Infrared anomalous Hall effect in Ca${}_{x}$Sr${}_{1\ensuremath{-}x}$RuO${}_{3}$ films

Infrared anomalous Hall effect in Ca $_{x}$ Sr $_{1 - x}$ RuO $_{3}$ films

M.-H. Kim, T. Tanaka, C. T. Ellis, A. Mukherjee, G. Acbas, I. Ohkubo, H. Christen, D. Mandrus, H. Kontani, and J. Cerne

Phys. Rev. B 88, 155101 – Published 1 October 2013

Abstract

The midinfrared anomalous Hall effect (AHE) can provide critical new information for resolving the controversial origins of the dc AHE in Ca $_{x}$ Sr $_{1 - x}$ RuO $_{3}$ . The complex Faraday and Kerr angles, as well as the complex Hall conductivity $σ_{x y}$ , are measured in Ca $_{x}$ Sr $_{1 - x}$ RuO $_{3}$ films as a function of mid- and near-infrared energy $E$ from 0.1 eV to 1.4 eV, magnetic field $H$ , temperature $T$ , and Ca concentration $x$ . For the ferromagnetic state from $x = 0$ to 0.4, the $(d_{x z}, d_{y z})$ -orbital tight-binding model is employed to investigate the quasiparticle role in the low energy response of the AHE $σ_{x y} (E)$ since the Berry curvature term becomes weak at low energies. The infrared Hall sign reversals with $T$ are observed only at $x = 0$ and 0.13, which is narrower than the Ca concentration range in which the dc Hall sign reversal appears. The similarity of the infrared Hall angles between paramagnetic and ferromagnetic Ca $_{x}$ Sr $_{1 - x}$ RuO $_{3}$ compounds demonstrates the symmetric nature of the Hall response around the quantum phase transition at $x = 0.7$ .

Received 2 May 2013

DOI:https://doi.org/10.1103/PhysRevB.88.155101

Authors & Affiliations

M.-H. Kim^1,2, T. Tanaka³, C. T. Ellis¹, A. Mukherjee¹, G. Acbas¹, I. Ohkubo⁴, H. Christen⁵, D. Mandrus⁵, H. Kontani³, and J. Cerne¹

¹Department of Physics, University at Buffalo, The State University of New York, Buffalo, New York 14260, USA
²Department of Physics, University of Maryland, College Park, Maryland 20742, USA
³Department of Physics, Nagoya University, Furo-cho, Nagoya 464-8602, Japan
⁴Department of Applied Chemistry, University of Tokyo, Tokyo, Japan
⁵Oak Ridge National Laboratory, Condensed Matter Science Division, Oak Ridge, Tennessee 37831, USA

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 88, Iss. 15 — 15 October 2013

