Superconductivity and ferromagnetism: how to
find a compromise
Mario Cuoco
∗†
, Paola Gentile
†
and Canio Noce
†∗∗
∗
Centre de Recherches sur les Très Basses Températures associé à l’Université Joseph Fourier,
C.N.R.S., BP 166, 38042 Grenoble-Cédex 9, France
†
Unità I.N.F.M. di Salerno, Dipartimento di Fisica “E. R. Caianiello”, Università di Salerno,
I-84081 Baronissi (Salerno), Italy
∗∗
Unità I.N.F.M. di Salerno-Coherentia
Abstract. We analyze the problem of the interplay of superconductivity and ferromagnetism,
by focusing on their coexistence. The interest in this field has been renewed after the recent
discovery of coexistence of superconductivity and ferromagnetism in UGe
2
,URhGe,ZrZn
2
,and
in rutheno-cuprate RuSr
2
RECu
2
O
8
compounds, with RE= Eu or Gd. In this paper we concentrate
on the competition between itinerant ferromagnetism and singlet superconductivity looking at the
case in which the same electrons participate in both the ordered phases. By using a mean field
approximation, we have studied the stability of the coexistence phase when the ferromagnetic
instability is described through the Stoner model, and when it can be ascribed to a kinetic exchange
mechanism.
INTRODUCTION
The problem of the interplay of superconductivity (SC) and ferromagnetism (FM) has
been studied since the sixties. The first theoretical inquiry into this problem was made
by Abrikosov and Gorkov [1], who provided an accurate description of the action of
magnetic impurities on superconductivity, showing that if introduced in a superconduc-
tor they lower the superconducting critical temperature significantly, and totally destroy
superconductivity, acting as an internal magnetic field.
There are two different mechanisms of pair breaking due to the action of a magnetic
field: the spin pair breaking and the orbital pair breaking. The first one is due to the
coupling of the magnetic field to the electron spins, which leads to the Zeeman effect,
lifting the degeneracy of spin-up and spin-down electron energies. By increasing the
strength of the magnetic field, the system passes, through a first-order phase transition,
from the BCS state to the normal state. The critical field above which the superconduct-
ing phase is destroyed is obtained by equating the magnetic energy the system gains as
a consequence of the pair breaking, with the condensation energy. In this way one can
obtain the so-called Pauli limiting field. As derived by Chandrasekhar and Clogston, for
singlet s-wave superconductivity, this limit is H
p
= Δ
0
/(
√
2
μ
B
),where
μ
B
is the Bohr
magneton and Δ
0
is the superconducting order parameter.
On the other hand, the orbital pair breaking is due to the electromagnetic interaction
between the potential vector associated with the magnetic field and the linear momentum
p of the superconducting electrons. This interaction leads to a shift in the kinetic energies
© 2003 American Institute of Physics 0-7354-0167-5/03/$20.00
CP695,
Highlights in Condensed Matter Physics,
edited by A. Avella et al.
215