194
6 Magnetism and Conduction
Fig. 6.8 Graphical
representation of the
perovskite Sr 2 CuO 3 .The
unit cell is given as a dashed
box. Cu ions are represented
as large white spheres and
oxygen as smaller gray
spheres, Sr ions are not
depicted for clarity
Fig. 6.9 Ferromagnetic
(left) and antiferromagnetic
(right) spin settings in the
unit cell of Sr 2 CuO 3 .The
spin on symmetry equivalent
copper ions are marked with
the same gray scale
E F (a, b, c) =−J a
4 ·
1
2
·
1
2
/4 + 2 ·
1
2
·
1
2
/2
− J b
4 ·
1
2
·
1
2
/4 + 2 ·
1
2
·
1
2
/2
− J d · 8 ·
1
2
·
1
2
=−2J d −
1
2
J a −
1
2
J b
(6.40)
The second step consists of the calculation of the energy per unit cell after flipping the spin on the central copper (right panel of Fig. 6.9) and relating it to the
energy expression obtained with the Ising Hamiltonian. As far as the interactions
along a and b are concerned, the situation remains unchanged with respect to the
ferromagnetic alignment. The expression only changes for the interaction along the
6 Magnetism and Conduction
Fig. 6.8 Graphical
representation of the
perovskite Sr 2 CuO 3 .The
unit cell is given as a dashed
box. Cu ions are represented
as large white spheres and
oxygen as smaller gray
spheres, Sr ions are not
depicted for clarity
Fig. 6.9 Ferromagnetic
(left) and antiferromagnetic
(right) spin settings in the
unit cell of Sr 2 CuO 3 .The
spin on symmetry equivalent
copper ions are marked with
the same gray scale
E F (a, b, c) =−J a
4 ·
1
2
·
1
2
/4 + 2 ·
1
2
·
1
2
/2
− J b
4 ·
1
2
·
1
2
/4 + 2 ·
1
2
·
1
2
/2
− J d · 8 ·
1
2
·
1
2
=−2J d −
1
2
J a −
1
2
J b
(6.40)
The second step consists of the calculation of the energy per unit cell after flipping the spin on the central copper (right panel of Fig. 6.9) and relating it to the
energy expression obtained with the Ising Hamiltonian. As far as the interactions
along a and b are concerned, the situation remains unchanged with respect to the
ferromagnetic alignment. The expression only changes for the interaction along the