In this paper we present a description of the Nernst electric field E generated by forced flux tube motion due to a temperature gradient VT. Depending on the value of VTwith respect to a critical gradient VTmt, we find for VT/VTc,lt << 1 a regime Eoc VT, in close analogy to the regime of thermally activated flux flow in transport current measurements (characterized by an electric field proportional to the transpoxt current). The theory for VT< VT~,~t is applied to an analysis of experimental results obtained for polycrystalline Tl2Ba2CaCu2Ox films. From the temperature dependence of the Nernst field we derive activation energies for flux depinning.Thermomagnetic effects in high-To superconductors have recently been observed by several groups [1][2][3]. From investigation of the Nernst effect in polycrystalline Tl2Ba2CaCu2Ox films using pulsed laser heating to induce temperature gradients in the film [ 1 ], activation energies for depinning of flux tubes have been derived assuming thermally activated flux motion. A Nernst effect was also observed in epitaxial Y-Ba-Cu-O films [2 ] by continuous heating [4]. From measurement of the Nernst field and the film resistivity due to flux motion, the transport entropy of flux tubes near Tc has been estimated. The transport entropy has also been investigated in a YBa2Cu307 single crystal, using the Ettingshausen effect [ 3 ]; from measurements of the entropy flow the transport line energy of a vortex has been determined. In this paper, we develop a theory to describe flux motion due to a temperature gradient and derive an expression for the Nernst electric field. We then use the theory for an analysis of experimental data reported in ref. [ 1 ].The °u°,.,,.;,. field ,,,,,,,.o,,a by nux m'~tio n i~ givon by E= ( 1/c)B×v [5], where B is the magnetic field in the material and v the velocity of B with respect to the material. For flux hopping transverse to B, with hopping rate v and hopping length l, E= (1/c)Bvl.For a derivation of E we follow a theory given by Brandt [ 6 ] for the case that the driving force on flux tubes is the Lorentz force due to a transport current.Instead of the Lorentz force we regard the thermal force Fth= -VT SL [ 7] that is due to a temperature gradient VT and a transport entropy SL of a flux tube, where S is the transport entropy per unit length and L is the flux tube length. For the net jump rate which is the difference of jump rates along and against the driving force we find then. using Andersons model of thermal activated hopping [ 8 ], _voexp [-(kTa~-kY~-'Sm/)] , (I) where kTa is an activation energy and Vo an attempt frequency~ At a critical temperature gradient VTcrit = kga/(SLI) the pinning energy and the work done by the thermal force over the hopping length I are equal. With this expression we findFor a small argument of sinh, i.e. VT/VTcrtt << 1, this expression can be simplified to
E-2Blv° Ta VT ( ~) TVT¢r, ------~tOur treatment shows therefore that for small driving 0921-4534/91/$03.50 © 1991 -Elsevier Science Publishers B.V. ( North...