Frustrated spin-1/2 ladder with ferro- and antiferromagnetic legs

Abstract

Two-leg spin-1/2 ladder systems consisting of a ferromagnetic leg and an antiferromagnetic leg are considered where the spins on the legs interact through antiferromagnetic rung couplings J 1 . These ladders can have two geometrical arrangements either zigzag or normal ladder and these systems are frustrated irrespective of their geometry. This frustration gives rise to incommensurate spin density wave, dimer and spin fluid phases in the ground state. The magnetization in the systems decreases linearly with J 2 1 , and the systems show an incommensurate phase for 0.0 < J 1 < 1.0. The spin-spin correlation functions in the incommensurate phase follow power law decay which is very similar to Heisenberg antiferromagnetic chain in external magnetic field. In large J 1 limit, the normal ladder behaves like a collection of singlet dimers, whereas the zigzag ladder behaves as a one dimensional spin-1/2 antiferromagnetic chain. Figure 1: (a) and (b) show the normal and the zigzag arrangements of the interfaces. The arrows show the spin arrangement and the question mark represents the frustrated spin.12]. Ladders with ferromagnetic legs/rungs and antiferromagnetic rungs/legs are also well studied and show interesting phases [14][15][16][17][18][19]. However, the AF zigzag ladder is completely different from normal ladder. The zigzag ladder in the weak rung coupling limit J 1 /J 2 < 0.44 behaves like two independent HAF spin-1/2 chains [2,20,21], and shows gapped spiral phase for 0.44 < J 1 < 2. It is gapped system with dimer configuration for 2 < J 1 /J 2 < 4.148 [2,[20][21][22][23].In this paper we consider spin ladders which have ferromagnetic (F) spin exchange interactions along one of the legs, and antiferromagnetic (AF) interactions on the other leg; and spins on these two legs are interacting through AF interaction. The focus of this paper is to study some universal theoretical aspects such as the existence of exotic phases in the ground state (GS) and low-lying excitations in this system. We show that the ferromagnetic-antiferromagnetic (F-AF) ladders pose quasi-long range behavior in incommensurate regime, and frustration can be induced even for very small rung coupling limit.These two lagged ladders can represent the interface of the two layered magnetic spin-1/2 system consisting of an antiferromagnetic and a ferromagnetic layer where the two layers interact with direct or indirect antiferromagnetic exchange. Similar interfaces are studied by Suhl et al. [24] and Hong et al. [25]. We further simplify the model by considering only a inter-facial line of spins in the interface of both the layers. We consider two possibilities of arrangement of inter-facial spins; first, when spins are directly facing each-other as in normal ladder (NL), and second, where spins on one leg is shifted by half of the lattice unit forming a zigzag ladder (ZL). The spin arrangements of NL and ZL are shown in the Fig. 1(a) and (b). These systems are interesting because both the ladders are frustrated irrespective to the nature of rung in...

Quantum Phase Diagram of a Frustrated Spin‐1/2 Ferro‐Antiferromagnetic Normal Ladder

“…Odd leg ladders like three leg ladder Sr 2 Cu 3 O 5 have gapless spectrum. [26] Frustrated zigzag spin-1/2 ladder systems provide an opportunity to study various kinds of exotic phases like dimer phase, [17,27,28] spiral phase, [17,27] ferromagnetic (FM) phase etc. at various rung interaction limit.…”

“…These NL are frustrated and the gs stabilizes the dimer singlet, non-collinear spin wave and ferri-magnetic phase. [27,34] This system exhibits ferrimagnetism and it can be explained in terms of Lieb-Mattis (LM) [35] theorem. The spin arrangements in NL is shown in the Figure 1.…”

“…This system is frustrated irrespective of the nature of rung exchange interactions. This ladder geometry with AFM inter-leg interaction has been studied in ref [27] keeping the interaction strength of both the leg same (J 1 = J 2 ) and it was shown that the ground state magnetization is proportional to R 2 where R is AFM rung interaction. The results agree well with spin wave theory studies.…”

Thermal Properties of Rung Disordered Two-leg Quantum Spin Ladders: Quantum Monte Carlo Study

“…The width of the spin gap for a two-leg ladder spin system with the isotropic coupling constant J can be roughly estimated as ∆ ≈ 0.5J by using QMC techniques within a reasonable computational time on modern computers 21 . The value of the spin gap can be altered or even eliminated by including disorder in the spin-spin coupling 22 , choosing a different kind of a lattice topology 23,24 or appliying external magnetic fields 25 . It has been shown that the spin gap is drastically reduced by a light doping on the pure system with non-magnetic impurities [26][27][28] .…”

“…Various properties of a wide range of different ladder models have been studied, like spin ladder systems with dimerization [35][36][37][38][39][40][41] , zig-zag ladders 23,[42][43][44][45] , mixed ladders [46][47][48][49][50] . A gapless phase has been found in two-leg zig-zag ladders with frustration by benefiting from exact diagonalization and density matrix renormalization group (DMRG) methods 23 . A ferrimagnetic spin-1 and spin-1/2 mixed spin ladder has been analyzed by using spin-wave theory and bosonization techniques 48 .…”