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Stripe magnetic order and field-induced quantum criticality in the perfect triangular-lattice antiferromagnet CsCeSe2

Tao Xie, N. Zhao, S. Gozel, Jie Xing, S. M. Avdoshenko, K. M. Taddei, A. I. Kolesnikov, L. D. Sanjeewa, Peiyue Ma, N. Harrison, C. dela Cruz, L. Wu, Athena S. Sefat, A. L. Chernyshev, A. M. Läuchli, A. Podlesnyak, and S. E. Nikitin
Phys. Rev. B 110, 054445 – Published 29 August 2024
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  • INTRODUCTION
  • EXPERIMENTAL DETAILS
  • RESULTS
  • DISCUSSION AND CONCLUSIONS
  • ACKNOWLEDGMENTS
  • APPENDICES
    • References

    Abstract

    The two-dimensional triangular-lattice antiferromagnet (TLAF) is a textbook example of frustrated magnetic systems. Despite its simplicity, the TLAF model exhibits a highly rich and complex magnetic phase diagram, featuring numerous distinct ground states that can be stabilized through frustrated next-nearest-neighbor couplings or anisotropy. In this paper, we report low-temperature magnetic properties of the TLAF material CsCeSe2. The inelastic neutron scattering (INS) together with specific heat measurements and density functional theory calculations of crystalline electric field suggest that the ground state of Ce ions is a Kramers doublet with strong easy-plane anisotropy. Elastic neutron scattering measurements demonstrate the presence of stripe-yz magnetic order that develops below TN=0.35K, with the zero-field ordered moment of mCe≈0.65μB. Application of magnetic field first increases the ordering temperature by about 20% at the intermediate field region and eventually suppresses the stripe order in favor of the field-polarized ferromagnetic state via a continuous quantum phase transition (QPT). The field-induced response demonstrates sizable anisotropy for different in-plane directions, B∥a and B⊥a, which indicates the presence of bond-dependent coupling in the spin Hamiltonian. We further show theoretically that the presence of anisotropic bond-dependent interactions can change the universality class of QPT for B∥a and B⊥a.

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    • Received 1 December 2023
    • Revised 13 June 2024
    • Accepted 22 July 2024

    DOI:https://doi.org/10.1103/PhysRevB.110.054445

    ©2024 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Frustrated magnetismMagnetic orderMagnetic phase transitionsQuantum criticality
    1. Techniques
    Exact diagonalizationNeutron scattering
    Condensed Matter, Materials & Applied Physics

    Authors & Affiliations

    Tao Xie1,2,*, N. Zhao3, S. Gozel4, Jie Xing5, S. M. Avdoshenko6, K. M. Taddei2,7, A. I. Kolesnikov2, L. D. Sanjeewa5, Peiyue Ma1, N. Harrison8, C. dela Cruz2, L. Wu9, Athena S. Sefat5, A. L. Chernyshev10, A. M. Läuchli4,11, A. Podlesnyak2, and S. E. Nikitin12,†

    • *Contact author: xiet69@mail.sysu.edu.cn
    • †Contact author: stanislav.nikitin@psi.ch

    See Also

    Quantum Spin Dynamics Due to Strong Kitaev Interactions in the Triangular-Lattice Antiferromagnet CsCeSe2

    Tao Xie, S. Gozel, Jie Xing, N. Zhao, S. M. Avdoshenko, L. Wu, Athena S. Sefat, A. L. Chernyshev, A. M. Läuchli, A. Podlesnyak, and S. E. Nikitin
    Phys. Rev. Lett. 133, 096703 (2024)

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    Vol. 110, Iss. 5 — 1 August 2024

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    • Figure 1
      Figure 1

      (a) Crystal structure of CsCeSe2. The light cyan, navy, and dark yellow balls represent Cs, Ce, and Se atoms respectively. The red arrows indicate the ordered moments of the stripe-yz AFM order at zero field. (b) The sample used for the single crystal neutron measurements. (c) Rocking scans at (0, 0, 3) and (0, −1, 4) Bragg peaks demonstrate good mosaicity of the sample. (d) Neutron powder diffraction pattern collected above TN shows good quality of the powder sample under study.

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    • Figure 2
      Figure 2

      Crystal electric field splittings of CsCeSe2. (a) Powder-averaged spectrum measured at T=5K. The dashed lines indicate the three excitations at E1, E2, and E3. (b) Powder-averaged spectrum measured at T=150K. (c)–(d) The top view of 2×2×1 supercell of CsCeSe2with spin density isosurfaces (ρα−ρβ) at DFT/PBE/PAW level shown for solutions with FM (c) and AFM (d) spin constraints. (e) 1D cuts of the spectra taken at T=5 and 150 K. The solid line is the CASSCF(1,7)/ANO-RCC-VDZP/RASSI/SO calculation of the CEF at T=0K.

