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Magnetoresistance Scaling and the Origin of H-Linear Resistivity in BaFe2(As1−xPx)2

Nikola Maksimovic, Ian M. Hayes, Vikram Nagarajan, James G. Analytis, Alexei E. Koshelev, John Singleton, Yeonbae Lee, and Thomas Schenkel
Phys. Rev. X 10, 041062 – Published 29 December 2020
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  • INTRODUCTION
  • THEORETICAL MODEL
  • RESULTS
  • DISCUSSION
  • ACKNOWLEDGMENTS
    • Supplemental Material
    References

    Abstract

    We explore field and temperature scaling of magnetoresistance in underdoped (x=0, x=0.19) and optimally doped (x=0.31) samples of the high-temperature superconductor BaFe2(As1−xPx)2. In all cases, the magnetoresistance is H linear at high fields. We demonstrate that the data can be explained by an orbital model in the presence of strongly anisotropic quasiparticle spectra and scattering time due to antiferromagnetism. In optimally doped samples, the magnetoresistance is controlled by the properties of small regions of the Fermi surface called “hot spots,” where antiferromagnetic excitations induce a large quasiparticle scattering rate. The anisotropic scattering rate results in hyperbolic H/T magnetoresistance scaling, which competes with the more conventional Kohler scaling. We argue that these results constitute a coherent picture of magnetotransport in BaFe2(As1−xPx)2, which links the origin of H-linear resistivity to antiferromagnetic hot spots. Implications for the T-linear resistivity at zero field are discussed.

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    • Received 2 July 2020
    • Revised 19 October 2020
    • Accepted 23 October 2020

    DOI:https://doi.org/10.1103/PhysRevX.10.041062

    Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

    Published by the American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    AntiferromagnetismCritical phenomenaDefectsElectrical conductivityImpurities in superconductorsMagnetoresistanceQuantum phase transitionsSuperconductors
    Condensed Matter, Materials & Applied Physics

    Authors & Affiliations

    Nikola Maksimovic*, Ian M. Hayes, Vikram Nagarajan, and James G. Analytis†

    • Department of Physics, University of California, Berkeley, California 94720, USA and Materials Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA

    Alexei E. Koshelev

    • Materials Science Division, Argonne National Laboratory, Lemont, Illinois 60439, USA

    John Singleton

    • National High Magnetic Field Laboratory, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA

    Yeonbae Lee and Thomas Schenkel

    • Materials Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA

    • *nikola_maksimovic@berkeley.edu
    • †analytis@berkeley.edu

    Popular Summary

    High-temperature superconductors exhibit remarkable behavior even in their nonsuperconducting phases. For example, the resistivity varies linearly with temperature and with applied magnetic field, in contrast to the quadratic variation expected in typical metals. It is thought that an understanding of high-temperature superconductivity first requires an understanding of these unusual phenomena in the nonsuperconducting state. In our study, we use a combination of experimental data and theoretical modeling of an iron-based superconductor to show that the momenta of charge carriers rapidly dissipate because of coupling to fluctuations of a nearby magnetic field, thus giving rise to the unconventional variation of electrical resistance.

    In our experiments, we measure the resistivity as a function of temperature and magnetic field of the iron-based superconductor BaFe2As2 with various levels of phosphorus. We then use a realistic theoretical model to capture the resistivity data as a function of temperature, magnetic field, phosphorus-doping level, and systematic defects induced by ion bombardment.

    An important implication of this work is that measurements of resistivity in a magnetic field can be used to characterize the properties of magnetic fluctuations, an important ingredient for the development of superconductivity in high-temperature superconducting materials.

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    Vol. 10, Iss. 4 — October - December 2020

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    • Figure 1
      Figure 1

      Hot-spot and turning-point magnetoresistance scaling functions and comparison with hyperbola. The MR [Δρ=ρ(H)−ρ(H=0)] in both the turning-point and hot-spot models is controlled by two parameters, rtp,hs and Htp,hs (tp and hs indicate turning-point and hot-spot, respectively). The derivations of the parameters in terms of antiferromagnetic gap, spin-susceptibility, and electronic-band parameters are given in the Supplemental Material [34]. The MR from the hot spots or turning points follows scaling functions (black lines), with exact expressions given in the Supplemental Material [34]. The functions are well approximated by a hyperbola Δρ/rtp,hs=1+(H/Htp,hs)−1 (red line).

