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Robust intralayer antiferromagnetism and tricriticality in the van der Waals compound VBr3

Dávid Hovančík, Marie Kratochvílová, Tetiana Haidamak, Petr Doležal, Karel Carva, Anežka Bendová, Jan Prokleška, Petr Proschek, Martin Míšek, Denis I. Gorbunov, Jan Kotek, Vladimír Sechovský, and Jiří Pospíšil
Phys. Rev. B 108, 104416 – Published 21 September 2023
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Abstract

We studied magnetic states and phase transitions in the van der Waals antiferromagnet VBr3 experimentally by specific heat and magnetization measurements of single crystals in high magnetic fields and theoretically by the density functional theory calculations focused on exchange interactions. The magnetization behavior mimics Ising antiferromagnets with magnetic moments pointing out-of-plane due to strong uniaxial magnetocrystalline anisotropy. The out-of-plane magnetic field induces a spin-flip metamagnetic transition of first-order type at low temperatures, while at higher temperatures, the transition becomes continuous. The first-order and continuous transition segments in the field-temperature phase diagram meet at a tricritical point. The magnetization response to the in-plane field manifests a continuous spin canting which is completed at the anisotropy field μ0HMA27T. At higher fields, the two magnetization curves above saturate at the same value of magnetic moment µsat1.2μB/f.u., which is much smaller than the spin-only (S=1) moment of the V3+ ion. The reduced moment can be explained by the existence of an unquenched orbital magnetic moment antiparallel to the spin. The orbital moment is a key ingredient of a mechanism responsible for the observed large anisotropy. The exact energy evaluation of possible magnetic structures shows that the intralayer zigzag antiferromagnetic (AFM) order is preferred, which renders the AFM ground state significantly more stable against the spin-flip transition than the other options. The calculations also predict that a minimal distortion of the Br ion sublattice causes a radical change of the orbital occupation in the ground state, connected with the formation of the orbital moment and the stability of magnetic order.

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  • Received 3 February 2023
  • Accepted 29 August 2023

DOI:https://doi.org/10.1103/PhysRevB.108.104416

©2023 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Dávid Hovančík1, Marie Kratochvílová1, Tetiana Haidamak1, Petr Doležal1, Karel Carva1, Anežka Bendová1, Jan Prokleška1, Petr Proschek1, Martin Míšek2, Denis I. Gorbunov3, Jan Kotek4, Vladimír Sechovský1, and Jiří Pospíšil1,*

  • 1Charles University, Faculty of Mathematics and Physics, Department of Condensed Matter Physics, Ke Karlovu 5, 121 16 Prague 2, Czech Republic
  • 2Institute of Physics, Czech Academy of Sciences, Na Slovance 2, 182 21 Prague 8, Czech Republic
  • 3Hochfeld-Magnetlabor Dresden (HLD-EMFL), Helmholtz-Zentrum Dresden-Rossendorf, 01328 Dresden, Germany
  • 4Department of Inorganic Chemistry, Faculty of Science, Charles University, Hlavova 8, 128 40 Prague 2, Czech Republic

  • *jiri.pospisil@matfyz.cuni.cz

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Issue

Vol. 108, Iss. 10 — 1 September 2023

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Images

  • Figure 1
    Figure 1

    (a) The temperature dependence of specific heat of VBr3 in zero magnetic field () and the field of 13.5 T applied parallel () and perpendicular () to c*. The arrows mark the positions of TN and Ts. The inset shows the variation of the TN-related anomaly for the magnetic fields applied in the c* direction. (b) The specific-heat isotherms of VBr3 at selected temperatures for the magnetic field parallel to c*.

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  • Figure 2
    Figure 2

    (a) The magnetization isotherms of VBr3 measured at 1.9 K in static fields (SFs) up to 18 T and pulsed fields (PFs) H||c* and Hc* up to 58 T. Inset: The detail of the plots for H||c* between 13 and 20 T. The arrow points to the critical field Hc. The absolute value of the calibrated magnetization isotherms can vary with an error bar ±10%. (b) Stoner-Wohlfarth simulation. Plotted M along H per one site as a function of applied external field H, for H parallel to the easy axis (blue) or perpendicular to the easy axis (red). Solid lines are calculated according to the model assuming purely uniaxial anisotropy (K2=0meV), while calculations depicted with dashed lines include a higher-order term (K2=0.2meV).

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  • Figure 3
    Figure 3

    The magnetization isotherms of VBr3 measured at various temperatures in pulsed fields (PFs) for H||c* up to 27 T.

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  • Figure 4
    Figure 4

    The HT phase diagram of VBr3 for magnetic field applied along the c*. The blue curve represents the inflection points on metamagnetic phase transition (MPT) in pulsed field data, the red curve the position of the anomaly in specific-heat data (Cp), the cyan curve represents the kink of MPT in steady-field data (see Fig. S1 in the SM [59]), and the magenta point shows the position of anomalies in field dependence of specific-heat data. The yellow point shows the estimated position of the tricritical point (TCP). The TCP is tentatively placed at TTCP=12K, μ0HTCP=16.4T. M(S2) represents data measured on a sample of lower quality (less stable in air) for comparison.

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  • Figure 5
    Figure 5

    (a) The predicted antiferromagnetic (AFM) structure of VBr3. Only a single layer of V3+ ions is displayed. The AFM structure consists of ferromagnetic (FM) zigzag chains coupled AFM within the plane. (b) Layered AFM structure (FM ordered layers with antiparallel orientation between neighboring layers) [33]. Two layers of V3+ ions are displayed, and lines in the vertical direction connect V ions stacked on top of each other (differing only in the z coordinate). (c) Calculated effective exchange J* and anisotropy K1 as a function of the distance r (in multiples of lattice parameter a). The occupation of the V3+ d states is calculated and schematically displayed in the diagrams.

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  • Figure 6
    Figure 6

    (a) VBr3 lattice plane, predicted relaxation is shown. (b) Heisenberg model with interactions up to the third nearest neighbor (J1J2J3).

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