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Field-temperature phase diagram of the enigmatic Nd2(Zr1−xTix)2O7 pyrochlore magnets

M. Léger, E. Lhotel, E. Ressouche, K. Beauvois, F. Damay, C. Paulsen, A. Al-Mawla, E. Suard, M. Ciomaga Hatnean, G. Balakrishnan, and S. Petit
Phys. Rev. B 103, 214449 – Published 28 June 2021
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  • INTRODUCTION
  • EXPERIMENTAL BACKGROUND AND…
  • METHODS
  • RESULTS
  • DISCUSSION
  • CONCLUSION
  • ACKNOWLEDGMENTS
  • APPENDICES
    • References

    Abstract

    By combining neutron scattering and magnetization measurements down to 80 mK, we determine the (H,T) phase diagram of the Nd2(Zr1−xTix)2O7 pyrochlore magnet compounds. In those samples, Zr is partially substituted by Ti, hence tuning the exchange parameters and testing the robustness of the various phases. In all samples, the ground state remains all in/all out, while the field induces phase transitions toward new states characterized by two in–two out or one out–three in/one in–three out configurations. These transitions manifest as metamagnetic singularities in the magnetization versus field measurements. Strikingly, it is found that moderate substitution reinforces the stability of the all in/all out phase: the Néel temperature, the metamagnetic fields along with the ordered magnetic moment, are higher in substituted samples with x< 10%.

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    • Received 29 April 2021
    • Revised 7 June 2021
    • Accepted 8 June 2021

    DOI:https://doi.org/10.1103/PhysRevB.103.214449

    ©2021 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Frustrated magnetismMagnetic phase transitionsMagnetismPhase diagrams
    1. Physical Systems
    Magnetic systemsPyrochlores
    1. Techniques
    AC susceptibility measurementsDilution refrigeratorMagnetization measurementsMean field theoryNeutron diffraction
    Condensed Matter, Materials & Applied Physics

    Authors & Affiliations

    M. Léger1,2,*, E. Lhotel1,†, E. Ressouche3, K. Beauvois3,4, F. Damay2, C. Paulsen1, A. Al-Mawla1, E. Suard4, M. Ciomaga Hatnean5, G. Balakrishnan5, and S. Petit2,‡

    • 1Institut Néel, CNRS and Université Grenoble Alpes, 38000 Grenoble, France
    • 2Laboratoire Léon Brillouin, Université Paris-Saclay, CNRS, CEA, CE-Saclay, F-91191 Gif-sur-Yvette, France
    • 3IRIG, CEA and Université Grenoble Alpes, CEA Grenoble, F-38054 Grenoble, France
    • 4Institut Laue Langevin, F-38042 Grenoble, France
    • 5Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom

    • *melanie.leger@neel.cnrs.fr
    • †elsa.lhotel@neel.cnrs.fr
    • ‡sylvain.petit@cea.fr

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    Issue

    Vol. 103, Iss. 21 — 1 June 2021

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    • Figure 1
      Figure 1

      Sketch of one configuration of the AIAO ordered state of the Nd pyrochlore lattice in the unit cell of Nd2Zr2O7. By convention, outer tetrahedra are red, while the central tetrahedron is green. Note that to avoid any confusion between the so-called all in/all out magnetic structure, and the possible magnetic domains associated to this state, we use different notations for the state (AIAO) and for the domains (AIAO¯ or AOAI¯). The depicted configuration, with red all out tetrahedra and green all in tetrahedron, is labeled AOAI¯. The other configuration, AIAO¯, would have red all in tetrahedra and green all out tetrahedron. The figure also features the Nd3+ ions labeled according to Table 1.

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    • Figure 2
      Figure 2

      Magnetization M versus internal field Hi measured with the field applied along the three main high-symmetry directions at 80 mK on the 10%-Ti substituted sample Nd2Zr1.8Ti0.2O7. Similar curves are observed in the 2.5%-Ti substituted sample. Inset: Zoom in of the low field data.

