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
Basics of semiconductor physics
Undoped (intrinsic)
semiconductors:
Band structure has energy
gap Eg at the Fermi energy
conduction band
gap
valence band
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:
Non-degenerate electron/hole gas in
bands (i.e., no Fermi sea), transport
similar to classical charged gas
Doping: Introduce charged impurities
Example: replace Ga by Si in GaAs
Example: replace Ga by Zn in GaAs
Si has one valence electron more
→ introduces extra electron: donor
Zn has one valence electron less
→ introduces extra hole: acceptor
Si4+ weakly binds the electron:
Zn2+ weakly binds the hole:
hydrogenic (shallow) donor state
hydrogenic (shallow) acceptor state
CB
EF
VB
excitation energy is
strongly reduced
(¿ Eg)
conduction at lower
temperatures
CB
EF
VB
 if impurity in crystal field has levels in the gap:
deep levels (not hydrogenic), e.g., Te in GaAs
CB
EF
 both shallow and deep levels can result from
native defects: vacancies, interstitials…
VB
 if donors and acceptors are present: lower carrier
concentration, compensation
Increasing doping:
CB
VB
density of states
hydrogenic impurity states overlap → form impurity band
VB
0
CB
EF
For heavy doping the impurity band overlaps with the VB or CB
E
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
CB (dEu)
Kasuya (1970)
fEu
FM
 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
Eu1-xGdxO with x = 0% – 19%:
Ott et al., cond-mat/0509722
• Eu2+ with 3d7 configuration
• Gd3+ with 3d7 configuration
concentrated spin system: all S = 7/2,
essentially only potential disorder
~ magnetization
• Gd is a donor: strongly n-type
more carriers & more disorder → higher Tc, more convex magnetization
 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)
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
• ferromagnetism with Tc = 2.5 K in bulk p-type (Be,Mn)Te:N
Hansen et al., APL 79, 3125 (2001)
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
Tc
Inverse susceptibility
Haury et al., PRL 79, 511 (1997)
Anomalous Hall effect: in the
absence of an applied magnetic
field (due to spin-orbit coupling)
carrier-mediated ferromagnetism
 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!
Rutile (Ti,Co)O2: Tc > 300 K
Toyosaki et al., Nature Mat. 3, 221 (2004)
Anomalous Hall effect
Strong anomalous Hall effect
depending on electron concentration
→ carrier-induced ferromagnetism
n-type
Controversial
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)
 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:
• antisites AsGa:
• Mn-interstitials:
acceptors
double donors
double donors
Ferromagnetic samples are p-type
(In,Mn)As: Ohno et al., PRL 68, 2664 (1992)
Key experiments on (Ga,Mn)As: Ferromagnetic order
Ohno, JMMM 200, 110 (1999)
metallic
insulating
 hard ferromagnet
bad
sample
 Tc ~ Mn concentration (importance
of carrier concentration?)
 metal-insulator transition at x ~ 3%
Metal-insulator transition at T = 0
with Mn doping:
Ohno, JMMM 200, 110 (1999)
with annealing:
Hayashi et al., APL 78, 1691 (2001)
insulating/localized
low
metallic
high
 typical for disorder-induced (Anderson) insulator
Anomalous Hall effect
Hall effect in the absence of an applied magnetic field
(in itinerant ferromagnets, due to spin-orbit coupling)
saturation of
magnetization
normal
Hall effect:
roughly
linear in B
(RH / B)
anomalous Hall effect
B (T)
Omiya et al., Physica E 7, 976 (2000)
(In,Mn)As:
(Ga,Mn)As: Ruzmetov et al.,
Ohno et al., PRL 68, 2664 (1992)
PRB 69, 155207 (2004)
 anomalous Hall resistivity ~ magnetization
→ holes couple to Mn moments
Resistivity maximum at Tc
Very robust feature: maximum
or shoulder in resistivity
Kato et al., Jap. J. Appl.
Phys. 44, L816 (2005)
Potashnik et al., APL 79,
1495 (2001)
Ga+-ion implanted (Ga,Mn)As:
highly disordered
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
Here: about 17% of Mn
in tetrahedral interstitial
sites
tilt angle
Curie temperature Tc
Ku et al., APL 82, 2302 (2003)
Sørensen et al., APL 82, 2287 (2003)
hole concentration
 annealing increases Tc
 highest Tc for thin samples
 interpretation: donors (Mn interstitials)
move to free surface and are “passivated”
 Tc depends roughly linearly on
hole concentration p
 similar results from Be codoping
carrier-mediated
ferromagnetism
Annealing dependence of magnetization curve
Potashnik et al., APL 79,
1495 (2001)
Mathieu et al., PRB 68,
184421 (2003)
 magnetization curves change straight/convex (upward curvature) →
concave (downward curvature, mean-field-like)
 degradation for very long annealing (precipitates?)
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?
(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
 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
strong disorder
Some reports on ferromagnetism in Mn or
Fe ion-implanted SiC and Mn implanted
Si (Tc > 400K); not for diamond
 IV-VI semiconductors
(Sn,Mn)Te, (Ge,Mn)Te, (Pb,Mn)Te etc.
structure: NaCl
narrow gap, p-type semiconductors
Ge1–xMnxTe:
x = 0.01
…
x = 0.50
Tc = 2.3 K
…
Tc = 167 K
x = 0.5
magnetization
Cochrane et al., PRB 9, 3013 (1974)
T = 4.2 K
good Mn solubility, highly p-doped,
a metal at high x
magnetic field
(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
 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+
Tc
Similar to III-V DMS
 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
 III-V heterostructures (towards applications)
(In,Mn)As field-effect transistor
Ohno et al., Nature 408, 944 (2000)
VG
(In,Mn)As
VG
shift of Tc with gate voltage and thus with hole concentration:
carrier-mediated ferromagnetism
p-doped (Ga,Mn)As -doped layer
Nazmul et al., PRL 95, 017201 (2005)
0.5 monolayer
MnAs
GaAs
Al0.5Ga0.5As:Be
Al0.5Ga0.5As
2DHG
||2
 allows higher local concentration of Mn
 tail of hole concentration of 2DHG in  layer
 Tc up to 250 K
 quasi-two-dimensional ferromagnet (interdiffusion?)
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?