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Magnetic Semiconductors

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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.

The spin of carriers is utilized in spintronics for current control by creating a nonequilibrium spin polarization. When phase effects can be neglected, the transport of spin-polarized carriers is described by a two-current model assuming two independent channels of different spin projections. Spintronic structures typically comprise two ferromagnetic layers, which are separated by a thin nonmagnetic spacer layer. For insulating spacers and antiparallel aligned ferromagnetic moments a large difference in resistance of the two spin-polarized channels is found, referred to as tunneling magnetoresistance. Similarly a giant magnetoresistance is observed for a thin conductive spacer. The orientation of the ferromagnetic magnetization can be altered by spin-transfer torque exerted by a spin-polarized current. Diluted magnetic semiconductors serve as a valuable test bench for exploratory physics of spintronic devices.

K. W. Böer: deceased.

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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 vacuum permeability μ0 was redefined in 2019 by the update of SI units; it is no longer a constant (by the former definition of the SI ampere), but needs to be determined experimentally.

  3. 3.

    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 to Eq. 1 applies for the vector components.

  4. 4.

    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 – y3/45 + ….

  5. 5.

    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.

  6. 6.

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

  7. 7.

    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.

  8. 8.

    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-xMnxAs in Sect. 2.2.

  9. 9.

    A slight departure from the Curie law found for Cd1-xMnxTe and Cd1-xMnxSe 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.

  10. 10.

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

  11. 11.

    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 = 1 A × m2 / kg = 1 J / (T × kg).

  12. 12.

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

  13. 13.

    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).

  14. 14.

    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.

  15. 15.

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

  16. 16.

    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.

  17. 17.

    In semiconductors, the terms majority and minority generally refer to the charge of the carriers; the symbols ↑ and ↓ then denote the quantum number mj with respect to the axis of an external magnetic field, or – in optical measurements – the direction of light propagation.

  18. 18.

    For GaAs, e.g., the energy of the spin-orbit interaction in the valence band is Δ0 = 0.34 eV.

  19. 19.

    The schematic band structure of a typical transition-metal ferromagnet depicts separately the spatially extended 4s states with their large energy spread and the more localized 3d states, although they are hybridized in a solid. The itinerant 3d electrons have a much higher density of states, but they are substantially less mobile than the 4s electrons.

  20. 20.

    Such a junction is usually made with metals, but it may also be made using a ferromagnetic diluted magnetic semiconductor and a degenerate semiconductor.

  21. 21.

    The vertical displacement between spin-up and spin-down densities of states originates from the exchange-energy splitting between the spin-up and spin-down energy bands.

  22. 22.

    A drawback of this approach is the usually low ferromagnetic transition temperature of ferromagnetic semiconductors, requiring operation below room temperature. In II–VI compounds, Mn2+ is isovalent with nonmagnetic cations; it provides only spin doping and can be introduced in high composition. In III–Vs, it yields both spin and carrier doping; the low solubility complicates growth due to cluster formation of metallic inclusions. Diluted magnetic semiconductors still serve as a valuable test bench for new and exploratory physics and ideas (Ohno 2010).

  23. 23.

    Planar thermally evaporated films of ∼100 Å thickness with bulk-like behavior were used.

  24. 24.

    The magnetic field H is given in Oersted (Oe). The conversion to SI units is 1 Oe = 79.5775 A/m. Multiplication with the vacuum permeability yields the magnetic induction B: μ0× 1 Oe = 10−4T.

  25. 25.

    Simultaneously the tunneling resistance (not the ratio) increases exponentially; an increase over six orders of magnitude was measured as the MgO barrier thickness increases from 1.2 nm to 3.2 nm (Yuasa et al. 2004).

  26. 26.

    The effect is termed giant due to the much smaller anisotropic magnetoresistance (AMR) discovered aready by Lord Kelvin 160 years ago. The AMR effect originates from a difference in the scattering cross-section when the electron current in a single magnetic sample is parallel or perpendicular to magnetically aligned atoms, an effect only on the order of a few per cent.

  27. 27.

    The ferromagnetic rare-earth metals have an analogous spin-split part-filled 4f band, but this is deep in the band structure and does not induce significant scattering.

  28. 28.

    This Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction was initially described for coupling of nuclear magnetic moments in a metal mediated by the interaction with conduction electrons (Ruderman and Kittel 1954).

  29. 29.

    The effects of giant magnetoresistance (GMR) and tunneling magnetoresistance (TMR) are also referred to as spin-valve effects. A spin-valve device utilizing this effect has an asymmetric ferromagnetic structure.

  30. 30.

    The measurement is performed in steps, because the TMR (ratio) is only large at small bias (<0.1 V), but switching requires a large bias (>0.5 V).

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Authors and Affiliations

  1. 138 Moorings Park Rd.?O 301, Naples, 34105, FL, USA

    Karl W. Böer

  2. Institut für Festkörperphysik, EW5-1, Technische Universität Berlin, Hardenbergstr. 36, 10623, Berlin, Germany

    Udo W. Pohl

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Böer, K.W., Pohl, U.W. (2022). Magnetic Semiconductors. In: Semiconductor Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-06540-3_9-4

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  1. Latest

    Magnetic Semiconductors
    Published:
    26 July 2022

    DOI: https://doi.org/10.1007/978-3-319-06540-3_9-4

  2. Magnetic Semiconductors
    Published:
    24 February 2020

    DOI: https://doi.org/10.1007/978-3-319-06540-3_9-3

  3. Magnetic Semiconductors
    Published:
    27 September 2017

    DOI: https://doi.org/10.1007/978-3-319-06540-3_9-2

  4. Original

    Magnetic Semiconductors
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    08 September 2014

    DOI: https://doi.org/10.1007/978-3-319-06540-3_9-1

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