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 CB

E0de

nsity

of

stat

es

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.

App

l. P

hys.

44,

L81

6 (2

005)

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?