Kondo-like mass enhancement of Dirac fermions in Ba(Fe${}_{1\ensuremath{-}x}$Mn${}_{x}$As)${}_{2}$

Kondo-like mass enhancement of Dirac fermions in Ba(Fe $_{1 - x}$ Mn $_{x}$ As) $_{2}$

T. Urata, Y. Tanabe, K. K. Huynh, H. Oguro, K. Watanabe, S. Heguri, and K. Tanigaki

Phys. Rev. B 89, 024503 – Published 13 January 2014

Abstract

The effect of Mn substitution, acting as a magnetic impurity for Fe, on the Dirac cone was investigated in Ba(Fe $_{1 - x}$ Mn $_{x}$ As) $_{2}$ . Both magnetoresistance and Hall resistivity studies clearly indicate that the cyclotron effective mass ( $m^{*}$ ) of the Dirac cone is anomalously enhanced at low temperatures by the impurity, although its evolution as a function of carrier number proceeds in a conventional manner at higher temperatures. Kondo-like band renormalization induced by the magnetic impurity scattering is suggested as the most plausible explanation for this, and the anomalous mass enhancement of the Dirac fermions is discussed.

Received 27 April 2013
Revised 25 December 2013

DOI:https://doi.org/10.1103/PhysRevB.89.024503

Authors & Affiliations

T. Urata¹, Y. Tanabe^1,*, K. K. Huynh², H. Oguro³, K. Watanabe³, S. Heguri², and K. Tanigaki^1,2,†

¹Department of Physics, Graduate School of Science, Tohoku University, Aoba, Aramaki, Aoba-ku, Sendai 980-8578, Japan
²WPI-Advanced Institutes of Materials Research, Tohoku University, Aoba, Aramaki, Aoba-ku, Sendai 980-8577, Japan
³High Field Laboratory for Superconducting Materials, Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan

^*Corresponding author: youichi@sspns.phys.tohoku.ac.jp
^†Corresponding author: tanigaki@sspns.phys.tohoku.ac.jp

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Vol. 89, Iss. 2 — 1 January 2014

