Abstract:
Triangular-lattice antiferromagnets with the general formula ATO2 (A = alkali metal, T = 3d transition metal) often adopt a slightly distorted crystal structure at low temperatures, accompanying a lifting of magnetic frustration and the appearance of long-range magnetic ordering and sometimes a particular orbital ordering. Taking NaVO2 as an example, we successfully demonstrate that the tiny structural distortion with a ratio of lattice parameters, am/bm = 1.755, and the formation of orbital ordering observed in recent neutron-diffraction experiments can be well interpreted by first-principles calculations including 3d electron correlations with parameter Ueff = 3.6 eV. This distinct study on “pure” structural distortion is expected to be applied in other triangular-lattice antiferromagnetic systems.
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I. INTRODUCTION
Geometrical frustration, which stems from the topological arrangements of spins, is an important and intriguing phenomenon in magnetism.1–7 Particularly interesting are the triangular-lattice systems composed of magnetic ions, in which once the first two spins are aligned antiparallely, the third one cannot simultaneously minimize its antiferromagnetic (AFM) interactions with both of the other two spins, giving rise to highly degenerate ground states. Such ground-state degeneracy, that is, magnetic frustration, may yield unconventional magnetic behavior, for example, spin-disordered liquid.2–4
..........In such systems, long-range AFM ordering is prohibited due to strong magnetic frustration. At low temperatures, these systems tend to decrease its symmetry by a tiny structural distortion accompanying a reduction in the energy of the system. As a result, the magnetic frustration is removed and the system may favor a particular ground state sometimes with an orbital ordering.
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Process of lattice distortion and its correlation with magnetism In addition to the prediction of the AFM ground state with am/bm = 1.750, Fig. 2 also elucidates the process of lattice distortion as well as its correlation with magnetism. On the one hand, as an equilateral triangle consisting of V ions in the rhombohedral phase (R-3m) is distorted into an isosceles triangle in the monoclinic phase (C2/m), the geometrical symmetry of the compound is reduced. An introduction of magnetism, either FM or AFM, prompts such a reduction in symmetry due to magnetoelastic coupling. However, only the introduction of the AFM state can induce an experimentally observed lattice distortion. This tiny lattice distortion slightly lowers the energy of the system by removing the magnetic frustration and establishing low-temperature long-range AFM ordering. On the other hand, based on the requirement of energy reduction, the general rule for the rhombohedralmonoclinic distortion is am/bm > 1.732. In this process, the original equal V-V bonds in the VO2 layer split into two short bonds along the [010] direction and four long bonds along the [110] and [110] directions.
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