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    • Figure 2
      Figure 2

      Transport in BaFe2As2 and magnetoresistance model based on turning points. (a) Isothermal magnetoresistance at various temperatures. Black lines are fits to the turning-point model given by Eq. (3). (b) Model parameters extracted from the fits; error bars are smaller than the data points. The grey lines show that both parameters vary with T3 with a finite offset. The red line shows that the zero-field resistivity similarly varies approximately with T3, suggesting that the MR parameters vary with the scattering rate.

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    • Figure 3
      Figure 3

      Kohler’s rule in BaFe2As2. Relative magnetoresistance versus reduced field for different temperatures. The inset shows the temperature dependence of the relative MR at a reduced field of μ0H/ρ(0)=0.03  T/μΩ cm.

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    • Figure 4
      Figure 4

      Transport in BaFe2(As0.81P0.19)2 and magnetoresistance model based on turning points. (a) Resistivity shows a transition to an AFM ordered state (TN≈95  K), and superconducting state beginning at Tc=22  K with zero resistance at 15 K. Inside the AFM state, the resistivity varies with T2, with a finite T=0 intercept. The data are fitted well by ρ(H=0)=122.8  [μΩ cm]+0.0085  [μΩ cm/K2]×T2 (black line). (b) Magnetoresistance for different temperatures with fits to the turning-point MR model [Eq. (3)] indicated by black lines. (c) Fit parameters of the model plotted as a function of temperature, with a best-fit line to the data below 70 K. Here, Htp=0.098[T]+0.0015  [T/K2]×T2, and rtp=0.69  [μΩ cm]+0.0023  [μΩ cm/K2]×T2.

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    • Figure 5
      Figure 5

      Comparison of hyperbolic magnetoresistance scaling and Kohler’s rule inside the AFM ordered state of BaFe2(As0.81P0.19)2. (a) A simple hyperbolic scaling relation holds, where the residual resistivity ρ0=122  μΩ cm is first subtracted. The dashed black line is the expression given by Eq. (9) with β=0.0039  [μΩ cm/K2], α′=0.0085  [μΩ cm/K2], and γ=0.0015  [T/K2]. (b) Kohler’s rule is violated as a function of temperature.

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    • Figure 6
      Figure 6

      Magnetoresistance, hot-spot model, and hyperbolic scaling in BaFe2(As0.81P0.31)2 with varying levels of disorder. (a) Samples showing clear H-linear dependence at high fields. Black lines are fits to the hot-spot MR model given by Eq. (6). Each panel is labeled by the extrapolated zero-temperature resistivity, which quantifies the level of disorder. (b) Hyperbolic scaling of MR for each respective sample. Dashed lines are hyperbolic functions with the parameters shown in each figure.

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    • Figure 7
      Figure 7

      Hot-spot parameters in BaFe2(As1−xPx)2 with x=0.31. (a) Characteristic field Hhs as a function of temperature with a linear fit for each sample. The inset shows the slope of Hhs(T) versus the residual resistivity. The dotted line shows the expected ρ01/2 dependence according to Eq. (7) of the hot-spot model. (b) Hot-spot MR amplitude. The inset shows the slope of rhs(T) versus the residual resistivity with a fit to the expected ρ01/2 dependence. Error bars are derived from the confidence intervals of the hot-spot fits and the linear fits in the present figure.

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    • Figure 8
      Figure 8

      Isothermal Kohler’s rule in quantum critical BaFe2(As1−xPx)2 (x=0.31). A comparison of the isothermal magnetoresistance of separate samples with varying doses of alpha-particle irradiation. The violation of Kohler’s rule in the linear MR regime suggests that disorder scattering alters the degree of scattering anisotropy, in agreement with the hot-spot model. Solid lines are fits to Eq. (6), for which the zero-field resistivity is extracted from each trace. The curves are labeled by the resistivity of the sample at zero field at the given temperature. Note that μ0H/ρ(0) is in units of Tesla/μΩ  cm.

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