Chiral Spin Order in Kondo-Heisenberg Systems

Abstract

We demonstrate that Kondo-Heisenberg systems, consisting of itinerant electrons and localized magnetic moments (Kondo impurities), can be used as a principally new platform to realize scalar chiral spin order. The underlying physics is governed by a competition of the Ruderman-KittelKosuya-Yosida (RKKY) indirect exchange interaction between the local moments with the direct Heisenberg one. When the direct exchange is weak and RKKY dominates the isotropic system is in the disordered phase. A moderately large direct exchange leads to an Ising-type phase transition to the phase with chiral spin order. Our finding paves the way towards pioneering experimental realizations of the chiral spin liquid in low dimensional systems with spontaneously broken time reversal symmetry.PACS numbers: 75.30. Hx, 71.10.Pm, 72.15.Nj Interactions between magnetic moments usually lead to some kind of magnetic order where rotational symmetry is broken and the order parameter is linear in spins [1]. This is what happens in ferromagnets, antiferromagnets and all sorts of helimagnets. Villain has demonstrated [2] that, in addition to the magnetic order, helical magnets possess a vector chiral order parameter. It is bilinear in spins and is related to the mutual orientation of neighboring spins. This chiral order breaks the discrete symmetry and can exist even without the magnetic order [3]. The discovery of the vector chiral order has given rise to the idea that there could exist an order which includes a combination of three spins. The corresponding order parameter is a mixed product of three neighboring spins, see O c in Eq.(1) below and Refs. [4,5]. It breaks time-reversal and parity symmetries. Such a local order parameter is considered as the key quantity for description of exotic magnetic phases [4]. In contemporary language, O c is referred to as "scalar chiral spin order" and the state of matter with (spontaneously) broken time-reversal and parity symmetries but with conserved spin rotational symmetry is called Chiral Spin Liquid (CSL) [6]. The seminal example possessing the CSL symmetry is the Kalmeyer-Laughlin model [7][8][9][10]. Its wave functions demonstrate the topological behavior inherent in the fractional quantum Hall effect. Thus, the Kalmeyer-Laughlin model links spin liquids and topologically nontrivial states [11][12][13][14][15][16] and can be called "topological CSL". An increasing interest in the topological CSL [17][18][19][20][21][22][23] has been stimulated, in part, by a search for exotic (anyon) superconductivity [24,25] and by the physics of skyrmions [26][27][28][29]. The latter can be realized in magnets with the chirality resulting either from the lattice structure or from the Dzyaloshinskii-Moriya interaction [30][31][32][33].Although the concept of CSL and its order parameter O c were introduced in the 80-ties, it still remains unclear (color on-line) Competition between two different spin interactions in KHS: The spin on each lattice site is decomposed in terms of an orthonormal triad e1,2,3 (green ar...

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“…We note in passing that, a competition of the RKKY interaction with a direct Heisenberg exchange in dense 1D KL introduces additional level of complexity and can lead to appearance of exotic phases with a nontrivial spin order, such as a chiral spin liquid [55] or a chiral lattice supersolid [56].…”

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“…To the best of our knowledge, this gives the firstever example of such a protection in the system where the spin-rotation symmetry is not (and cannot be) broken. It would be interesting to study in the future how the direct Heisenberg interaction between the spins could modify out theory [85,86].…”

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