This document discusses magnetic semiconductors and their properties. It covers: 1) Concentrated magnetic semiconductors like chromium chalcogenides and europium chalcogenides which are ferromagnetic due to kinetic exchange and Coulomb interactions between localized magnetic moments. 2) Diluted magnetic semiconductors (DMS) where magnetic ions substitute into semiconductor hosts, including II-VI, oxide, and III-V semiconductors. Many DMS show carrier-mediated ferromagnetism driven by holes. 3) Key open questions about the mechanism of ferromagnetism, the nature of carrier states, and the origin of metal-insulator transitions and resistivity maxima observed

1. 2. Magnetic semiconductors: classes of materials,
basic properties, central questions
 Basics of semiconductor physics
 Magnetic semiconductors
• Concentrated magnetic semiconductors
• Diluted magnetic semiconductors
 Some central questions

2. Basics of semiconductor physics
Undoped (intrinsic)
semiconductors:
Band structure has energy
gap Eg at the Fermi energy
Conduction only if electrons
are excited (e.g., thermally,
optically) over the gap
Same density of electrons in
conduction band and holes
in valence band:
gap
conduction band
valence band
Non-degenerate electron/hole gas in
bands (i.e., no Fermi sea), transport
similar to classical charged gas

3. Doping: Introduce charged impurities
Example: replace Ga by Si in GaAs
Si has one valence electron more
→ introduces extra electron: donor
Si4+
weakly binds the electron:
hydrogenic (shallow) donor state
Example: replace Ga by Zn in GaAs
Zn has one valence electron less
→ introduces extra hole: acceptor
Zn2+
weakly binds the hole:
hydrogenic (shallow) acceptor state
EF
CB
VB
EF
CB
VB
excitation energy is
strongly reduced
(¿ Eg)
conduction at lower
temperatures

4.  if impurity in crystal field has levels in the gap:
deep levels (not hydrogenic), e.g., Te in GaAs
 both shallow and deep levels can result from
native defects: vacancies, interstitials…
 if donors and acceptors are present: lower carrier
concentration, compensation
EF
CB
VB
Increasing doping:
hydrogenic impurity states overlap → form impurity band
CB
VB
For heavy doping the impurity band overlaps with the VB or CB
E
0
densityofstates
VB CB
EF

5. Magnetic semiconductors
Concentrated magnetic semiconductors:
 Ferromagnetic CrBr3 (Tc = 37 K)
Tsubokawa, J. Phys. Soc. Jpn. 15, 1664 (1960)
structure: bayerite (rare and complicated)
 Stoichiometric Eu chalcogenides (1963)
EuO: ferromagnet (Tc = 77 K)
EuS: ferromagnet (Tc = 16.5 K)
EuSe: antiferro-/ferrimagnet
EuTe: antiferromagnet
structure: NaCl
good realizations of Heisenberg models with
J1 (nearest neighbor) and J2 (NNN) relevant
Mechanism: kinetic and Coulomb
Kasuya (1970)
CB (dEu)
fEu
FM

6.  n-doped Eu chalcogenides:
Eu-rich EuO, (Eu,Gd)O, (Eu,Gd)S, …
oxygen vacancy: double donor (missing O fails to bind two electrons)
Gd3+
substituted for Eu2+
: single donor
The systems are not diluted: every cation is magnetic
Electrons increase Tc to ~150 K (Shafer and McGuire, 1968)
Mechanism: carrier-mediated, see Lecture 3
Electrons lead to metal-insulator transition close to Tc:
Eu-rich EuO
Torrance et al., PRL 29, 1168 (1972)
One possible origin:
Valence band edge shifts with T
(related to exchange splitting),
crosses deep impurity level

7. Eu1-xGdxO with x = 0% – 19%:
Ott et al., cond-mat/0509722
• Eu2+
with 3d7
configuration
• Gd3+
with 3d7
configuration
• Gd is a donor: strongly n-type
concentrated spin system: all S = 7/2,
essentially only potential disorder
~magnetization
more carriers & more disorder → higher Tc, more convex magnetization
theory
Mauger (1977)

8.  Ferromagnetic Cr chalcogenide spinels
CdCr2S4, CdCr2Se4 (Tc = 129 K)
 Manganites
(La,X)MnO3, …
structure: based on perovskite, tilted
Mechanism: double exchange, due to
mixed valence Mn3+
Mn4+
$ Mn4+
Mn3+
Very complicated (i.e. interesting) system! Many types of magnetic order,
stripe phases, orbital order, metal-insulator transitions, colossal
magnetoresistance…See Salamon & Jaime, RMP 73, 583 (2001)
E. Dagotto, Science 309, 257 (2005);
J. F. Mitchell et al., J. Phys. Chem. B
105, 10731 (2001)

