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Understanding the μSR spectra of MnSi without magnetic polarons

A. Amato, P. Dalmas de Réotier, D. Andreica, A. Yaouanc, A. Suter, G. Lapertot, I. M. Pop, E. Morenzoni, P. Bonfà, F. Bernardini, and R. De Renzi
Phys. Rev. B 89, 184425 – Published 30 May 2014
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  • INTRODUCTION
  • EXPERIMENTAL DETAILS
  • RESULTS AND DISCUSSION
  • CONCLUSIONS
  • ACKNOWLEDGEMENTS
    • References

    Abstract

    Transverse-field muon-spin rotation (μSR) experiments were performed on a single crystal sample of the noncentrosymmetric system MnSi. The observed angular dependence of the muon precession frequencies matches perfectly the one of the Mn-dipolar fields acting on the muons stopping at a 4a position of the crystallographic structure. The data provide a precise determination of the magnetic dipolar tensor. In addition, we have calculated the shape of the field distribution expected below the magnetic transition temperature TC at the 4a muon site when no external magnetic field is applied. We show that this field distribution is consistent with the one reported by zero-field μSR studies. Finally, we present ab initio calculations based on the density-functional theory which confirm the position of the muon stopping site inferred from transverse field μSR. In view of the presented evidence we conclude that the μSR response of MnSi can be perfectly and fully understood without invoking a hypothetical magnetic polaron state.

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    • Received 2 May 2014

    DOI:https://doi.org/10.1103/PhysRevB.89.184425

    ©2014 American Physical Society

    Authors & Affiliations

    A. Amato1,*, P. Dalmas de Réotier2,3, D. Andreica4, A. Yaouanc2,3, A. Suter1, G. Lapertot2,3, I. M. Pop4,5, E. Morenzoni1, P. Bonfà6, F. Bernardini7, and R. De Renzi6

    • 1Laboratory for Muon Spin Spectroscopy, Paul Scherrer Institut, 5232 Villigen PSI, Switzerland
    • 2Université Grenoble Alpes, INAC-SPSMS, 38000 Grenoble, France
    • 3CEA, INAC-SPSMS, 38000 Grenoble, France
    • 4Faculty of Physics, Babes-Bolyai University, 400084 Cluj-Napoca, Romania
    • 5Yale University, Applied Physics Department, New Haven, Connecticut 06520-8284, USA
    • 6Dipartimento di Fisica e Scienze della Terra and Unità CNISM di Parma, Università di Parma, 43124 Parma, Italy
    • 7CNR-IOM-Cagliari and Dipartimento di Fisica, Università di Cagliari, 09042 Monserrato, Italy

    • *alex.amato@psi.ch

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    Issue

    Vol. 89, Iss. 18 — 1 May 2014

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    Images

    • Figure 1
      Figure 1

      Sample used for the TF-μSR measurements. The sample was rotated along the cylinder axis.

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    • Figure 2
      Figure 2

      Example of one μSR time spectrum plotted in a rotating reference frame (RRF) with frequency 65 MHz. The gray line represents the fit to the data (open points) using Eq. (1) and the four individual signals are also displayed (color code is the same as in Fig. 4). Note that the actual fits were performed without RRF and without time binning (i.e., original bin of 0.9766 ns). Notice that the four signals have very similar depolarization rates.

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    • Figure 3
      Figure 3

      Fourier transform of TF spectra taken at different orientations. The color code of the different signals is the same as in Figs. 2 and 4.

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    • Figure 4
      Figure 4

      Angular dependence of the fitted μSR frequencies. The lines are guides to the eye. The green dashed line represents the average frequency ν¯(ϕ′) (see text).

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    • Figure 5
      Figure 5

      Angular dependence of the dipolar contributions of the four frequencies reported on Fig. 4. The symbols are obtained after the subtraction described in Eq. (3). The lines correspond to the theoretical calculations positioning the muon at the site (0.532,0.532,0.532) and taking into account the rotation axis (see text).

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    • Figure 6
      Figure 6

      Definition of the Euler angles defining the rotation axis and of the polar and azimuth angles defining the direction of the external field. The reference frame (x,y,z) is the reference frame of the crystal and (x′,y′,z′) is the one defined by the rotating plane and rotation axis.

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    • Figure 7
      Figure 7

      Dipolar sum calculation of the parameter adip characterizing the representation [Aijc] of the dipolar tensors in the crystal reference frame for the 4a sites. The divergence occurs at the 4a position of the Mn ion. The red dotted line corresponds to the results of the fits as explained in the text.

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    • Figure 8
      Figure 8

      Sketch of the crystallographic structure of MnSi (Mn ions are drawn in purple, Si ions in blue). The muon position (0.532,0.532,0.532) is also indicated (red) as well as the other three equivalent sites. Note that six Mn ions, which do not belong to the primary unit cell, are also displayed.

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    • Figure 9
      Figure 9

      (Upper panel) Exact [blue line and symbols; see Eq. (10)] and approximated [red line; see Eq. (15)] field distributions expected at sites II, III, and IV. (Lower panel) Muon polarization function deduced from the field distributions shown on the upper panel (see also text).

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    • Figure 10
      Figure 10

      ZF-μSR data taken at 5 K (initial muon polarization parallel to the [111] direction). The line represents a fit of Eq. (17) to the data using the parameters given in the text (for better visibility a time binning corresponding to 5 ns was chosen, whereas the fits were performed with a time binning of 1.25 ns).

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    • Figure 11
      Figure 11

      (Upper panel) Fast Fourier transform of the ZF-μSR data obtained at 5 K and shown on Fig. 10. The blue and red components represent, respectively, the first and second component of the right-hand side of Eq. (17). (Lower panel) Computed field distributions for the I site (blue) and for the II, III and IV sites (red). For better visibility, these field distributions have been slightly folded by Lorentzian distributions with widths (full width at half maximum) of 5 and 20 G, respectively.

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    • Figure 12
      Figure 12

      Sketch of the crystallographic structure of MnSi with minima regions of the electrostatic potential (yellow). The rest of the color scheme is the same as in Fig. 8. The yellow regions define isosurfaces with an energy set to V=E0/2 with E0 being the ground-state energy obtained from the solution of the Schrödinger equation for the muon in the electrostatic potential. The equivalent muon stopping sites determined by TF-μSR are also indicated and are enclosed in the minima regions. Note that compared to Fig. 8, we also report the muon sites located just outside of the primary unit cell, which are enclosed in minima regions extending into the primary unit cell.

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