Magnetic properties of electron gas

Magnetic properties of electron gas - electron gas in an external magnetic field has paramagnetic properties. The magnetic properties of an electron gas are composed of diamagnetic and three times its paramagnetic effects. The diamagnetic effect of an electron gas is explained by a change in the translational motion of an electron in a magnetic field, the paramagnetic effect is explained by a change in the orientation of the electron spin relative to an external magnetic field ^[1] .

Content

Non-degenerate electron gas

In a non-degenerate electron gas, all available electrons are able to change their state in an external magnetic field. Diamagnetic susceptibility of electron gas $\chi _{D}$ ${\ displaystyle \ chi _ {D}}$ determined by the formula: $\chi _{D}=-{\frac {1}{3}}{\frac {N\mu _{B}^{2}}{kT}}$ ${\ displaystyle \ chi _ {D} = - {\ frac {1} {3}} {\ frac {N \ mu _ {B} ^ {2}} {kT}}}$ . Here $N$ ${\ displaystyle N}$ Is the total number of electrons in the electron gas, $\mu _{B}$ ${\ displaystyle \ mu _ {B}}$ - magneton of Bora, $k$ ${\ displaystyle k}$ - Boltzmann constant $T$ ${\ displaystyle T}$ - temperature. Paramagnetic susceptibility of electron gas $\chi _{P}$ ${\ displaystyle \ chi _ {P}}$ determined by the formula: $\chi _{P}={\frac {N\mu _{B}^{2}}{kT}}$ ${\ displaystyle \ chi _ {P} = {\ frac {N \ mu _ {B} ^ {2}} {kT}}}$ . The total magnetic susceptibility of the electron gas is equal to the sum of the diamagnetic and paramagnetic susceptibilities: $\chi _{E}=\chi _{D}+\chi _{P}={\frac {2N\mu _{B}^{2}}{3kT}}$ ${\ displaystyle \ chi _ {E} = \ chi _ {D} + \ chi _ {P} = {\ frac {2N \ mu _ {B} ^ {2}} {3kT}}}$ .

Degenerate Electronic Gas

For a degenerate electron gas, only electrons at the boundary of the Fermi distribution, which have free levels in the neighborhood, can change their state. In a degenerate electron gas in metals, the number of electrons $N^{'}$ ${\ displaystyle N '}$ changing their state is determined by the formula: $N'\approx N{\frac {kT}{kT_{0}}}={\frac {kT}{E_{F}}}N$ {\ displaystyle N '\ approx N {\ frac {kT} {kT_ {0}}} = {\ frac {kT} {E_ {F}}} N} where $N$ ${\ displaystyle N}$ - the total number of electrons per unit volume, $E_{F}$ ${\ displaystyle E_ {F}}$ - Fermi energy. Therefore, for a degenerate electron gas in metals, the magnetic susceptibility is determined by the formula: $\chi _{E}={\frac {2N\mu _{B}^{2}}{3E_{F}}}$ ${\ displaystyle \ chi _ {E} = {\ frac {2N \ mu _ {B} ^ {2}} {3E_ {F}}}}$ . The magnetic susceptibility of a degenerate electron gas is temperature independent.

Notes

↑ Nozdrev, 1969 , p. 270-273.

Literature

Nozdrev V.F., Senkevich A.A. Course in statistical physics. - M .: Higher school, 1969. - 287 p.

[_b82dfcf4104ae981-1] Nozdrev, 1969 , p. 270-273.