9. Diluted magnetic semiconductors (DMS):
Magnetic ions are introduced into a non-magnetic semiconductor host
Typically substitute for the cation as 2+-ions, e.g. Mn2+
(high spin, S = 5/2)
 II-VI semiconductors (excluding oxides)
(Cd,Mn)Te, (Zn,Mn)Se, (Be,Mn)Te… zinc-blende structure
studied extensively in 70’s, 80’s
Mn2+
is isovalent → low carrier concentration
• usually paramagnetic or spin-glass
(antiferromagnetic superexchange)
• ferromagnetism hard to achieve by
additional homogeneous doping
• ferromagnetic at T < 4 K employing
modulation p-doping (acceptors and
Mn in different layers):
Haury et al., PRL 79, 511 (1997)
Mn2+ additional dopand

10. Inverse susceptibility
Haury et al., PRL 79, 511 (1997)
Tc
Significant p-doping is required to
overcome antiferromagnetic
superexchange – mechanism?
Hint: anomalous Hall effect and
direct SQUID magnetometry find
very similar magnetization
→ holes couple to local moments
carrier-mediated ferromagnetism
Anomalous Hall effect: in the
absence of an applied magnetic
field (due to spin-orbit coupling)
• ferromagnetism with Tc = 2.5 K in bulk p-type (Be,Mn)Te:N
Hansen et al., APL 79, 3125 (2001)

11.  Oxide semiconductors
(Zn,X)O wurtzite, (Ti,X)O2 anatase or rutile, (Sn,X)O2 cassiterite
Wide band gap → transparent ferromagnets
(Zn,Fe,Co)O: Tc ¼ 550 K
Han et al., APL 81, 4212 (2002)
• intrinsically n-type
(Zn interstitials)
• no anomalous Hall effect
Not carrier-mediated ferromagnetism,
possibly double exchange in deep (Fe d)
impurity band?
But Theodoropoulou et al. (2004) see
anomalous Hall effect…
Is ferromagnetism effect of “dirt” (Co clusters)? Many papers report
absense of ferromagnetism – strong dependence on growth!

12. Rutile (Ti,Co)O2: Tc > 300 K
Toyosaki et al., Nature Mat. 3, 221 (2004)
Strong anomalous Hall effect
depending on electron concentration
→ carrier-induced ferromagnetism
Question: Why is Tc high for this n-type compound?
Why not? Electrons in CB: mostly s-orbitals, exchange interaction
between s and Co d-orbitals is weak (no overlap, only direct Coulomb
exchange)
Anomalous Hall effect
n-type Controversial

13.  III-V bulk semiconductors
(In,Mn)As, (Ga,Mn)As, (Ga,Mn)N, (In,Mn)Sb,… zinc-blende structure
focus of studies since ~ 1992
Problem: low solubility of Mn
→ low-temperature MBE:
up to ~ 8% of Mn
Mn2+
introduces spin 5/2 and
hole (shallow acceptor)
→ high hole concentration,
but partially compensated:
• substitutional MnGa: acceptors
• antisites AsGa: double donors
• Mn-interstitials: double donors
Ferromagnetic samples are p-type
(In,Mn)As: Ohno et al., PRL 68, 2664 (1992)

14. Key experiments on (Ga,Mn)As: Ferromagnetic order
Ohno, JMMM 200, 110 (1999)
insulating
metallic
bad
sample
 hard ferromagnet  Tc ~ Mn concentration (importance
of carrier concentration?)
 metal-insulator transition at x ~ 3%

15. with Mn doping:
Ohno, JMMM 200, 110 (1999)
with annealing:
Hayashi et al., APL 78, 1691 (2001)
Metal-insulator transition at T = 0
highmetallic
insulating/localized
low
 typical for disorder-induced (Anderson) insulator

16. Anomalous Hall effect
Hall effect in the absence of an applied magnetic field
(in itinerant ferromagnets, due to spin-orbit coupling)
Omiya et al., Physica E 7, 976 (2000)
anomalous Hall effect
normal
Hall effect:
roughly
linear in B
(RH / B)
B (T)
saturation of
magnetization

17. (In,Mn)As:
Ohno et al., PRL 68, 2664 (1992)
(Ga,Mn)As: Ruzmetov et al.,
PRB 69, 155207 (2004)
 anomalous Hall resistivity ~ magnetization
→ holes couple to Mn moments

18. Resistivity maximum at Tc
Very robust feature: maximum
or shoulder in resistivity
Potashnik et al., APL 79,
1495 (2001)
Ga+
-ion implanted (Ga,Mn)As:
highly disordered
Katoetal.,Jap.J.Appl.
Phys.44,L816(2005)

19. Defects
 MBE growth of (Ga,Mn)As with As4 ! As2 cracker leads to enhanced Tc
(110 K ! 160 K): Edmonds et al., Schiffer/Samarth group
→ control of antisite donors
 Mn interstitials detected by X-ray channeling Rutherford backscattering
Yu et al., PRB 65, 201303(R), 2002
X rays
MnI
tilt angle
Here: about 17% of Mn
in tetrahedral interstitial
sites

