First-Order Vortex Lattice Melting and Magnetization of YBa 2 Cu 3 O$_{7-δ}
Abstract
We present the first non-mean-field calculation of the magnetization
M(T)
of YBa
2
Cu
3
O
7−δ
both above and below the flux-lattice melting temperature
T
m
(H)
. The results are in good agreement with experiment as a function of transverse applied field
H
. The effects of fluctuations in both order parameter
ψ(r)
and magnetic induction
B
are included in the Ginzburg-Landau free energy functional:
ψ(r)
fluctuates within the lowest Landau level in each layer, while
B
fluctuates uniformly according to the appropriate Boltzmann factor. The second derivative
(
∂
2
M/∂
T
2
)
H
is predicted to be negative throughout the vortex liquid state and positive in the solid state. The discontinuities in entropy and magnetization at melting are calculated to be
∼0.034
k
B
per flux line per layer and
∼0.0014
~emu~cm
−3
at a field of 50 kOe.