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Magnetic Semiconductors

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Semiconductor Physics
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Abstract

Magnetic properties are introduced into solids by paramagnetic ions. These are transition-metal ions of the iron series with a partially filled electronic 3d shell or rare-earth ions of the lanthanide series with an incomplete 4f shell. In magnetic semiconductors, they represent a cation component of the crystal, while in diluted magnetic semiconductors, they are a substitutional alloy component on the cation sublattice. The magnetic moments of the paramagnetic ions are coupled by different kinds of exchange interactions. Superexchange mediated by p states of anion ligands favors antiferromagnetism with antiparallel alignment of the magnetic moments, while double exchange and p–d exchange favor ferromagnetism with parallel alignment. Magnetic ordering is disturbed if the thermal energy exceeds the exchange energy; critical Curie and Néel temperatures exist for the transition from the paramagnetic high-temperature range to magnetically ordered respective ferromagnetic and antiferromagnetic regimes at lower temperature.

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Notes

  1. 1.

    There is also a small diamagnetic contribution arising from filled electronic shells with zero spin and orbital angular momentum known as Larmor (or Langevin) diamagnetic susceptibility; this contribution does not depend on temperature and is generally counteracting paramagnetism in solids.

  2. 2.

    The susceptibility χ is generally a tensor. For simplicity we assume a magnetization vector M parallel to H in Eq. 1, yielding a scalar χ. In a vector relation a set of equations according Eq. 1 applies for the vector components.

  3. 3.

    The Brillouin function is defined by \( {B}_J(x)=\frac{2J+1}{2J}\coth \left(\frac{2J+1}{2J}x\right)-\frac{1}{2J}\coth \left(\frac{x}{2J}\right) \) and varies from 0 to 1 for x = 0 to ∞. For high temperature or small splitting, x ≪ 1 applies, and the hyperbolic cotangent can be approximated by coth y = 1/y + y/3 – y 3/45 + ….

  4. 4.

    The poor agreement for Sm and Eu originates from excited states lying closely above the ground state; such conditions were excluded for the validity of Eqs. 7, 8, and 9.

  5. 5.

    The additional paramagnetism of nuclear spins is negligible compared to electronic contributions (a fraction below 10−3).

  6. 6.

    Besides ferro- and antiferromagnetic coupling, the magnetic moments can be ordered in a ferrimagnetic coupling with a not canceling antiparallel alignment for the moments of neighboring (not identical) magnetic ions.

  7. 7.

    Occasionally also incorporation on an interstitial site of the host crystal is found. Such incorporation in parallel to substitutional alloying may be detrimental for the intended magnetic properties as, e.g., pointed out for Ga1-x Mn x As in Sect. 2.2.

  8. 8.

    A slight departure from the Curie law found for Cd1-x Mn x Te and Cd1-x Mn x Se at T < 0.1K was attributed to the small crystal-field splitting of the 6S ground state enabled by minute contributions of excited states and the additional effect of the nuclear spin.

  9. 9.

    Also a Curie–Weiss law according to Eq. 16 with a characteristic temperature |Θ| ≪ 1 was widely applied, indicating some minor residual coupling effects among the magnetic ions.

  10. 10.

    The mass magnetization is given here in the conventionally used units of emu/g; the conversion factor to the SI unit is 1 emu/g = 10−3 A × m2 = 10−3 J/T.

  11. 11.

    The sublattice of the cations is fcc in (cubic) zincblende and hcp in (hexagonal) wurtzite lattices.

  12. 12.

    In some cases an observed ferromagnetism did solely originate from precipitates of magnetic ions alloyed into nonmagnetic II–VI host crystals (Saito et al. 2003).

  13. 13.

    Molecular-beam epitaxy is performed at low deposition temperatures down to 180 °C to allow for high nonequilibrium alloying levels; due to the limited kinetics at such low temperature, point defects are easily created.

  14. 14.

    At highest Mn composition, a deviation from expected values even for annealed samples indicates some onset of compensation.

  15. 15.

    In the chalcopyrite structure (Fig. 13 in chapter “The Structure of Semiconductors”), the 1nn and 3nn neighbors are located at \( \left(\frac{a}{2},0,\frac{c}{4}\right) \)and \( \left(\frac{a}{2},\frac{a}{2},\frac{c}{2}\right) \), respectively.

References

  • Balzarotti A, Czyzyk M, Kisiel A, Motta N, Podgòrny M, Zimnal-Starnawska M (1984) Local structure of ternary semiconducting random solid solutions: extended x-ray-absorption fine structure of Cd1-x Mn x Te. Phys Rev B 30:2295

    Article  ADS  Google Scholar 

  • de Seze L (1977) Antiferromagnetic dilute bond Ising model exhibiting a spin-glass phase transition. J Phys C: Sol State Phys 10:L353

    Article  Google Scholar 

  • Dietl T, Ohno H, Matsukura F, Cibert J, Ferrand D (2000) Zener model description of ferromagnetism in zinc-blende magnetic semiconductors. Science 287:1019

    Article  ADS  Google Scholar 

  • Dietl T, Awschalom DD, Kaminska M, Ohno H (eds) (2008) Spintronics, Semiconductors and semimetals, vol 82. Academic Press/Elsevier, Amsterdam

    Google Scholar 

  • Furdyna JK, Kossut J (eds) (1988) Diluted magnetic semiconductors, Semiconductors and semimetals. vol 25, Academic Press, Boston

