forth. In this case, l = 0. The quantum number m is known as the magnetic quantum number and describes the orientation of the orbital in space. For, v orbitals (as in this case), mt always equals 0. For p orbitals, mt can take on the values of -1, 0, and +1. For d orbitals, can take on the values -2, -1, 0, +1, and +2. The quantum number ms is known as the electron spin quantum number and can take only two values, +1/2 and -1/2, depending on the spin of the electron. 

Figure 10.5 Energy levels of atomic orbitals, n is the principal quantum number, and the 5, p, d notation indicates the azimuthal quantum number (/). For / = 1 and above the orbital is split into multiple suborbitals (indicated by the number of lines), corresponding to the values of the magnetic quantum number m Each of these lines can hold two electrons (corresponding to spin up and spin down ), giving rise to the rules for filling up the orbitals.

It is interesting to note that 12C nucleus is not magnetically active (spin quantum number I = 0),... 

The Pauli Exclusion Principle. No two electrons in an atom may have the same four quantum numbers n, t, m, ms where m and ms are respectively the magnetic and spin quantum numbers. 

All electrons in an atom can be defined in terms of four quantum numbers. The four quantum numbers are the principal quantum number, n, the angular momentum quantum number, /, the magnetic quantum number, m, and the spin quantum number, s. 

Principle quantum number n Orbital angular momentum quantum number / Magnetic quantum number nil Spin quantum number s Atomic orbital designation... 

Yamashita M, Nakata N, Kasahara Y, Sasaki T, Yoneyama N, Kobayashi N, Fujimoto S, Shibauchi T, Matsuda Y (2009) Thermal-transport measurements in a quantum spin-liquid state of the frustrated triangular magnet k-(BEDT-TTF)2Cu2(CN)3. Nat Phys 5 44-47... 

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