Magnetic semiconductors: classes of materials, basic properties, central questions
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Transcript of Magnetic semiconductors: classes of materials, basic properties, central questions
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 only if electrons are excited (e.g., thermally, optically) over the gap
Same density of electrons in conduction band and holes in valence band:
gapconduction band
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
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
VBEF
CB
VB
excitation energy is strongly reduced
(¿ Eg)
conduction at lower temperatures
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 CBE
0dens
ity o
f sta
tes
VB CB
EF
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
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 EuOTorrance 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
• Gd is a donor: strongly n-type
concentrated spin system: all S = 7/2,essentially only potential disorder
~ m
agne
tizat
ion
more carriers & more disorder → higher Tc, more convex magnetization
theory
Mauger (1977)
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
Inverse susceptibilityHaury 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)
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 KHan 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 KToyosaki 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
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)
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%
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
Anomalous Hall effectHall 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
normalHall effect:roughly linear in B
(RH / B)
B (T)
saturation ofmagnetization
(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
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
Kat
o et
al.,
Jap
. J. A
ppl.
Phy
s. 4
4, L
816
(200
5)
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 raysMnI
tilt angle
Here: about 17% of Mn in tetrahedral interstitial sites
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
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)
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
Some reports on ferromagnetism in Mn or Fe ion-implanted SiC and Mn implanted Si (Tc > 400K); not for diamond
strong disorder
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 fieldm
agne
tizat
ion
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
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)
shift of Tc with gate voltage and thus with hole concentration:
carrier-mediated ferromagnetism
VG
(In,Mn)As
VG
p-doped (Ga,Mn)As -doped layer
Nazmul et al., PRL 95, 017201 (2005)
Al0.5Ga0.5As
Al0.5Ga0.5As:Be
GaAs
0.5 monolayer MnAs
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?