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
Energy dependence of the infrared AHE $θ_{F}$ and $θ_{K}$ for the Ca composition $x = 0$ to 0.47. The AHE (a) Re( $θ_{F}$ ), (b) Im( $θ_{F}$ ), (c) Re( $θ_{K}$ ), and (d) Im( $θ_{K}$ ) with the sample fully magnetized perpendicular to the sample surface at 0 T and 10 K. The intensity of transmitted light is too weak to measure $θ_{F}$ in the 0.4–0.7 eV energy range.Reuse & Permissions
Figure 2
Infrared longitudinal conductivity $σ_{x x}$ for the Ca composition $x = 0$ to 0.4. (a) Calculated and (b) measured Re( $σ_{x x}$ ), and (c) calculated and (d) measured Im( $σ_{x x}$ ). Lines in (a) and (c) present the ( $d_{x z}$ , $d_{y z}$ )-orbital tight binding model calculation. $γ$ is the quasiparticle damping rate. The vertical dashed lines in (a) and (c) indicate the minimum band splitting energy $Δ = 82$ meV. Symbols ( $\times$ ) in (a) and (c) shows the Berry phase calculation of the intrinsic AHE in SrRuO $_{3}$ by Fang et al.[2] $σ_{x x}$ in (b) and (d) were obtained from AHE $θ_{F}$ and $θ_{K}$ in Fig. 1 by using the analysis technique in Ref. 24. All measurements were performed at $T = 10$ K. Note that the error bar is about 10–15% of the data.Reuse & Permissions
Figure 3
Transverse AHE conductivity $σ_{x y}$ for the Ca composition $x = 0$ to 0.4. (a) Calculated and (b) measured Re( $σ_{x y}$ ), and (c) calculated and (d) measured Im( $σ_{x y}$ ). Lines in (a) and (c) present the ( $d_{x z}$ , $d_{y z}$ )-orbital tight binding model calculation. $γ$ is the quasiparticle damping rate. Vertical dashed lines in (a) and (c) indicate minimum band splitting $Δ = 82$ meV. Symbols ( $\times$ ) in (a) and (c) shows the Berry phase calculation of the intrinsic AHE in SrRuO $_{3}$ by Fang et al.[2] $σ_{x y}$ in (b) and (d) were obtained from AHE $θ_{F}$ and $θ_{K}$ in Fig. 1 by using the analysis technique in Ref. 24. All measurements were performed at $T = 10$ K. Note that the error bar is about 2.5% of the data.Reuse & Permissions
Figure 4
Temperature and magnetic field dependences of the infrared AHE $θ_{F}$ for the Ca composition from $x = 0$ to 0.4. The temperature dependent AHE Re( $θ_{F}$ ) at (a) 117 meV and (b) 224 meV. The temperature dependent AHE Im( $θ_{F}$ ) at (c) 117 meV and (d) 224 meV. Both Re( $θ_{F}$ ) and Im( $θ_{F}$ ) were measured at $H = 0$ T with the sample fully magnetized out of plane in the temperature range from 10 K up to 160 K. The hysteresis loops of (e) Re( $θ_{F}$ ) at two temperatures 50 K and 70 K and (f) Im( $θ_{F}$ ) at two temperatures 40 K and 60 K were observed for the Ca composition $x = 0.13$ . The sign change of the hysteresis loops appears near $H = 0$ T. Note that the error bar is about 10–20% above 40 K and a few percent below 20 K.Reuse & Permissions
Figure 5
Energy dependence of $θ_{F}$ and $θ_{K}$ for the Ca composition $x = 0.75$ –1. (a) Re( $θ_{F}$ ), (b) Im( $θ_{F}$ ), (c) Re( $θ_{K}$ ), and (d) Im( $θ_{K}$ ) at $H = 1$ T and $T = 10$ K. $θ_{F}$ and $θ_{K}$ include contributions from the ordinary Hall effect. The dc values of Re( $θ_{F}$ ) and Re( $θ_{K}$ ) in (a) and (c) are determined in Ref. 5.Reuse & Permissions
Figure 6
Temperature dependence of the infrared $θ_{F}$ for the Ca composition $x = 0.75$ –1. (a) Re( $θ_{F}$ ) and (b) Im( $θ_{F}$ ) at 117 meV and $H = 1$ T. $θ_{F}$ includes the OHE contribution.Reuse & Permissions

Physical Review B

covering condensed matter and materials physics

Infrared anomalous Hall effect in Ca $_{x}$ Sr $_{1 - x}$ RuO $_{3}$ films

M.-H. Kim, T. Tanaka, C. T. Ellis, A. Mukherjee, G. Acbas, I. Ohkubo, H. Christen, D. Mandrus, H. Kontani, and J. Cerne

Phys. Rev. B 88, 155101 – Published 1 October 2013

Abstract

Authors & Affiliations

Article Text (Subscription Required)

References (Subscription Required)

Issue

Access Options

Physical Review B

covering condensed matter and materials physics

Infrared anomalous Hall effect in CaxSr1−xRuO3 films

M.-H. Kim, T. Tanaka, C. T. Ellis, A. Mukherjee, G. Acbas, I. Ohkubo, H. Christen, D. Mandrus, H. Kontani, and J. Cerne

Phys. Rev. B 88, 155101 – Published 1 October 2013

Abstract

Authors & Affiliations

Article Text (Subscription Required)

References (Subscription Required)

Issue

Access Options

Authorization Required

Other Options

Download & Share

Images

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Figure 6

Log In

Search

Article Lookup

Paste a citation or DOI

Enter a citation

Infrared anomalous Hall effect in Ca $_{x}$ Sr $_{1 - x}$ RuO $_{3}$ films