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    • Figure 3
      Figure 3

      Neutron diffraction results of CsCeSe2. (a)–(c) Powder diffraction results collected at HB-2A. In panel (a), the black crosses are experimental data points measured at 250 mK, the red curves are Rietveld refinements with stripe-yz (Γ2) magnetic order, the blue curves are the differences of the data and refinement. The magenta and olive tick marks indicate the nuclear and magnetic peak positions. The cyan dashed line represents the Rietveld refinement from the irreducible representation Γ1, i.e., the stripe-x order. Panels (b) and (c) show the difference between 250 mK and 550 mK and refinements with stripe-x (Γ1) and stripe-yz (Γ2) magnetic states. (d)–(i) Single-crystal diffraction data measured on CNCS at 70 mK in a series of magnetic fields. In panel (f), the data are obtained by subtracting 0-T dataset from 5 T one, I(Q)=I(Q)B=5T−I(Q)B=0T at the central part of the plot and by subtraction of 5-T dataset from 0-T for the left and right parts, I(Q)=I(Q)B=0T−I(Q)B=5T, as indicated in the plot. Diffraction pattern at zero field shows AFM Bragg peaks at Q = (0, 1/2, 1±3n) and Q = (0, −1/2, 2±3n) (n = integer) that correspond to the stripe-yz magnetic ground state. Strong positive intensities at Q = (0, 0, 3n) indicate the FM intensity of Bragg peaks in the field-polarized (FP) state at 5 T.

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    • Figure 4
      Figure 4

      Low-temperature magnetization measurements of CsCeSe2. Panels (a)–(c) and (e)–(g) demonstrate data collected with magnetic field applied along [110] and [100] directions. Panels (a) and (e) present the temperature dependence of static spin susceptibility M(T)/B measured at several fields up to saturation. Panels (b) and (f) show the field dependence of magnetization, M(B). Panels (c) and (g) are the distribution of dM/dB as a function of temperature and magnetic field. The weak intensity at low fields at B<0.2 T in panel (c) is an external artefact. Panels (d) and (h) present the anisotropy of magnetization in CsCeSe2. Panel (d) shows isothermal magnetization as a function of the magnetic field along and perpendicular to the a axis in ab plane. The red curves are the first derivatives of M(B). The dashed lines mark the saturation magnetic field. (h) Isothermal magnetization curve measured under pulsed field with magnetic field along the c axis.

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    • Figure 5
      Figure 5

      Thermodynamic characterizations and phase diagram of CsCeSe2 with field applied along [100] axis. (a) The normalized specific heat (C/T) as a function of temperature at different magnetic fields with B∥a. The inset shows the calculated magnetic entropy as a function of temperature at B=0T. (b) The specific heat as a function of magnetic field at different temperatures with B∥a. (c) The MCE of CsCeSe2 measured with ramping up the magnetic fields. The inset is a comparison between the MCE with ramping up (black) and ramping down (red) the magnetic fields at T=0.1K. (d) A magnetic B−T phase diagram, deduced from the specific heat and MCE results. The open and solid circles are data points extracted from peak positions of the specific heat (SH) data, which indicate the transitions from the paramagnetic (PM) state to the AFM state, and the crossover from the PM to the FP state. The open stars are the data points obtained from the MCE in panel (c). The white dashed line indicates the crossover between the PM and FP phases. The arrows on triangles show the sketches of the corresponding ordered states.

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    • Figure 6
      Figure 6

      (a), (b) LSWT dispersion just above the critical field applied (a) parallel to a (Bc,LSWT∥a=4.458T) and (b) perpendicular to a (Bc,LSWT⊥a=3.742T). Note that LSWT overestimates Bc and the values used for these calculations are larger than experimental values and those determined by ED. The red circles show the minimum of the dispersion, which vanishes when B=Bc, at M in (a) and M′ in (b). (c) Magnetic Brillouin zone (in normalized units). When the magnetic field vanishes, the three M points, M, M′, and M″ are inequivalent, while for a nonvanishing magnetic field, the BZ is folded and M′ and M″ become equivalent. (d) Finite-size gap Δ from the zero-momentum ground state to the first excited state at the M point multiplied by N for different system sizes N in proximity to the critical field. (e) Finite-size spectrum versus magnetic field of the N=32 sites torus, restricted to states at Γ, M≡M2 and M′≡M0. The vertical-dashed line shows the critical field as obtained in (d), Bc≃3.7T. The filled markers show three gaps appearing at Γ and M at B=Bc, which allow us to identify the nature of the phase transition. The numerically obtained renormalized values Δ/Δ0 are written beside each gap.

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    • Figure 7
      Figure 7

      Rietveld refinement of single-crystal x-ray diffraction data. Fobs2 and Fcal2 denote, respectively, the observed and calculated structure factors.

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    • Figure 8
      Figure 8

      Time-resolved ICP results (a) and the mass spectra [(b)–(d)] of the CsCeSe2 single crystals.

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