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					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)
Band structure has energy               conduction band
gap Eg at the Fermi energy                       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         Zn has one valence electron less
→ introduces extra electron: donor       → introduces extra hole: acceptor
Si4+ weakly binds the electron:          Zn2+ weakly binds the hole:
hydrogenic (shallow) donor state         hydrogenic (shallow) acceptor state

             CB              excitation energy is            CB
     EF                       strongly reduced
                                    (¿ Eg)
                             conduction at lower     EF
             VB                 temperatures                 VB
 if impurity in crystal field has levels in the gap:
  deep levels (not hydrogenic), e.g., Te in GaAs                  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:
hydrogenic impurity states overlap → form impurity band

                                     density of states

        VB                                                   VB         CB
                                                                   EF    E
For heavy doping the impurity band overlaps with the VB or CB
                  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)    FM
                   Kasuya (1970)           fEu
 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      concentrated spin system: all S = 7/2,
                  • Gd3+ with 3d7 configuration      essentially only potential disorder

                  • Gd is a donor: strongly n-type
~ magnetization

                  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
                                                 Mn2+           additional dopand
    Mn in different layers):
    Haury et al., PRL 79, 511 (1997)
 • 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                  Anomalous Hall effect: in the
                                        absence of an applied magnetic
                                        field (due to spin-orbit coupling)
Inverse susceptibility
Haury et al., PRL 79, 511 (1997)       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
 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   sample

 hard ferromagnet                   Tc ~ Mn concentration (importance
                                      of carrier concentration?)
                                     metal-insulator transition at x ~ 3%
  Metal-insulator transition at T = 0

          with Mn doping:                           with annealing:
    Ohno, JMMM 200, 110 (1999)             Hayashi et al., APL 78, 1691 (2001)



       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
                                                                   Hall effect:
                                                                   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

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
 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

                                                     Here: about 17% of Mn
                                                     in tetrahedral interstitial

                      tilt angle
Curie temperature Tc

Ku et al., APL 82, 2302 (2003)           Sørensen et al., APL 82, 2287 (2003)

                                                        hole concentration

 annealing increases Tc                       Tc depends roughly linearly on
                                                hole concentration p
 highest Tc for thin samples
                                               similar results from Be codoping
 interpretation: donors (Mn interstitials)
  move to free surface and are “passivated”           carrier-mediated
 Annealing dependence of magnetization curve

       Potashnik et al., APL 79,                  Mathieu et al., PRB 68,
            1495 (2001)                              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

           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

 Cochrane et al., PRB 9, 3013 (1974)
                                                        x = 0.5

 x = 0.01          Tc = 2.3 K
 …                 …
 x = 0.50          Tc = 167 K
                                                        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+

                                    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)



     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


 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
 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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