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Orientation dependence of the magnetic phase diagram of Yb2Ti2O7

S. Säubert, A. Scheie, C. Duvinage, J. Kindervater, S. Zhang, H. J. Changlani, Guangyong Xu, S. M. Koohpayeh, O. Tchernyshyov, C. L. Broholm, and C. Pfleiderer
Phys. Rev. B 101, 174434 – Published 21 May 2020
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  • INTRODUCTION
  • EXPERIMENTAL METHODS
  • EXPERIMENTAL RESULTS
  • DISCUSSION
  • CONCLUSIONS
  • ACKNOWLEDGMENTS
  • APPENDICES
    • References

    Abstract

    In the quest to realize a quantum spin liquid (QSL), magnetic long-range order is hardly welcome. Yet it can offer deep insights into a complex world of strong correlations and fluctuations. Much hope was placed in the cubic pyrochlore Yb2Ti2O7 as a putative U(1) QSL but a new class of ultrapure single crystals make it abundantly clear that the stoichiometric compound is a ferromagnet. Here we present a detailed experimental and theoretical study of the corresponding field-temperature phase diagram. We find it to be richly anisotropic with a critical endpoint for B∥〈100〉, while a field parallel to 〈110〉 or 〈111〉 enhances the critical temperature by up to a factor of two and shifts the onset of the field-polarized state to finite fields. Landau theory shows that Yb2Ti2O7 in some ways is remarkably similar to pure iron. However, it also pinpoints anomalies that cannot be accounted for at the classical mean-field level including a dramatic enhancement of TC and a reentrant phase boundary under applied magnetic fields with a component transverse to the easy axes, as well as the anisotropy of the upper critical field in the quantum limit.

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    • Received 10 January 2020
    • Accepted 15 April 2020

    DOI:https://doi.org/10.1103/PhysRevB.101.174434

    ©2020 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    FerromagnetismFrustrated magnetismPhase diagramsQuantum spin liquid
    1. Physical Systems
    Pyrochlores
    1. Techniques
    Magnetization measurementsNeutron diffractionSpecific heat measurementsSusceptibility measurements
    Condensed Matter, Materials & Applied Physics

    Authors & Affiliations

    S. Säubert1,2,*, A. Scheie3, C. Duvinage1, J. Kindervater3, S. Zhang3,4, H. J. Changlani5,6,3, Guangyong Xu7, S. M. Koohpayeh3,8, O. Tchernyshyov3, C. L. Broholm3,7,8, and C. Pfleiderer1

    • 1Physik-Department, Technische Universität München, D-85748 Garching, Germany
    • 2Heinz Maier-Leibnitz Zentrum, Technische Universität München, D-85748 Garching, Germany
    • 3Institute for Quantum Matter and Department of Physics and Astronomy, Johns Hopkins University, Baltimore, Maryland 21218, USA
    • 4Department of Physics and Astronomy, University of California, Los Angeles, California 90095, USA
    • 5Department of Physics, Florida State University, Tallahassee, Florida 32306, USA
    • 6National High Magnetic Field Laboratory, Tallahassee, Florida 32304, USA
    • 7NIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
    • 8Department of Materials Science and Engineering, Johns Hopkins University, Baltimore, Maryland 21218, USA

    • *Present address: Department of Physics, Colorado State University, Fort Collins, Colorado 80523-1875, USA; steffen.saeubert@colostate.edu

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    Vol. 101, Iss. 17 — 1 May 2020

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    • Figure 1
      Figure 1

      Magnetic phase diagram of Yb2Ti2O7 for applied fields along (a) 〈111〉, (b) 〈110〉, and (c) 〈100〉 as inferred from field and temperature-dependent magnetization, specific heat, AC susceptibility, and neutron scattering. (B) and (T) indicate field and temperature scans, respectively. Hysteretic effects observed under field and temperature sweeps are indicated by means of blue and red shading, respectively. Tsf denotes a feature seen in the temperature dependence of the magnetization reminiscent of spin freezing, cf. Figs. 2–2.

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    • Figure 2
      Figure 2

      [(a)–(c)] Temperature dependence of the magnetization of Yb2Ti2O7 in high [(a1)–(c1)], intermediate [(a2)–(c2) and (a3)–(c3)], and small [(a3)–(c3)] applied fields. In small applied fields and below 100 mK, a distinct difference between data recorded under zero-field cooling (zfc) and field cooling (fc) emerges (Tsf), which has been attributed to spin freezing in related rare-earth pyrochlore systems [42, 43]. This feature vanishes for finite internal fields. [(d)–(f)] Magnetization and differential susceptibility of Yb2Ti2O7 as a function of internal magnetic field after correction of demagnetization fields for the 〈111〉 (d), 〈110〉 (e), and 〈100〉 (f) directions, respectively. The differential susceptibility data are shifted with respect to each other for clarity.

