Half-magnetization plateau in a Heisenberg antiferromagnet on a triangular lattice

Abstract

We present the phase diagram in a magnetic field of a 2D isotropic Heisenberg antiferromagnet on a triangular lattice. We consider spin-S model with nearest-neighbor (J1) and next-nearest-neighbor (J2) interactions. We focus on the range of 1/8 < J2/J1 < 1, where the ordered states are different from those in the model with only nearest neighbor exchange. A classical ground state in this range has four sublattices and is infinitely degenerate in any field. The actual order is then determined by quantum fluctuations via "order from disorder" phenomenon. We argue that the phase diagram is rich due to competition between competing four-sublattice quantum states which break either Z3 orientational symmetry or Z4 sublattice symmetry. At small and high fields, the ground state is a Z3-breaking canted stripe state, but at intermediate fields the ordered states break Z4 sublattice symmetry. The most noticeable of such states is "three up, one down" state in which spins in three sublattices are directed along the field and in one sublattice opposite to the field. Such a state breaks no continuous symmetry and has gapped excitations. As the consequence, magnetization has a plateau at exactly one half of the saturation value. We identify gapless states, which border the "three up, one down" state and discuss the transitions between these states and the canted stripe state. IntroductionRecent experimental and theoretical advances renewed the interest in the physics of frustrated spin systems. In many of these systems the classical ground state is infinitely degenerate, and the actual ground state spin configuration is selected by quantum fluctuations (the "order from disorder" phenomenon). The resulting ground state is often rather unconventional and in several cases displays a non-monotonic behavior of magnetization in an applied field, with kinks, jumps, and plateaus [1][2][3][4][5][6][7]. The most known example of such behavior is in the case of a two-dimensional (2D) quantum antiferromagnet on a triangular lattice with nearestneighbor exchange J 1 [8,9]. Classically, all spin configurations, which satisfy S r + S r+δ1 + S r+δ2 = hS/(3J 1 ) for each triad of neighboring spins, have the same ground state energy. Quantum fluctuations lift the degeneracy and select a set of three coplanar configurations, between which the systems transforms upon increasing field. The middle configuration, which exists at h around 1/3 of the saturation field h sat = 9J 1 (h scaled), is a collinear state with two spins up (U) and one spin down (D) in every elementary triangle (an UUD state). In such a state only a discrete Z 3 symmetry is broken (one spin in a triad is selected to be antiparallel to a field), and, as a result, all excitations are gapped and the magnetization has a plateau at exactly one-third of the saturation value [8][9][10][11][12]. This plateau has been observed in Cs 2 CuBr 4 [13][14][15][16][17] and in Ba 3 CoSb 2 O 9 [18]. An UUD state survives in a finite range of perturbations, like the spatial anisotropy of the exch...

Spin liquids in geometrically perfect triangular antiferromagnets

“…In NaYbO 2 , external magnetic field triggers long-range order above 2 T with an up-up-down spin pattern [146] typical of the 1 3 -plateau phase of triangular antiferromagnets. In the fully isotropic (Heisenberg) case, this up-updown phase occurs only at J 2 /J 1 < 0.125 [150,151] suggesting that J 2 /J 1 should be lower than in YbMgGaO 4 , in agreement with the fact that the absolute value of J 1 increases.…”

“…First, with the exception of Ba 3 CoSb 2 O 9 field-induced behavior is largely unknown, and even theory studies of the anisotropic J 1 − J 2 Hamiltonians in the applied field remain scarce [150,151]. NaYbO 2 shows a quite unusual transition between the spin-liquid phase in zero field and the collinear up-up-down phase in the applied field [145,146] (a similar transformation was claimed in randomness-influenced YbMgGaO 4 too [166]).…”

Frustrated two dimensional quantum magnets

“…Another example of quantum plateau formation is found in an extended J 1 − J 1 − J 3 isotropic triangular model with n.n.n. exchange J 3 [136] (see also Sec. 10).…”

Itinerant fermions on a triangular lattice: Unconventional magnetism and other ordered states

“…the order in the plane transverse to the field remains 120 • spiral, and the order in the direction of the field is ferromagnetic, due to an imbalance of spin up and down electrons. In this respect, the field evolution of the 120 • order in an itinerant system is different from the one in the Heisenberg model with nearest neighbor exchange, where spins remain in the same plane during the field evolution and pass through an intermediate up-up-down phase [38][39][40] . We next argue that in a field, spin-polarization operators for spin components along and transverse to the field become different, and the bubbles made out of spinup c−fermion and spin-down f −fermion and out of spindown c−fermion and spin-up f −fermion also become different.…”

“…Suppose we start with 120 • spin ordering in zero field. For a system of localized spins on a 2D triangular lattice quantum fluctuations select field reorientation in which spins remain in the same plane in a finite field 38,40 . We show below that for itinerant fermions the evolution of the spin configuration with a field h = hẑ proceeds differently -in a finite field the SDW becomes a non-coplanar cone state in which spins preserve a 120 • order in the xy plane and simultaneously develop a net magnetization along the field.…”