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    • Figure 3
      Figure 3

      Real and imaginary parts of the AC susceptibility χ′ (left) and χ″ (right) for the pure (red dots), 2.5% (blue dots), and 10% (green dots) substituted samples, along the [11¯0] direction. Measurements were performed with HAC=2.7 Oe and a frequency f=5.7 Hz.

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    • Figure 4
      Figure 4

      Field dependence for H∥[001] in the 2.5%-substituted sample. (a) Sketch of the four spins in the all out state, obtained in zero field and (b) of the 2I2O state obtained at saturation. (c)–(e) Neutron diffraction results: (c) mAIAO, (d) m2I2O, and (e) total y component versus H [see Eq. (3)]. The left (respectively, right) branch results from mAIAO>0—all out component (mAIAO<0—all in component). Fullprof refinements are displayed as full black dots. Colored points indicate the most probable values obtained from the field-sweeping measurement analysis (see Appendix pp3). The color scale indicates the χ2 value obtained from Eq. (C1). The inset of (d) shows the intensity of the (1¯11¯) reflection. (f) dM/dHi versus Hi. The field was always swept from negative to positive values.

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    • Figure 5
      Figure 5

      Pictures of the two domains of the AIAO state. (a) AIAO¯ domain: Red tetrahedra are all in and green tetrahedra are all out. (b) AOAI¯ domain: Red tetrahedra are all out and green tetrahedra are all in.

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    • Figure 6
      Figure 6

      Field dependence for H∥[11¯0] in the 2.5%-substituted sample. (a) Sketch of the four spins in the all out state, obtained in zero field and (b) of the partially ordered state obtained at saturation. (c)–(e) Neutron diffraction results: (c) mAIAO, (d) m∥, and (e) total m3 component versus H [see Eq. (4)]. The right (respectively, left) branch results from mAIAO>0—all out component (mAIAO<0—all in component). Fullprof refinements are displayed as full black dots. Colored points indicate the most probable values obtained from the field-sweeping measurements analysis (the color scale corresponds to the χ2 value, see Appendix pp3). The inset of (d) shows the intensity of the (11¯3) reflection. (f) dM/dHi versus Hi at different temperatures between 70 and 500 mK. The inset shows the whole curve at 70 mK. The field was always swept from negative to positive values.

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    • Figure 7
      Figure 7

      Field dependence for H∥[111] in the 10%-substituted sample. (a) Sketch of the four spins in the all out state, obtained in zero field and (b) of the 1I3O state obtained at saturation in a positive field. (c)–(e) Neutron diffraction results: (c) mapex and (d) mkagome components versus H [see Eq. (5)]. Fullprof refinements are displayed as full black dots. Colored points indicate the most probable values obtained from the field-sweeping measurement analysis (the color scale corresponds to the χ2 value, see Appendix pp3). (e) Intensity of the (1¯3¯1) reflection versus H. (f) dM/dHi versus Hi at different temperatures between 80 and 500 mK. The inset shows the whole curve at 80 mK. The field was always swept from negative to positive values.

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    • Figure 8
      Figure 8

      Field-temperature (H,T) phase diagrams determined from M versus H experiments for the three high-symmetry directions (a) [001], (b) [11¯0], (c) [111], and for the studied samples: the pure (green squares), the 2.5%-substituted (red diamonds), and the 10%-substituted (blue dots) compounds. Lines are guides to the eye.

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    • Figure 9
      Figure 9

      M/Hi versus temperature for the 10%-Ti substituted sample obtained in ZFC-FC measurements at different applied magnetic fields along [111]. T1 is defined as the temperature where the ZFC and the FC curves split and Tm is defined as the temperature where M/Hi reaches its maximum.

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    • Figure 10
      Figure 10

      Phase diagrams (H,T) for H∥[111] from M versus T (T1, red diamonds, and Tm, green squares) and M versus H (H1, blue dots) measurements for the 2.5 and 10%-substituted samples.

