Ebook Quantum theory of magnetism - Magnetic properties of materials (3/E): Part 2
➤ Gửi thông báo lỗi ⚠️ Báo cáo tài liệu vi phạmNội dung chi tiết: Ebook Quantum theory of magnetism - Magnetic properties of materials (3/E): Part 2
Ebook Quantum theory of magnetism - Magnetic properties of materials (3/E): Part 2
5The Static Susceptibility of Interacting Systems: MetalsThe long-range magnetic order ill metals Is very similar to that oliscrved in insulators as i Ebook Quantum theory of magnetism - Magnetic properties of materials (3/E): Part 2illustrated by the magnetization curve of nickel shown in Fig. 5.1. However, the electrons participating in this magnetic state are itinerant as determined by the existence of a Fermi surface; that is, they also have translational degrees of freedom. How such a system of interacting electrons respon Ebook Quantum theory of magnetism - Magnetic properties of materials (3/E): Part 2ds to a magnetic field is a many-body problem with all its attendant difficulties.The many-lxaly corrections to the Landau susceptibility and the PaulEbook Quantum theory of magnetism - Magnetic properties of materials (3/E): Part 2
i susceptibility must be treated separately. Kanazawa and Matsudaira '1(H) found that the many-body corrections to the Landau susceptibility are small5The Static Susceptibility of Interacting Systems: MetalsThe long-range magnetic order ill metals Is very similar to that oliscrved in insulators as i Ebook Quantum theory of magnetism - Magnetic properties of materials (3/E): Part 2ways. The first, Fermi liquid theory, is a phenomenological approach. It involves parameters completely analogous to the parameters entering the spin Hamiltonian. These parameters may be determined experimentally or they may be obtained from the second approach which is to assume a specific microsco Ebook Quantum theory of magnetism - Magnetic properties of materials (3/E): Part 2pic model from which various physical properties can 1>C calculated.5.1 Fermi Liquid Theory'The phenomenological theory of an interacting fermion systEbook Quantum theory of magnetism - Magnetic properties of materials (3/E): Part 2
em was developed by Landau in 1956 [106], Although Landau was mainly interested in the properties of liquid He3, his theory may also be applied to met5The Static Susceptibility of Interacting Systems: MetalsThe long-range magnetic order ill metals Is very similar to that oliscrved in insulators as i Ebook Quantum theory of magnetism - Magnetic properties of materials (3/E): Part 2d state of a system of jV electrons. For a noninteracting system the ground state corresponds to a well-defined Fermi sphere. Landau assumed that as the interaction between the electrons is gradually “turned on" the new ground state evolves smoothly out of the1705 Tho Static Susceptibility of Intera Ebook Quantum theory of magnetism - Magnetic properties of materials (3/E): Part 2cting SystemsFig. 5.1. Magnetization of nickel as a function of temperature. The original data of Weiss and Forcer [105] taken at constant pressure haEbook Quantum theory of magnetism - Magnetic properties of materials (3/E): Part 2
s been corrected to constant volume to eliminate the effects of thermal expansionoriginal Fermi sphere: if |0) is this new ground state, it is related5The Static Susceptibility of Interacting Systems: MetalsThe long-range magnetic order ill metals Is very similar to that oliscrved in insulators as i Ebook Quantum theory of magnetism - Magnetic properties of materials (3/E): Part 2this assumption to the excitations of the interacting system. For example. suppose we add one electron, with momentum Ilk. to the non-interacting system. This state has the form MfcJFSJ. where is the creation operator for an electron. If the interactions are gradually turner! on. let us approximate Ebook Quantum theory of magnetism - Magnetic properties of materials (3/E): Part 2the new state as\kơ} = Uola\FS).-5.2Because the electron possesses spin, this wave function is a spinor.Let Its define the difference between the enerEbook Quantum theory of magnetism - Magnetic properties of materials (3/E): Part 2
gy of kơ) and |0) as €°(Ắf. ơj. Since the wave function is a spinor, this energy will l>e a 2 X 2 matrix. If the system is isotropic, and in particula5The Static Susceptibility of Interacting Systems: MetalsThe long-range magnetic order ill metals Is very similar to that oliscrved in insulators as i Ebook Quantum theory of magnetism - Magnetic properties of materials (3/E): Part 2ed itself as a result of the interact ions, the energy CU(A-) will be quite different from the energy of a free particle. As we do not know this energy, we shall assume that k is close to fcf and expand in powers of k - kp. Tints we obtainf°(k) = /4 4——- fcr) 4- • ■ ■ I-5.3III*5.1 Fermi Liquid Theor Ebook Quantum theory of magnetism - Magnetic properties of materials (3/E): Part 2y 171 where'«• ■ 0* L/(5-4>This electron, “dressed” by all the other electrons, is called a quasipartưle. Notice that the energy required to create aEbook Quantum theory of magnetism - Magnetic properties of materials (3/E): Part 2
quasiparticle at the Fermi surface is /4, the chemical potential. Its increase in energy as it moves away from the Fermi surface is characterized by i5The Static Susceptibility of Interacting Systems: MetalsThe long-range magnetic order ill metals Is very similar to that oliscrved in insulators as i Ebook Quantum theory of magnetism - Magnetic properties of materials (3/E): Part 2are long enough to make their description meaningful.We could just as well have removed an electron from some point within the Fermi sphere. This would have created a “hole", which the interactions would convert into a quasi-hote. The energy associated with a hole is the energy required to remove an Ebook Quantum theory of magnetism - Magnetic properties of materials (3/E): Part 2 electron at the Fermi surface, -fl. plus the energy it takes to move the electron at k up to the surface,— k).However, if we define the total energyEbook Quantum theory of magnetism - Magnetic properties of materials (3/E): Part 2
of the system containing a quad-hole as Eo - thenfO(A..) = p + ^|A:-A-F|. tnThus the excitation spectrum associated with our Fermi liquid has the form5The Static Susceptibility of Interacting Systems: MetalsThe long-range magnetic order ill metals Is very similar to that oliscrved in insulators as i Ebook Quantum theory of magnetism - Magnetic properties of materials (3/E): Part 2eld producing electronhole pairs. Since the energy of a quasipartide depends on the distribution of all the other quadparticles, any change in distribution will lead to a change in the quasiparticle energy. Let US denote the change in the distribution by Ẵn(k.ơ).The quasipart icle distribution is es Ebook Quantum theory of magnetism - Magnetic properties of materials (3/E): Part 2sentially the density matrix associated with the quasiparticle. In particular, it is a 2 X 2 matrix. For example, ổn(k.ơ)i) gives the probability of fEbook Quantum theory of magnetism - Magnetic properties of materials (3/E): Part 2
inding an electron of momentum Ilk withKxõutionOKtgyFig. 5.2. Single-particle excitation spectrum of a Fermi liquid1725 The Static Susceptibility of I5The Static Susceptibility of Interacting Systems: MetalsThe long-range magnetic order ill metals Is very similar to that oliscrved in insulators as i5The Static Susceptibility of Interacting Systems: MetalsThe long-range magnetic order ill metals Is very similar to that oliscrved in insulators as iGọi ngay
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