Ultra-robust high-field magnetization plateau and supersolidity in bond-frustrated MnCr2S4

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Science Advances  17 Mar 2017:
Vol. 3, no. 3, e1601982
DOI: 10.1126/sciadv.1601982


  • Fig. 1 Temperature dependence of sound velocity and magnetic susceptibility in MnCr2S4.

    (A) Relative change of the sound velocity Δv/v of the longitudinal acoustic mode propagating along the <111> axis in zero magnetic field (left scale). Inverse susceptibility was measured in an external field of 1 T applied along <111> (right scale). The dashed line corresponds to a high-temperature Curie-Weiss law. Inset: Inverse susceptibility versus temperature below 18 K. Vertical arrows mark the ferrimagnetic transition at TC = 65 K and the low-temperature magnetic transition TYK = 5 K, establishing a triangular spin configuration. (B) Relative change of the sound velocity Δv/v (left scale) and sound attenuation Δα (right scale) of the same acoustic mode below 20 K. The vertical arrow indicates TYK.

  • Fig. 2 Illustration of crystallographic and spin structure of MnCr2S4 at low temperature in the YK phase in external magnetic fields below 10 T.

    The ferromagnetically aligned Cr spins are always oriented along the external magnetic field. The Mn spins are divided into two sublattices, with canted spin configuration and resulting moment antiparallel to the Cr moments. In the figure, we indicated the directions of the spins of the two Mn sublattices in low field. This angle increases with increasing magnetic field.

  • Fig. 3 Field dependence of magnetization and ultrasound velocity in MnCr2S4 single crystals.

    (A) Magnetization (left scale), in Bohr magneton per f.u. (formula unit), and relative change of the sound velocity Δv/v of the longitudinal acoustic mode propagating along the <111> axis (right scale) at 1.5 K as a function of the external magnetic field applied along <111>. Error bars mark uncertainties of calibration, which increase with increasing fields. (B) Magnetization for different temperatures between 7.2 and 28 K. For clarity, the curves at T < 28 K are shifted. Anomalies at 11, 25, and 50 T are consecutively numbered, and dotted lines indicate their temperature-dependent shifts.

  • Fig. 4 Field dependence of ultrasound velocity and attenuation in single-crystalline MnCr2S4.

    (A) Relative change of the sound velocity Δv/v of the longitudinal acoustic mode propagating along the <111> axis versus the magnetic field at different temperatures. The external magnetic field was applied parallel to the direction of sound propagation k and sound polarization u. Arrows mark critical fields at the magnetostructural phase transitions. Dotted lines indicate the broadening of the phase boundaries of anomaly 4. (B) Change of the sound attenuation Δα versus the magnetic field at different temperatures. The inset highlights the unusual damping behavior at 8.8 K and documents the suppression of damping close to 40 T. This field corresponds to an effective zero magnetic field at the manganese site. The dashed line in the inset is drawn to guide the eye.

  • Fig. 5 Thermodynamic phase diagram.

    (A) Color-coded plot of the derivative of the sound velocity dv/dH. Open circles represent anomalies in the field-dependent magnetization. The solid lines denote maxima in the field derivatives of the sound velocity, taking the experimentally determined critical fields into consideration. The most probable spin configurations are shown for the different magnetic phases. (B) Theoretical phase diagram of a quantum lattice-gas model by Liu and Fisher (26). Liquid, superfluid, supersolid, and solid phases are assigned in analogy to bosonic systems, only taking symmetry considerations into account. Only the corresponding spin configurations of the manganese spins are indicated. The chromium moments always follow the external magnetic field and allow for field tuning at the manganese sites from about −40 T < Heff < 20 T.

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