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    • Figure 11
      Figure 11

      Mean-field (H,T) phase diagrams calculated for (a) H∥[001] and (b) H∥[11¯0] for the pure compound parameters. The color scale indicates the value of mzAIAO. Phase diagrams were obtained upon decreasing the temperature in FC conditions.

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    • Figure 12
      Figure 12

      Magnetic components along z as a function of field in the pure sample. (a), (b) H∥[001]: for (a) y=m3 and (b) mAIAO [see Eq. (3)]. (c), (d) H∥[11¯0]: for (c) m∥ and (b) mAIAO [see Eq. (4)]. The color scale represents the energy difference between the calculated configuration and the absolute minimum energy configuration (logarithmic scale), the red color referring to the smallest energy. Black dots correspond to the experimental values obtained from the field-sweeping measurement analysis. Labels (1)–(3) in panel (d) refer to the three branches discussed in the text.

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    • Figure 13
      Figure 13

      Mean-field (H,T) phase diagrams obtained for H∥[111] upon decreasing the temperature in field-cooled conditions for the pure compound parameters. The left and right sides show the same results but projected along the z and z̃ components of the pseudospins, respectively. (a), (b) show the aiao parameter (equal to 1 if all the spins are in (or out) and 0 otherwise). (c), (d) display the kagomé spin component mkagome, (e), (f) the apical spin component mapex. Dashed lines are guides to the eye to highlight the region delimited by the aiao parameter in (b).

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    • Figure 14
      Figure 14

      Mean-field (H,T) phase diagrams obtained for H∥[111] when the field is swept from −1.5 to 1.5T for the pure compound parameters. The left and right sides show the same results but projected along the z and z̃ components of the pseudospins, respectively. (a), (b) display the aiao parameter; (c), (d) the kagomé spins component mkagome; (e), (f) the apical spin component mapex. Dashed lines are guides to the eye to show the regions delimited by the aiao parameter in (a) and (b).

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    • Figure 15
      Figure 15

      Sketch of the pseudospins in a tetrahedron (a) in the blue region and (b) in the gray region of the phase diagram of Fig. 10. The black and gray arrows, respectively, represent the z̃ and z local axes. Red arrows represent the total pseudospin components, the blue ones their projection on the z̃ axes, and the green ones their projection on the z axes. In (a), an all out configuration is obtained for both projections, while in (b), only the z̃ components are all out, the z ones being 1O3I.

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    • Figure 16
      Figure 16

      Magnetic moment as a function of field for the pure [(a), (b)] and the 2.5% [(c), (d)] compounds when a field is applied along [111] for the (a)–(c) kagomé and (b)–(d) the apical spins. The color scale represents the energy difference between the calculated configuration and the absolute minimum energy configuration (logarithmic scale), the red color referring to the smallest energy. Black dots correspond to the experimental values obtained from the field-sweeping measurement analysis.

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    • Figure 17
      Figure 17

      (a), (b) aiao parameter versus (H,T) determined from mean-field calculations considering H∥[111] and swept from −1.5 to 1.5T performed with the exchange parameters determined for the 2.5% substituted sample. (a) [respectively, (b)] shows the results for the z (respectively, z̃) component of the pseudospins.

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    • Figure 18
      Figure 18

      (a) Powder neutron diffractograms measured on G4.1 for the x=2.5% sample at 80 mK (red dots) and 600 mK (blue dots). (b) Difference intensity obtained when subtracting the 600 mK to the 80 mK data (red dots). The black line shows the AIAO Fullprof refinement, giving an ordered moment of 1.36μB.

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    • Figure 19
      Figure 19

      Contour plot of the classical energy E as a function of Φ1 and Φ3 for H∥[001] with the pure sample exchange parameters. The black dots show the positions of the minima and the color scale displays the energy in meV.

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