    Google Scholar 

  • Giriat W, Furdyna JK (1988) Crystal structure, composition, and materials preparation of diluted magnetic semiconductors. In: Furdyna JK, Kossut J (eds) Diluted magnetic semiconductors, Semiconductors and semimetals. Academic Press, vol 25, Boston, pp 1–34

    Google Scholar 

  • Goodenough JB (1955) Theory of the role of covalence in the perovskite-type manganites [La, M(II)]MnO3. Phys Rev 100:564

    Article  ADS  Google Scholar 

  • Grundmann M (2006) The physics of semiconductors. Springer, Berlin

    Google Scholar 

  • Jungwirth T, Wang KY, Mašek J, Edmonds KW, König J, Sinova J, Polini M, Goncharuk NA, MacDonald AH, Sawicki M, Rushforth AW, Campion RP, Zhao LX, Foxon CT, Gallagher BL (2005) Prospects for high temperature ferromagnetism in (Ga, Mn)As semiconductors. Phys Rev B 72:165204

    Article  ADS  Google Scholar 

  • Kanamori J (1959) Superexchange interaction and symmetry properties of electron orbitals. J Phys Chem Solids 10:87

    Article  ADS  Google Scholar 

  • Kreitman MM, Barnet DL (1965) Probability tables for clusters of foreign atoms in simple lattices assuming next-nearest-neighbor interactions. J Chem Phys 43:364

    Article  ADS  Google Scholar 

  • Mahadevan P, Zunger A (2004) First-principles investigation of the assumptions underlying model-Hamiltonian approaches to ferromagnetism of 3d impurities in III-V semiconductors. Phys Rev B 69:115211

    Article  ADS  Google Scholar 

  • Nagata S, Galazka RR, Mullin DP, Akbarzadeh H, Khattak GD, Furdyna JK, Keesom PH (1980) Magnetic susceptibility, specific heat, and the spin-glass transition in Hg1−x Mn x Te. Phys Rev B 22:3331

    Google Scholar 

  • Ohno H, Shen A, Matsukura F, Oiwa A, Endo A, Katsumoto S, Iye Y (1996) (Ga, Mn)As: a new diluted magnetic semiconductor based on GaAs. Appl Phys Lett 69:363

    Article  ADS  Google Scholar 

  • Ohno H, Chiba D, Matsukura F, Omiya T, Abe E, Dietl T, Ohno Y, Ohtani K (2000) Electric-field control of ferromagnetism. Nature 408:944

    Article  ADS  Google Scholar 

  • Oseroff S (1982) Magnetic susceptibility and EPR measurements in concentrated spin-glasses: Cd1-x Mn x Te and Cd1-x Mn x Se. Phys Rev B 25:6584

    Article  ADS  Google Scholar 

  • Oseroff S, Keesom PH (1988) Magnetic properties: macroscopic studies. In: Furdyna JK, Kossut J (eds) Diluted magnetic semiconductors, Semiconductors and semimetals. Academic Press, Boston, vol 25, pp 73–123

    Google Scholar 

  • Pohl UW, Busse W (1989) Probability tables for small clusters of impurity atoms in sc, bcc and fcc lattices assuming long range interaction. J Chem Phys 90:6877

    Article  ADS  Google Scholar 

  • Saito H, Zayets V, Yamagata S, Ando K (2003) Room-temperature ferromagnetism in a II-VI diluted magnetic semiconductor Zn1-x Cr x Te, Phys Rev Lett 90:207202

    Article  ADS  Google Scholar 

  • Sato K, Katayama-Yoshida H (2002) First principles materials design for semiconductor spintronics. Semicond Sci Technol 17:367

    Article  ADS  Google Scholar 

  • Sato K, Bergqvist L, Kudrnovský J, Dederichs PH, Eriksson O, Turek I, Sanyal B, Bouzerar G, Katayama-Yoshida H, Dinh VA, Fukushima T, Kizaki H, Zeller R (2010) First-principles theory of dilute magnetic semiconductors. Rev Mod Phys 82:1633

    Article  ADS  Google Scholar 

  • Wolos A, Kaminska M (2008) Magnetic impurities in wide band-gap III-V semiconductors. In: Dietl T, Awschalom DD, Kaminska M, Ohno H (eds) Spintronics, Semiconductors and semimetals, vol 82. Academic Press/Elsevier, Amsterdam

    Google Scholar 

  • Zener C (1951a) Interaction between the d-shells in the transition metals. II. Ferromagnetic compounds of manganese with perovskite structure. Phys Rev 82:403

    Article  ADS  Google Scholar 

  • Zener C (1951b) Interaction between the d-shells in the transition metals. Phys Rev 81:440

    Article  ADS  MATH  Google Scholar 

  • Zhao Y-J, Mahadevan P, Zunger A (2004) Comparison of predicted ferromagnetic tendencies of Mn substituting the Ga site in III–V’s and in I–III–VI2 chalcopyrite semiconductors. Appl Phys Lett 84:3753

    Google Scholar 

  • Zunger A (1986) Electronic structure of 3d transition-atom impurities in semiconductors. In: Zeits F, Ehrenreich H, Turnbull D (eds) Solid state physics, vol 39. Academic Press, New York, pp 275–464

    Google Scholar 

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Böer, K.W., Pohl, U.W. (2018). Magnetic Semiconductors. In: Semiconductor Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-69150-3_9

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