17.3 Diluted Magnetic Semiconductors
467
Fig. 17.2 Diagrammatic
overview of A II
1−x Mn x B VI
alloys and their crystal
structures. The bold lines
indicate ranges of the
molar fraction x for which
homogeneous crystal
phases form. ‘Hex’ and
‘Cub’ indicate wurtzite and
zincblende, respectively.
From [1526]
Fig. 17.3 a Energies of
6 → 8 transitions versus
magnetic field for
Hg 0.996 Mn 0.004 Te at
T = 2 K. Symbols are
experimental values for
two polarization directions
as indicated. Numbers
denote quantum numbers
of transitions. Solid lines
are theoretical fits. b
Interaction gap versus Mn
concentration for
Hg 1−x Mn x Te at
T = 4.2 K. Various
symbols represent data
from different authors and
methods. Dashed line is a
guide to the eye. Adapted
from [1528]
(a)
370
350
330
310
290
270
0
1
2
3
4
5
Hg Mn Te
x=0.004
1-x
x
0
(b)
300
200
100
0
-100
-200
-300
0 (meV)
x
0
0.1
0.15
0.05
Hg Mn Te
1-x
x
order to allow the electrons to get out of their way in real space). Thus, the atoms have a sizeable spin
and a magnetic moment. The spin of Mn is S = 5/2. Most transition metals have a 4s
2 configuration
that makes them isovalent in II–VI compounds. We note that Zn has a complete 3d shell and thus no
net spin. In Fig. 17.2, an overview of the crystallographic properties is given for Mn-alloyed II–(Se, S,
Te, O) based DMS [1526] (DMS with Se, S, and Te have been discussed in [1527]).
As an example, the properties of Hg 1−x Mn x Te are discussed. This alloy is semiconducting (positive
band gap 0 ) for x > 0.075 and a zero-gap material (negative interaction gap 0 ) for smaller Mn
concentration (cf. Fig. 6.46). The transitions between the 6 and 8 bands can be determined with
magnetoabsorption spectra in the infrared [1528]. In Fig. 17.3a, the magnetic field dependence of
transition energies between different Landau levels is shown that can be extrapolated to yield the
interaction gap. The interaction gap is shown in Fig. 17.3b as a function of the Mn concentration.
For small Mn concentrations, the DMS behaves like a paramagnetic material. For larger concentrations, the Mn atoms have increasing probability to be directly neighbored by another Mn atom and
suffer superexchange interaction (cf. (3.24b)). At a certain critical concentration x c , the cluster size
467
Fig. 17.2 Diagrammatic
overview of A II
1−x Mn x B VI
alloys and their crystal
structures. The bold lines
indicate ranges of the
molar fraction x for which
homogeneous crystal
phases form. ‘Hex’ and
‘Cub’ indicate wurtzite and
zincblende, respectively.
From [1526]
Fig. 17.3 a Energies of
6 → 8 transitions versus
magnetic field for
Hg 0.996 Mn 0.004 Te at
T = 2 K. Symbols are
experimental values for
two polarization directions
as indicated. Numbers
denote quantum numbers
of transitions. Solid lines
are theoretical fits. b
Interaction gap versus Mn
concentration for
Hg 1−x Mn x Te at
T = 4.2 K. Various
symbols represent data
from different authors and
methods. Dashed line is a
guide to the eye. Adapted
from [1528]
(a)
370
350
330
310
290
270
0
1
2
3
4
5
Hg Mn Te
x=0.004
1-x
x
0
(b)
300
200
100
0
-100
-200
-300
0 (meV)
x
0
0.1
0.15
0.05
Hg Mn Te
1-x
x
order to allow the electrons to get out of their way in real space). Thus, the atoms have a sizeable spin
and a magnetic moment. The spin of Mn is S = 5/2. Most transition metals have a 4s
2 configuration
that makes them isovalent in II–VI compounds. We note that Zn has a complete 3d shell and thus no
net spin. In Fig. 17.2, an overview of the crystallographic properties is given for Mn-alloyed II–(Se, S,
Te, O) based DMS [1526] (DMS with Se, S, and Te have been discussed in [1527]).
As an example, the properties of Hg 1−x Mn x Te are discussed. This alloy is semiconducting (positive
band gap 0 ) for x > 0.075 and a zero-gap material (negative interaction gap 0 ) for smaller Mn
concentration (cf. Fig. 6.46). The transitions between the 6 and 8 bands can be determined with
magnetoabsorption spectra in the infrared [1528]. In Fig. 17.3a, the magnetic field dependence of
transition energies between different Landau levels is shown that can be extrapolated to yield the
interaction gap. The interaction gap is shown in Fig. 17.3b as a function of the Mn concentration.
For small Mn concentrations, the DMS behaves like a paramagnetic material. For larger concentrations, the Mn atoms have increasing probability to be directly neighbored by another Mn atom and
suffer superexchange interaction (cf. (3.24b)). At a certain critical concentration x c , the cluster size