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Colloquium
November 04 at 4:30 PM to 5:30 PMWilder Auditorium, Knight Physics Bldg.
Physics Lecture
Faraday's 1831 law of induction E = - dΦ/dt relates the rate of change of magnetic flux Φ to the electromotive-force E produced in a circuit. This accounts only for the forces acting on the charge of an electron. When the forces acting on the spin are accounted for this is better stated as
E = - ( hbar / e ) dγ/dt where γ is the (1984) Berry phase acquired while the electron passes around a circuit. The Anaronov-Bohm contribution to γ gives back E = - dΦ/dt while adding the spin Berry phase leads to a spin-motive-force which in a ferromagnetic material implies an electromotive-force. Feynman, in 1948, anticipated Berry by showing the velocity commutation rule [vi,vj ] = i (e hbar / m2) εijk Bk, defining the Berry curvature Bk, implies Faraday's law.
A ferromagnetic has broken rotational symmetry and implies a result for Bk which is a Pauli matrix corresponding a a SU(2) rather than U(1) gauge group. In turn this leads to the additional spin terms in Faraday's law. Nearly all generation of electrical power reflects Faraday's law, while essentially all storage batteries convert chemical to electrical energy and both lead to currents due to the forces on the electron's charge. A spin battery converts energy stored in a magnetic material into electric power via the extended Faraday's law using the spin-transfer-torque effect and corresponds to forces acting on the electron's spin. The energy density stored in such a battery based upon nano-magnets is perhaps comparable to that of a lead-acid battery. Might this one day power electric cars?
E = - ( hbar / e ) dγ/dt where γ is the (1984) Berry phase acquired while the electron passes around a circuit. The Anaronov-Bohm contribution to γ gives back E = - dΦ/dt while adding the spin Berry phase leads to a spin-motive-force which in a ferromagnetic material implies an electromotive-force. Feynman, in 1948, anticipated Berry by showing the velocity commutation rule [vi,vj ] = i (e hbar / m2) εijk Bk, defining the Berry curvature Bk, implies Faraday's law.
A ferromagnetic has broken rotational symmetry and implies a result for Bk which is a Pauli matrix corresponding a a SU(2) rather than U(1) gauge group. In turn this leads to the additional spin terms in Faraday's law. Nearly all generation of electrical power reflects Faraday's law, while essentially all storage batteries convert chemical to electrical energy and both lead to currents due to the forces on the electron's charge. A spin battery converts energy stored in a magnetic material into electric power via the extended Faraday's law using the spin-transfer-torque effect and corresponds to forces acting on the electron's spin. The energy density stored in such a battery based upon nano-magnets is perhaps comparable to that of a lead-acid battery. Might this one day power electric cars?
For more information contact:
- Dr. Massimiliano Galeazzi
- (305) 284-2326
- galeazzi@physics.miami.edu
