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 E g 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 Si 4+ 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 Zn 2+ weakly binds the hole: hydrogenic (shallow) acceptor state EFEF CB VB EFEF CB VB excitation energy is strongly reduced (¿ E g ) 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 EFEF 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 density of states VBCB EFEF

5. Magnetic semiconductors Concentrated magnetic semiconductors:  Ferromagnetic CrBr 3 ( T c = 37 K ) Tsubokawa, J. Phys. Soc. Jpn. 15, 1664 (1960) structure: bayerite (rare and complicated)  Stoichiometric Eu chalcogenides (1963) EuO :ferromagnet ( T c = 77 K ) EuS :ferromagnet ( T c = 16.5 K ) EuSe :antiferro-/ferrimagnet EuTe :antiferromagnet structure: NaCl good realizations of Heisenberg models with J 1 (nearest neighbor) and J 2 (NNN) relevant Mechanism: kinetic and Coulomb Kasuya (1970) CB ( d Eu ) f Eu 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) Gd 3+ substituted for Eu 2+ : single donor The systems are not diluted: every cation is magnetic Electrons increase T c to ~150 K (Shafer and McGuire, 1968) Mechanism: carrier-mediated, see Lecture 3 Electrons lead to metal-insulator transition close to T c : 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. Eu 1-x Gd x O with x = 0% – 19% : Ott et al., cond-mat/0509722 Eu 2+ with 3d 7 configuration Gd 3+ with 3d 7 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 T c, more convex magnetization theory Mauger (1977)

8.  Ferromagnetic Cr chalcogenide spinels CdCr 2 S 4, CdCr 2 Se 4 (T c = 129 K)  Manganites (La,X)MnO 3, … structure: based on perovskite, tilted Mechanism: double exchange, due to mixed valence Mn 3+ Mn 4+ $ Mn 4+ Mn 3+ 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. Mn 2+ (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 Mn 2+ 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) Mn 2+ additional dopand

10. Inverse susceptibility Haury et al., PRL 79, 511 (1997) TcTc 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 T c = 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)O 2 anatase or rutile, (Sn,X)O 2 cassiterite Wide band gap → transparent ferromagnets (Zn,Fe,Co)O : T c 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)O 2 : T c > 300 K Toyosaki et al., Nature Mat. 3, 221 (2004) Strong anomalous Hall effect depending on electron concentration → carrier-induced ferromagnetism Question: Why is T c 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 Mn 2+ introduces spin 5/2 and hole (shallow acceptor) → high hole concentration, but partially compensated: substitutional Mn Ga :acceptors antisites As Ga :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  T c ~ 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 (R H / 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 T c Very robust feature: maximum or shoulder in resistivity Potashnik et al., APL 79, 1495 (2001) Ga + -ion implanted (Ga,Mn)As : highly disordered Kato et al., Jap. J. Appl. Phys. 44, L816 (2005)

19. Defects  MBE growth of (Ga,Mn)As with As 4 ! As 2 cracker leads to enhanced T c ( 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 Mn I tilt angle Here: about 17% of Mn in tetrahedral interstitial sites

20. Curie temperature T c Ku et al., APL 82, 2302 (2003)  annealing increases T c  highest T c for thin samples  interpretation: donors ( Mn interstitials) move to free surface and are “passivated” Sørensen et al., APL 82, 2287 (2003) hole concentration  T c 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): T c up to 370 K, Reed et al., APL 79, 3473 (2001) Anomalous Hall effect Resistivity Looks similar to (Ga,Mn)As, except for high T c and weak resistivity peak Sonoda et al. (2002) report T c > 750 K, but no anomalous Hall effect → inhomogeneous?

23. (Ga,Cr)N, (Al,Cr)N : T c > 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: Mn x Ge 1–x structure: diamond x < 4%, T c up to 116 K Park et al., Science 295, 651 (2002) Tc » xTc » x highly resistive Some reports on ferromagnetism in Mn or Fe ion-implanted SiC and Mn implanted Si ( T c > 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 Ge 1–x Mn x Te: Cochrane et al., PRB 9, 3013 (1974) x = 0.01T c = 2.3 K …… x = 0.50T c = 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 Ba 6 Ge 25–x Fe x Li & Ross, APL 83, 2868 (2003) x ¼ 3, T c = 170 K highly disordered, reentrant spin-glass transition at T s = 110 K  Tetradymite Sb 2–x V x Te 3 : layered narrow-gap DMS Dyck et al., PRB 65, 115212 (2002) x up to 0.03, T c ¼ 22 K intrinsically strongly p-doped probably isovalent V 3+ Similar to III-V DMS TcTc

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: sp 2 /sp 3 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 T c with gate voltage and thus with hole concentration: carrier-mediated ferromagnetism VGVG (In,Mn)As VGVG

29. p-doped (Ga,Mn)As  -doped layer Nazmul et al., PRL 95, 017201 (2005) Al 0.5 Ga 0.5 As Al 0.5 Ga 0.5 As:Be GaAs 0.5 monolayer MnAs 2DHG ||2||2  allows higher local concentration of Mn  tail of hole concentration of 2DHG in  layer  T c 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 T c ?