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Diluted magnetic Dirac-Weyl materials: Susceptibility and ferromagnetism in three-dimensional chiral gapless semimetals

Sanghyun Park, Hongki Min, E. H. Hwang, and S. Das Sarma
Phys. Rev. B 98, 064425 – Published 29 August 2018
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  • INTRODUCTION
  • MODEL
  • RKKY INTERACTION AND EFFECTIVE MAGNETIC…
  • DISCUSSION AND CONCLUSION
  • ACKNOWLEDGMENTS
  • APPENDICES
    • References

    Abstract

    We theoretically investigate the temperature-dependent static susceptibility and long-range magnetic coupling of three-dimensional (3D) chiral gapless electron-hole systems (semimetals) with arbitrary band dispersion [i.e., ɛ(k)∼kN, where k is the wave vector and N is a positive integer]. We study the magnetic properties of these systems in the presence of dilute random magnetic impurities. Assuming carrier-mediated Ruderman-Kittel-Kasuya-Yosida indirect exchange interaction, we find that the magnetic ordering of intrinsic 3D chiral semimetals in the presence of dilute magnetic impurities is ferromagnetic for all values of N. Using finite-temperature self-consistent field approximation, we calculate the ferromagnetic transition temperature (Tc). We find that Tc increases with increasing N due to the enhanced density of states, and the calculated Tc is experimentally accessible, assuming reasonable coupling between the magnetic impurities and itinerant carriers.

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    • Received 1 May 2018

    DOI:https://doi.org/10.1103/PhysRevB.98.064425

    ©2018 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    RKKY interaction
    1. Physical Systems
    Dirac semimetalWeyl semimetal
    Condensed Matter, Materials & Applied Physics

    Authors & Affiliations

    Sanghyun Park1, Hongki Min1,*, E. H. Hwang2,†, and S. Das Sarma3

    • 1Department of Physics and Astronomy, Seoul National University, Seoul 08826, Korea
    • 2SKKU Advanced Institute of Nanotechnology and Department of Nano Engineering, Sungkyunkwan University, Suwon 16419, Korea
    • 3Condensed Matter Theory Center and Joint Quantum Institute, Department of Physics, University of Maryland, College Park, Maryland 20742-4111, USA

    • *hmin@snu.ac.kr
    • †euyheon@skku.edu

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    Vol. 98, Iss. 6 — 1 August 2018

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    Images

    • Figure 1
      Figure 1

      The calculated finite-temperature static susceptibility χ(q,T) as a function of wave vector for various temperatures T=0,0.02,0.04,0.06,0.08, and 0.1T0, and for different values of N (a) N=1, (b) N=2, (c) N=3, and (d) N=4. Here, T0=ɛ0/kB, D1(a−1)=gk02π2ɛ0a2, and a=0.343 nm (lattice constant of TaAs). For N=1, the finite momentum cutoff a−1 is used for the convergence of the integral.

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    • Figure 2
      Figure 2

      The range function χ(r,T) as a function of distance for different values of N (a) N=1, (b) N=2, (c) N=3, and (d) N=4. In each figure, the curves with different colors represent different temperatures T=0, 0.1, 0.2, 0.3, 0.4, and 0.5 T0. Here, D0=D1(a−1)/a3. In this calculation, the ultraviolet momentum cutoff qc=a−1 is used.

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    • Figure 3
      Figure 3

      The calculated effective coupling (solid lines) as a function of temperature for different values of N=1,2,3,4. In this calculation, the ultraviolet cutoff qc=a−1 and exponential cutoff R=100a are used. Here, the normalization factor Jeff(0)=4π[Jexa3]2D1(a−1)/4Ωunit is independent of N and temperature T. The dashed line represents 3kBT/[S(S+1)x], and the intersections with Jeff(T) indicate the transition temperatures solved self-consistently. Here, Jex=0.1 eV, x=0.05 and S=5/2.

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    • Figure 4
      Figure 4

      The calculated transition temperature Tc as a function of (a) the exchange coupling Jex, (b) the magnetic impurity concentration x=nimpa3, and (c) the degeneracy factor g for different values of N=1,2,3,4. Here, for fixed parameters, we used Jex=0.1 eV, x=0.05 and g=4.

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