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    • Figure 3
      Figure 3

      (a) Specific heat of Yb2Ti2O7 as a function of temperature at different 〈110〉 oriented magnetic fields. Note the sharp first-order-like anomaly at zero field which broadens and becomes a second-order lambdalike anomaly at finite field. [(b) and (c)] Real and imaginary components of the AC susceptibility as a function of 〈110〉 field at different temperatures. The negative field sweeps show invariance of field sweep direction for nonzero internal fields. Solid lines indicate increasing magnetic field and dashed lines show decreasing magnetic field.

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    • Figure 4
      Figure 4

      Neutron scattering of the (002) peak in Yb2Ti2O7 for magnetic fields applied along the 〈110〉 direction. (a) Field dependence of (002) at different temperatures, showing a quadratic dependence at low fields and a clear upper critical field. (b) Theoretical (002) scattering calculated with mean-field theory using the Ross, Robert, and Thompson Hamiltonians [15, 22, 34]. (c) Temperature-dependent scattering at different applied fields. No hysteresis is visible. Error bars represent one standard deviation.

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    • Figure 5
      Figure 5

      Experimental data [(a) and (b)] and calculated magnetization via the coarse-grained model [(c)–(f)] and mean-field theory [(g)–(l)] for Yb2Ti2O7. (a) Magnetic field dependence of the magnetization of Yb2Ti2O7 at 0.1 K for the 〈111〉, 〈110〉, and 〈100〉 direction. (b) Differential susceptibility dM/dH calculated from the magnetization data. [(c)–(f)] Magnetization versus field as obtained from the coarse-grained model and differential susceptibility. [(g)–(l)] Mean-field calculation at T=0, taking into account a cubic anisotropy and the Zeeman field. Calculations were performed for the exchange parameters from Ross et al. [22] [(g) and (h)], Thompson et al. [15] [(i) and (j)], and Robert et al. [34] [(k) and (l)]. [(h), (j), and (l)] Susceptibility calculated from the theoretical model of the magnetization shown in (g), (i), and (k).

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    • Figure 6
      Figure 6

      Field-dependent magnetic structure of Yb2Ti2O7 for applied fields along 〈111〉, 〈110〉, and 〈100〉. In small fields, out of the six domains the system selects three and two domains for field along 〈111〉 and 〈110〉, respectively. In higher fields, the spins enter a polarized state where the spins either lie in or are canted towards their easy-plane defined by the local 〈111〉 axis. For field along 〈100〉, application of a magnetic field immediately stabilizes the configuration shown in blue shading.

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    • Figure 7
      Figure 7

      (a) Stoichiometric, pure, and colourless Yb2Ti2O7 single crystal grown by the traveling solvent floating zone (TSFZ) technique (image taken from Ref. [8]). (b) spherical sample ground from the stoichiometric single crystal and the oxygen-free Cu sample holder composed of two matching sections fitting accurately the size of the sphere. (c) sample holder mounted on the cold finger which is then bolted to the Cu tail attached to the mixing chamber of the dilution refrigerator.

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    • Figure 8
      Figure 8

      Magnetic hysteresis in Yb2Ti2O7 for temperatures T≤TC (0.06 K, 0.10 K, 0.15 K, 0.20 K, and 0.27 K) and for T=0.9 K in the paramagnetic regime. The coercive field Hcoerc. in the paramagnetic regime is finite due to instrumental resolution around H=0. The coercive field in the ferromagnetic regime of Yb2Ti2O7 is vanishingly small, suggesting that magnetic domain walls in the ordered state move freely in response to an applied magnetic field.

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    • Figure 9
      Figure 9

      Field-dependent neutron scattering from Yb2Ti2O7 at 0.1 K and 5 K compared to theoretical calculated intensity from mean-field simulations. For strong Bragg peaks, the data do not match the simulations because of field-dependent extinction, but for the weak Bragg peaks (002) and (220), the theory does match. Error bars represent one standard deviation.

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    • Figure 10
      Figure 10

      High-field and high-temperature scattering from the (002) Yb2Ti2O7 peak. The high-field scattering at 100 mK in (a) shows that an applied field of 8 T does not produce a collinear spin structure. The high-temperature scattering in (b) shows that an increase in temperature reduces the sublattice magnetization as expected. Error bars represent one standard deviation.

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