468
17 Magnetic Semiconductors
Fig. 17.4 Magnetic phase
diagram of Hg 1−x Mn x Te,
‘P’ (‘SG’) denotes the
paramagnetic (spin glass)
phase. Various symbols
represent data from
different authors and
methods. Dashed line is a
guide to the eye. Adapted
from [1528]
25
20
15
10
5
0
0.1 0.2 0.3 0.4 0.5
T (K)
C
x
Hg Mn Te
1-x
x
P
SG
becomes comparable with the size of the sample. If interaction up to the first, second or third neighbor
are taken into account for a fcc lattice, the critical concentrations are given by x c = 0.195, 0.136, and
0.061, respectively [1529]. The nearest-neighbor interaction between Mn atoms in such DMS as (Zn,
Cd, Hg) Mn(S, Se, Te) was found to be antiferromagnetic,
1 i.e. neighboring spins are aligned antiparallel. Due to frustration of antiferromagnetic long-range order on a fcc lattice, an antiferromagnetic
spin glass forms. The transition temperature T C between the paramagnetic and spin-glass phases of
Hg 1−x Mn x Te is shown in Fig. 17.4.
In III–V compounds, the 3d transition metals represent an acceptor if incorporated on the site of
the group-III element as, e.g., in the much investigated compound Ga 1−x Mn x As. This material will
be used in the following to discuss some properties of magnetic semiconductors. It seems currently
well understood and has a fairly high Curie temperature of T C ≈ 160 K. Ferromagnetism in a diluted
magnetic semiconductor is believed to be caused by indirect exchange through itinerant charge carriers. The ferromagnetic coupling can be invoked by the Ruderman–Kittel–Kasuya–Yoshida (RKKY)
interaction, i.e. the spins of the paramagnetic ions are aligned via interaction with the free carriers in
the semiconductor. A related concept is the double exchange
2 [1530–1532] in which carriers move in a
narrow Mn-derived d-band (for d-wave character see Fig. 7.16c). Such a mechanism was first invoked
for PbSnMnTe [1533]. Later, ferromagnetism was discovered in InMnAs [1534] and GaMnAs [1535].
In (In,Ga)MnAs a Mn ion (spin up) spin polarizes the surrounding hole gas (spin down), which has
been supplied from the Mn acceptors. This mechanism lowers the energy of the coupled system. The
interaction
H = −β N 0 x S s
(17.1)
between the Mn d-shell electrons (S = 5/2) and the p-like free holes (s = 1/2) is facilitated by p–d
hybridization of the Mn states. N 0 denotes the concentration of cation sites in the A 1−x Mn x B alloys.
The coupling via electrons is much weaker (coupling coefficient α). The holes interact with the next
Mn ion and polarize it (spin up), thus leading to ferromagnetic order. The ferromagnetic properties
are evident from the hysteresis shown in Fig. 17.6a. Without the carrier gas such interaction is not
present and the material is only paramagnetic. Theoretical results for the Curie temperature of various
p-type semiconductors are shown in Fig. 17.5. Generally, the quest for higher Curie temperatures (well
above room temperature) is underway and wide band gap materials such as GaN or ZnO doped with
transition metals have shown some encouraging results. Mn-substituted chalcopyrite semiconductors
1 Such superexchange leads to antiferromagnetic interaction if the bond angle is ‘close’ to 180 ◦ .
2 This model is also called the Zener model.
17 Magnetic Semiconductors
Fig. 17.4 Magnetic phase
diagram of Hg 1−x Mn x Te,
‘P’ (‘SG’) denotes the
paramagnetic (spin glass)
phase. Various symbols
represent data from
different authors and
methods. Dashed line is a
guide to the eye. Adapted
from [1528]
25
20
15
10
5
0
0.1 0.2 0.3 0.4 0.5
T (K)
C
x
Hg Mn Te
1-x
x
P
SG
becomes comparable with the size of the sample. If interaction up to the first, second or third neighbor
are taken into account for a fcc lattice, the critical concentrations are given by x c = 0.195, 0.136, and
0.061, respectively [1529]. The nearest-neighbor interaction between Mn atoms in such DMS as (Zn,
Cd, Hg) Mn(S, Se, Te) was found to be antiferromagnetic,
1 i.e. neighboring spins are aligned antiparallel. Due to frustration of antiferromagnetic long-range order on a fcc lattice, an antiferromagnetic
spin glass forms. The transition temperature T C between the paramagnetic and spin-glass phases of
Hg 1−x Mn x Te is shown in Fig. 17.4.
In III–V compounds, the 3d transition metals represent an acceptor if incorporated on the site of
the group-III element as, e.g., in the much investigated compound Ga 1−x Mn x As. This material will
be used in the following to discuss some properties of magnetic semiconductors. It seems currently
well understood and has a fairly high Curie temperature of T C ≈ 160 K. Ferromagnetism in a diluted
magnetic semiconductor is believed to be caused by indirect exchange through itinerant charge carriers. The ferromagnetic coupling can be invoked by the Ruderman–Kittel–Kasuya–Yoshida (RKKY)
interaction, i.e. the spins of the paramagnetic ions are aligned via interaction with the free carriers in
the semiconductor. A related concept is the double exchange
2 [1530–1532] in which carriers move in a
narrow Mn-derived d-band (for d-wave character see Fig. 7.16c). Such a mechanism was first invoked
for PbSnMnTe [1533]. Later, ferromagnetism was discovered in InMnAs [1534] and GaMnAs [1535].
In (In,Ga)MnAs a Mn ion (spin up) spin polarizes the surrounding hole gas (spin down), which has
been supplied from the Mn acceptors. This mechanism lowers the energy of the coupled system. The
interaction
H = −β N 0 x S s
(17.1)
between the Mn d-shell electrons (S = 5/2) and the p-like free holes (s = 1/2) is facilitated by p–d
hybridization of the Mn states. N 0 denotes the concentration of cation sites in the A 1−x Mn x B alloys.
The coupling via electrons is much weaker (coupling coefficient α). The holes interact with the next
Mn ion and polarize it (spin up), thus leading to ferromagnetic order. The ferromagnetic properties
are evident from the hysteresis shown in Fig. 17.6a. Without the carrier gas such interaction is not
present and the material is only paramagnetic. Theoretical results for the Curie temperature of various
p-type semiconductors are shown in Fig. 17.5. Generally, the quest for higher Curie temperatures (well
above room temperature) is underway and wide band gap materials such as GaN or ZnO doped with
transition metals have shown some encouraging results. Mn-substituted chalcopyrite semiconductors
1 Such superexchange leads to antiferromagnetic interaction if the bond angle is ‘close’ to 180 ◦ .
2 This model is also called the Zener model.