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Figure 1
Schematic images: (a) a ( $k_{x}$ , $k_{y}$ ) projection of the FS for Ba(FeAs) $_{2}$ in the spin-density-wave phase, as calculated by DFT [14] and (b) the Kondo effect between Dirac fermions and 3 $d$ -Mn localized electron spins.
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Figure 2
(a) Magnetic field ( $B$ ) dependence of magnetoresistance ( $R_{M}$ ) in Ba(Fe $_{1 - x}$ Mn $_{x}$ As) $_{2}$ at various temperatures. (b) Derivative of $R_{M}$ ( $d R_{M} / d B$ ) in Ba(Fe $_{1 - x}$ Mn $_{x}$ As) $_{2}$ with $x = 0$ –0.035 at 30 K. (c) Temperature ( $T$ ) dependence of the square root of $B^{*}$ in Ba(Fe $_{1 - x}$ Mn $_{x}$ As) $_{2}$ with $x = 0$ –0.035. $B^{*}$ is defined as the onset field for the linear magnetoresistance. Solid lines indicate the fit vs Eq. (2) for $T$ $\geq$ 15 K. Error bars for $B^{*}$ were estimated from a least mean-square fit of $d R_{M} / d B$ as a function of B, where $d R_{M} / d B$ develops linearly for low- $B$ and saturates for under high- $B$ (d) $x$ dependence of Fermi energy $E_{F}$ and $v_{F}$ for $x = 0$ –0.035. Error bars were estimated from a least mean-square fit of the $B^{*}$ vs $T$ .
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Figure 3
(a) Magnetic field ( $B$ ) dependence of Hall resistivity ( $ρ$ $_{y x}$ ) for Ba(Fe $_{1 - x}$ Mn $_{x}$ As) $_{2}$ at 2 K for $x = 0$ –0.035. (b)–(f) Magnetic field ( $B$ ) dependence of the first derivative of magnetoresistance ( $d R_{M} / d B$ ), and the Hall resistivity ( $ρ$ $_{y x}$ ) from $-$ 4 to 4 T. (g) Temperature ( $T$ ) dependence of averaged mobility [ $μ_{ave} = (μ_{e} + μ_{h}) / 2$ ] for Ba(Fe $_{1 - x}$ Mn $_{x}$ As) $_{2}$ with $x = 0$ –0.035. The inset in (g) shows a magnified plot for $x$ = 0.028 and 0.035.
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Figure 4
(a) $T$ dependence of electrical resistivity ( $ρ$ ) divided by $ρ$ at 300 K ( $ρ / ρ_{300 K}$ ) for $x = 0.007$ –0.035. Arrows indicate the local minima of $ρ$ ( $ρ$ $_{m}$ ). (b) $T$ dependence of $Δ$ $ρ$ [= ( $ρ - ρ_{m}) / ρ_{300 K}$ ]. The inset of (b) shows the $T$ dependence of the magnetic susceptibility for $x$ = 0.035. A fit to the Curie-law ( $χ = χ_{0} + C / T$ , where $C$ is the Curie constant) is indicated by the solid line. (c) Inverse of $μ_{ave}$ (1/ $μ_{ave}$ ) as a function of the square root of carrier number for the Dirac cone ( $n_{D}$ $^{0.5}$ ) of Ba(Fe $_{1 - x}$ Mn $_{x}$ As) $_{2}$ . For comparison, the dependence of Ba(Fe $_{1 - x}$ Ru $_{x}$ As) $_{2}$ is also shown [17]. Solid lines are the results of a linear fit for Ba(Fe $_{1 - x}$ Ru $_{x}$ As) $_{2}$ . The error bars of 1/ $μ_{ave}$ are calculated from the least squares error of the semiclassical transport parameters. The estimated error of less than 1 $%$ is much less than the difference of 1/ $μ_{ave}$ between the Mn and Ru substituted samples. (d) The cyclotron effective mass as a function of $n_{D}$ $^{0.5}$ at 2 K ( $m^{*}$ $_{2 K}$ ) for Ba(Fe $_{1 - x}$ Mn $_{x}$ As) $_{2}$ (red open circle). The dependence of $m^{*}$ estimated from the parameters as shown in Fig. 2 is also plotted (red closed circle). The $m^{*}$ values for Ba(Fe $_{1 - x}$ Ru $_{x}$ As) $_{2}$ are also shown [17] (closed square). A linear fit for Ba(Fe $_{1 - x}$ Ru $_{x}$ As) $_{2}$ is indicated by the solid line. Error bars for $m^{*}$ are calculated based on the error of $E_{F}$ and $v_{F}$ .
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Figure 5
Powder x-ray diffraction patterns for Ba(Fe $_{1 - x}$ Mn $_{x}$ As) $_{2}$ with (a) $x = 0.007$ , (b) 0.016, (c) 0.025, and (d) 0.035. The open black circles indicate the observed intensities. The red lines are their Rietveld fits. Pink bar lines correspond to the Bragg-peak positions of Ba(FeAs) $_{2}$ . The blue curve shows the calculated differences between the Rietveld fitting and the observed intensities.
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Figure 6
First derivative of normalized resistivity for Ba(Fe $_{1 - x}$ Mn $_{x}$ As) $_{2}$ .
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Kondo-like mass enhancement of Dirac fermions in Ba(Fe $_{1 - x}$ Mn $_{x}$ As) $_{2}$

T. Urata, Y. Tanabe, K. K. Huynh, H. Oguro, K. Watanabe, S. Heguri, and K. Tanigaki

Phys. Rev. B 89, 024503 – Published 13 January 2014

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Kondo-like mass enhancement of Dirac fermions in Ba(Fe1−xMnxAs)2

T. Urata, Y. Tanabe, K. K. Huynh, H. Oguro, K. Watanabe, S. Heguri, and K. Tanigaki

Phys. Rev. B 89, 024503 – Published 13 January 2014

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Kondo-like mass enhancement of Dirac fermions in Ba(Fe $_{1 - x}$ Mn $_{x}$ As) $_{2}$