20. Curie temperature Tc
Ku et al., APL 82, 2302 (2003)
 annealing increases Tc
 highest Tc for thin samples
 interpretation: donors (Mn interstitials)
move to free surface and are “passivated”
Sørensen et al., APL 82, 2287 (2003)
hole concentration
 Tc depends roughly linearly on
hole concentration p
 similar results from Be codoping
carrier-mediated
ferromagnetism

21. Mathieu et al., PRB 68,
184421 (2003)
Annealing dependence of magnetization curve
 magnetization curves change straight/convex (upward curvature) →
concave (downward curvature, mean-field-like)
 degradation for very long annealing (precipitates?)
Potashnik et al., APL 79,
1495 (2001)

22. Wide-gap III-V DMS
(Ga,Mn)N (wurtzite): Tc up to 370 K, Reed et al., APL 79, 3473 (2001)
Anomalous Hall effect Resistivity
Looks similar to (Ga,Mn)As, except for high Tc and weak resistivity peak
Sonoda et al. (2002) report Tc > 750 K, but no anomalous Hall effect
→ inhomogeneous?

23. (Ga,Cr)N, (Al,Cr)N:
Tc > 900 K, Liu et al., APL 85, 4076 (2004)
Highly resistive (AlN) or thermally
activated hopping (GaN)
→ localized (d-) impurity levels
Different mechanism of
ferromagnetism?
Results on wide-gap III-V DMS are controversial

24.  group-IV semiconductor: MnxGe1–x
structure: diamond
x < 4%, Tc up to 116 K
Park et al., Science 295, 651 (2002)
Tc » x highly resistive
Some reports on ferromagnetism in Mn or
Fe ion-implanted SiC and Mn implanted
Si (Tc > 400K); not for diamond
strong disorder

25.  IV-VI semiconductors
(Sn,Mn)Te, (Ge,Mn)Te, (Pb,Mn)Te etc.
structure: NaCl
narrow gap, p-type semiconductors
Ge1–xMnxTe:
Cochrane et al., PRB 9, 3013 (1974)
x = 0.01 Tc = 2.3 K
… …
x = 0.50 Tc = 167 K
good Mn solubility, highly p-doped,
a metal at high x
(Pb,Mn)Te: low hole concentration, no ferromagnetism, spin glass?
(Pb,Sn,Mn)Te: Story et al., PRL 56, 777 (1986)
magnetic interaction is sensitive to hole concentration and long ranged
x = 0.5
T = 4.2 K
magnetic field
magnetization

26.  Chiral clathrate Ba6Ge25–xFex
Li & Ross, APL 83, 2868 (2003)
x ¼ 3, Tc = 170 K
highly disordered, reentrant spin-glass
transition at Ts = 110 K
 Tetradymite Sb2–xVxTe3: layered narrow-gap DMS
Dyck et al., PRB 65, 115212 (2002)
x up to 0.03, Tc ¼ 22 K
intrinsically strongly p-doped
probably isovalent V3+
Similar to III-V DMS
Tc

27.  Carbon nanofoam: C
structure: highly amorphous low-density foam
produced by high-energy laser ablation (not an aerogel)
strongly paramagnetic, indications of ferromagnetism, mostly at T < 2K,
semiconducting with low conductivity
Rode et al., PRB 70, 054407 (2004) weak hysteresis
T = 1.8 K
Possible origin: sp2
/sp3
mixed compound → unpaired electrons

28.  III-V heterostructures (towards applications)
(In,Mn)As field-effect transistor
Ohno et al., Nature 408, 944 (2000)
shift of Tc with gate voltage and thus with hole concentration:
carrier-mediated ferromagnetism
VG
(In,Mn)As
VG

29. p-doped (Ga,Mn)As δ-doped layer
Nazmul et al., PRL 95, 017201 (2005)
Al0.5Ga0.5As
Al0.5Ga0.5As:Be
GaAs
0.5 monolayer
MnAs
2DHG
|ψ|2
 allows higher local concentration of Mn
 tail of hole concentration of 2DHG in δ layer
 Tc up to 250 K
 quasi-two-dimensional ferromagnet (interdiffusion?)

30. Some central questions
 In some DMS ferromagnetism is carrier-mediated – is it in all of
them?
 In what kind of states are the carriers?
Weakly overlapping deep (d-like) levels in gap or shallow levels?
Impurity band or valence/conduction band?
 What is the mechanism?
 What drives the T=0 metal-insulator transition when it is observed?
 Magnetization curves are mean-field-like for good samples,
convex or straight for bad samples – why?
 What causes the robust resistivity maximum close to Tc?