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Anisotropic field response of specific heat for a ferromagnetic superconductor UCoGe in magnetic fields

Shota Nakamura, Shunichiro Kittaka, Kazushige Machida, Yusei Shimizu, Ai Nakamura, Dai Aoki, and Toshiro Sakakibara
Phys. Rev. B 106, 035152 – Published 28 July 2022
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  • INTRODUCTION
  • EXPERIMENTAL PROCEDURE
  • EXPERIMENTAL RESULTS
  • THEORETICAL CONSIDERATIONS
  • CONCLUSION AND SUMMARY
  • ACKNOWLEDGMENTS
    • References

    Abstract

    Magnetic-field-angle-resolved specific heat and magnetization measurements were conducted on a ferromagnetic superconductor UCoGe with remarkable anisotropic upper critical field Hc2. Although Hc2 reaches a high magnetic field (∼20T) along the b axis, it is small (∼0.6T) when a magnetic field is applied along the magnetic easy c axis. This study indicates that the specific heat is abruptly suppressed when the magnetic field is applied toward the c axis from the a and b axes in the ferromagnetic state. The field response of density of states (DOS) is anisotropic, relative to the c axis, and its angle dependence is slightly singular. The Ising-type magnetic anisotropy of the ferromagnetic state is dominant even in the anisotropic reinforced superconducting state. These facts indicate that the suppression of DOS may closely relate to the superconducting state. We theoretically analyze these findings together with URhGe and UTe2 by highlighting the common and distinctive features among three compounds.

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    • Received 16 January 2022
    • Revised 27 June 2022
    • Accepted 14 July 2022

    DOI:https://doi.org/10.1103/PhysRevB.106.035152

    ©2022 American Physical Society

    Physics Subject Headings (PhySH)

    1. Physical Systems
    ActinidesFerromagnetic superconductorsIntermetallic compounds
    1. Techniques
    Magnetization measurementsSpecific heat measurements
    Condensed Matter, Materials & Applied Physics

    Authors & Affiliations

    Shota Nakamura1,2, Shunichiro Kittaka2,3, Kazushige Machida4, Yusei Shimizu2,5, Ai Nakamura5, Dai Aoki5, and Toshiro Sakakibara2

    • 1Nagoya Institute of Technology, Aichi, Nagoya 466-8555, Japan
    • 2Institute for Solid State Physics, The University of Tokyo, Kashiwa 277-8581, Japan
    • 3Department of Physics, Faculty of Science and Engineering, Chuo University, Kasuga, Bunkyo-ku, Tokyo 112-8551, Japan
    • 4Department of Physics, Ritsumeikan University, Kusatsu 525-8577, Japan
    • 5Institute for Materials Research, Tohoku University, Oarai 311-1313, Japan and Japan Atomic Energy Agency, Tokai 319-1106, Japan

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    Issue

    Vol. 106, Iss. 3 — 15 July 2022

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    Images

    • Figure 1
      Figure 1

      Temperature dependence of C/T measured at the several magnetic fields along the b axis (θb=0). For clarity, the data are vertically shifted by 0.015. The arrows depict the critical temperature position of the SC state TSC(H). Note the upturns of C/T in H=10 and 14 T at lowest temperatures.

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    • Figure 2
      Figure 2

      H−T phase diagram obtained at field angles θb=0∘, 1∘, 2∘, and 3∘ on the bc plane, where θb=0 denotes H∥b. The inset shows the initial slopes of Hc2 as a function of θb, thereby indicating substantial enhancements of Hc2 toward the b axis.

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    • Figure 3
      Figure 3

      Temperature dependence of C/T measured at field angles θb=0∘, 1∘, 2∘, 3∘, and 9∘ on the bc plane at 2 T, where θb=0 is H∥b. The small arrows denote the position of the critical temperature of the SC state TSC(H).

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    • Figure 4
      Figure 4

      Magnetic field dependence of C/T measured at field angles θb=0∘, 1∘, 2∘, and 9∘ on the bc plane at 0.8 K in the FM state, where θb=0 is H∥b. The gray closed symbols are obtained from the resistivity data for H∥b and c in Ref. [16]. To compare with C/T, these data are multiplied by C/T(H=0)=0.057J/K2mol.

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    • Figure 5
      Figure 5

      Field-angle ϕ dependences of C/T at 0.3 and 0.8 K measured in a rotating magnetic field within the ab plane. For clarity, the data at 0.8 K are vertically shifted by 0.006 from the lowest field data of 0.5 T. Open circles represent data mirrored by the a axis.

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    • Figure 6
      Figure 6

      Field-angle θa dependences of C/T at 0.2 and 0.8 K measured in a rotating magnetic field within the ac plane. For clarity, the data are vertically shifted by 0.01 and 0.015 at 0.2 and 0.8 K from the lowest field data of 0.2 T, respectively. Open circles represent the data mirrored by the a axis.

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    • Figure 7
      Figure 7

      Field-angle θb dependences of C/T at 0.1 and 0.6 K measured in a rotating magnetic field within the bc plane. For clarity, the data are vertically shifted by 0.015 and 0.02 at 0.1 and 0.6 K from the lowest field data, respectively. Open circles denote the data mirrored by the b axis.

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    • Figure 8
      Figure 8

      (a) C/T vs Hc plot of the data shown in Fig. 6, which were measured at 0.8 K on the ac plane. A solid line denotes a function that is proportional to (Hc)−0.04. Open circles represent the data mirrored by the a axis. (b) Comparison between C/T vs Hc plot at 3 T in Fig. 8(a) and longitudinal spin fluctuation 〈(δH)2〉 calculated from 1/T1 at 3.5 T and 1.7 K in previous NMR measurements [11].

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    • Figure 9
      Figure 9

      Temperature dependences of the magnetization M(T) for H∥c in various field strengths. The dots denote the experimental data where Hc=0.02, 0.04, 0.06, 0.08, 0.1, 0.5, 1.0, and 1.5 T from the bottom. Here, we also plot the approximate spontaneous moment curve MFM(T) with TC=2.5 K and MFM(T=0)=0.05μB/U in red. The continuous lines denote M(T) parabola curves obtained from Eq. (3).

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    • Figure 10
      Figure 10

      By using the data in Fig. 9, β(Hc) values are evaluated. We assume that the M(T) curves centered at T=0 are approximated by parabolas. The value at β(H=0) is evaluated by β0=−M0/TC2. The smooth curve expresses the fitting with β(Hc)∝−(Hc)−3/2 for 0.3T<Hc<1.5T. From β(Hc), γ(Hc) (green curve) is evaluated. The inset shows the linear behaviors of β(Hc) in Hc up to Hc=0.1T.

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