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2. Magnetic semiconductors: classes of materials, basic properties, central questions Basics of semiconductor physics

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.

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2. Magnetic semiconductors: classes of materials, basic properties, central questions Basics of semiconductor physics

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  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 gapEg 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: conduction band gap valence band Non-degenerate electron/hole gas in bands (i.e., no Fermi sea), transport similar to classical charged gas

  3. CB CB EF EF VB VB 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 excitation energy is strongly reduced(¿Eg) conduction at lower temperatures

  4. CB EF VB CB density of states VB CB VB 0 EF E • 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 fromnative defects: vacancies, interstitials… • if donors and acceptors are present: lower carrier concentration, compensation Increasing doping: hydrogenic impurity states overlap → form impurity band For heavy doping the impurity band overlaps with the VB or CB

  5. CB (dEu) FM fEu Magnetic semiconductors • Concentrated magnetic semiconductors: • Ferromagnetic CrBr3 (Tc = 37 K)Tsubokawa, J. Phys. Soc. Jpn. 15, 1664 (1960)structure: bayerite (rare and complicated) • StoichiometricEu chalcogenides(1963)EuO: ferromagnet (Tc = 77 K)EuS: ferromagnet (Tc = 16.5 K)EuSe: antiferro-/ferrimagnetEuTe: antiferromagnet structure: NaCl good realizations of Heisenberg models withJ1 (nearest neighbor) and J2 (NNN) relevant Mechanism: kinetic and Coulomb Kasuya (1970)

  6. n-doped Eu chalcogenides:Eu-rich EuO, (Eu,Gd)O, (Eu,Gd)S, … oxygen vacancy: double donor (missing Ofails 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

  7. Eu1-xGdxO with x = 0% –19%:Ott et al., cond-mat/0509722 • Eu2+ with 3d7 configuration • Gd3+ with 3d7configuration • Gd is a donor: strongly n-type concentrated spin system: all S = 7/2,essentially only potential disorder ~ magnetization theoryMauger (1977) more carriers & more disorder →higher Tc, more convex magnetization

  8. Ferromagnetic Cr chalcogenide spinelsCdCr2S4, 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. Mn2+ additional dopand 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 structurestudied 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 andMn in different layers):Haury et al., PRL 79, 511 (1997)

  10. Tc • ferromagnetism withTc= 2.5 K in bulk p-type (Be,Mn)Te:NHansen 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 Anomalous Hall effect: in the absence of an applied magnetic field (due to spin-orbit coupling) Inverse susceptibilityHaury et al., PRL 79, 511 (1997) carrier-mediated ferromagnetism

  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: Tc¼ 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!

  12. Rutile (Ti,Co)O2: Tc> 300 KToyosaki et al., Nature Mat. 3, 221 (2004) Anomalous Hall effect Strong anomalous Hall effect depending on electron concentration →carrier-induced ferromagnetism Controversial n-type 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)

  13. III-V bulk semiconductors(In,Mn)As, (Ga,Mn)As, (Ga,Mn)N, (In,Mn)Sb,…zinc-blende structurefocus of studies since ~ 1992 Problem: low solubility of Mn→ low-temperature MBE: up to ~ 8% of Mn Mn2+ introduces spin 5/2andhole (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. Ohno, JMMM 200, 110 (1999) metallic bad sample insulating Key experiments on (Ga,Mn)As: Ferromagnetic order • hard ferromagnet • Tc ~Mn concentration (importance of carrier concentration?) • metal-insulator transition at x ~ 3%

  15. Metal-insulator transition at T = 0 insulating/localized low metallic high • typical for disorder-induced (Anderson) insulator

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

  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) Kato et al., Jap. J. Appl. Phys. 44, L816 (2005) Ga+-ion implanted (Ga,Mn)As:highly disordered

  19. X rays MnI 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 backscatteringYu et al., PRB 65, 201303(R), 2002 Here: about 17% of Mn in tetrahedral interstitial sites tilt angle

  20. hole concentration Curie temperature Tc Ku et al., APL 82, 2302 (2003) Sørensen et al., APL 82, 2287 (2003) • 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

  21. 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?)

  22. Wide-gap III-V DMS(Ga,Mn)N (wurtzite): Tc up to 370 K, Reed et al., APL 79, 3473 (2001) Resistivity Anomalous Hall effect 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 strong disorder Some reports on ferromagnetism in Mn or Fe ion-implanted SiC and Mn implanted Si(Tc > 400K); not for diamond

  25. x = 0.5 magnetization T = 4.2 K magnetic field • 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

  26. Tc • Chiral clathrate Ba6Ge25–xFexLi & Ross, APL 83, 2868 (2003) x¼ 3, Tc = 170 Khighly disordered, reentrant spin-glass transition atTs = 110 K • Tetradymite Sb2–xVxTe3: layered narrow-gap DMSDyck et al., PRB 65, 115212 (2002) x up to 0.03, Tc¼ 22 Kintrinsically strongly p-doped probably isovalent V3+ Similar to III-V DMS

  27. weak hysteresis T = 1.8 K • 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) Possible origin:sp2/sp3 mixed compound → unpaired electrons

  28. VG (In,Mn)As VG • 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

  29. p-doped (Ga,Mn)As-doped layer Nazmul et al., PRL 95, 017201 (2005) 0.5 monolayer MnAs GaAs Al0.5Ga0.5As:Be 2DHG Al0.5Ga0.5As ||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?)

  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?

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