Chiral Spin Pairing in Helical Magnets

Abstract

A concept of chiral spin pairing is introduced to describe a vector-chiral liquid-crystal order in frustrated spin systems. It is found that the chiral spin pairing is induced by the coupling to phonons through the Dzyaloshinskii-Moriya interaction and the four-spin exchange interaction of the Coulomb origin under the edge-sharing network of magnetic and ligand ions. This produces two successive second-order phase transitions upon cooling: an O(2) chiral spin nematic, i.e., spin cholesteric, order appears with an either parity, and then the O(2) symmetry is broken to yield a helical magnetic order. Possible candidate materials are also discussed as new multiferroic systems.PACS numbers: 75.10. Hk, 05.50.+q, 63.70.+h, The chirality in the electronic spin texture introduced by a geometrical frustration and/or the relativistic spinorbit interaction has been one of the key concepts in strongly correlated electron systems. The scalar spin chirality [1, 2, 3], i.e., the scalar triple product of three noncoplanar spins, is odd under the time-reversal (T ) and even under the space-inversion (I), and gives rise to a large anomalous Hall effect [4,5,6,7,8]. On the other hand, central to this Letter is the vector spin chirality [9], i.e., the vector product of two noncollinear spins. It is T -even and I-odd, and can produce the ferroelectric polarization in Mott insulators through the spin-orbit interaction [10,11,12,13,14,15,16,17], even for spin-1/2 systems [17,18,19].The vector-chiral spin order is realized in conventional helical magnets. In principle, it is even possible that the chiral or parity symmetry is broken but the time-reversal symmetry is not. This state having finite spin correlation lengths is categorized into a liquid or a liquid crystal of spins, which is of our main interest, while the magnetically ordered state into a solid. The issue of the chiral spin order in the absence of any magnetic order is not only a problem of statistical mechanics, but has been intensively studied since the discovery of high-T c cuprates, and even gives a new "multiferroic" phenomenon which has attracted current great interests, as discussed below. However, conditions for the order being stabilized have not been fully understood.It has been argued that the vector or pseudoscalar chiral ordering [20,21,22] takes place separately from the XY transition in the antiferromagnetic (AF) XY model on the triangular lattice [23]. The intermediate phase is characterized by the vector-chiral order. It has also been obtained for frustrated quantum spin systems in one dimension [24], and discussed in two dimensions [25] and for odd-time states [26]. However, it usually appears only in a tiny region of the global phase diagram. For classical AF Heisenberg and XY models on stacked triangular lattices, Monte-Carlo simulations and field-theoretical analyses have suggested a single phase transition from paramagnet to helical magnet, which is either weakly first-order or a second-order one, which belongs to a different universality class from t...

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