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1.2. THE PHASE DIAGRAM 17
La 2 CuO 4 ,inYBa 2 Cu 3 O 6 ,orinBi 2 Sr 2 YCu 3 O 8 , respectively.
It is widely accepted that the CuO 2 planes host electronic excitations which
are most relevant to the superconductivity. The intervening layers are viewed as
inert charge reservoirs. However, there is still some controversy about the role of
the co-called apical oxygen atoms, which are located above and below the CuO 2
plane.
Moreover, it is experimentally well established that the parent compounds 1
La 2 CuO 4 and YBa 2 Cu 3 O 6 are charge transfer insulators and ordered antiferromagnetically
below a Néel temperature T N . Below the Néel temperature T N ,
the unpaired holes of the Cu 2+ ions are antiferromagnetically coupled via superexchange
through the oxygen O 2− . The maximum Néel temperature is of the
order of several hundred Kelvin (in YBa 2 Cu 3 O 6 T N ≈ 420K).
The picture of a magnetic insulator contradicts the simple band-structure
point of view. In fact, the formal valencies of lanthanum, oxygen, and copper in
La 2 CuO 4 are La + 3 ,O − 2 ,andCu + 2 , respectively. Hence the planar copper constitutes
the only open shell atomic configuration. It is in a 3d 9 state which contains
a single d-hole. This hole is expected to be mainly located in a planar d x2−y2
orbital. Therefore, a naive argument would suggest that the parent compounds
are simple metals with the charge carriers moving in the planes. But the localized
copper spins provide the magnetic moments for the antiferromagnetic
order. The in-plane antiferromagnetic exchange coupling J is generated by a
copper spin super-exchange and the undoped CuO 2 plane is well described by a
two-dimensional spin−1/2 antiferromagnetic Heisenberg model.
Typically, J is of the order of a few hundred meV and depends on the parent
compound. Let us note that long-range AFM order at finite temperature requires
an inter-plane coupling J ⊥ , since a pure two dimensional long-range magnetic order
is ruled out by the Mermin-Wagner theorem [3], which forbids any continuous
symmetry breaking at a finite temperature in one and two dimensions.
1.2 The phase diagram
Besides the question of the nature of the parent compound, one of the early questions
was whether there are Cooper pairs in these materials or some new exotic
form of superconductivity that takes place when the system is doped with electrons
or holes. In this regards, it is quite remarkable that the cuprate perovskites
allow for a continuous variation of the in-plane carrier concentration by doping
which leads to a complex phase diagram. The parent compounds can be doped
by adding or removing holes, which eventually leads to metallic behavior and
superconductivity. Doping is achieved either by hetero-valent substitution as in
La 2−x Sr x CuO 4 and in Bi 2 Sr 2 Cy 1−x YxCu 2 O 8 or by a variation of the total oxygen
content as in YBa 2 Cu 3 O 6+x . Doping introduces additional charge carriers into
1 Undoped materials are for historical reasons usually referred to as parent compounds.