Magnetoelastic effects and magnetization plateaus in two-dimensional systems

Abstract

We show the importance of both strong frustration and spin-lattice coupling for the stabilization of magnetization plateaus in translationally invariant two-dimensional systems. We consider a frustrated spin-1/2 Heisenberg model coupled to adiabatic phonons under an external magnetic field. At zero magnetization, simple structures with two or at most four spins per unit cell are stabilized, forming dimers or 2 × 2 plaquettes, respectively. A much richer scenario is found in the case of magnetization m = 1/2, where larger unit cells are formed with non-trivial spin textures and an analogy with the corresponding classical Ising model is detectable. Specific predictions on lattice distortions and local spin values can be directly measured by X-rays and Nuclear Magnetic Resonance experiments.PACS numbers: 75.10. Jm, 71.27.+a, 74.20.Mn A magnetization plateau occurs when the magnetization remains constant over a range ∆h of applied magnetic fields. The width of the plateau can be expressed in term of the excitation spectrum ∆h = E(M + 1) − 2E(M ) + E(M − 1), where E(M ) is the total energy at fixed magnetization M (measured in units of gµ B ). This, in turn, implies that the energy (per site) as a function of the magnetization (per site) displays a cusp-like singularity in the thermodynamic limit. In general, plateaus are absent in classical models with magnetic ground states whenever the magnetization is not collinear with the field.[1] Instead, they identify particularly stable quantum phases characterized by a spin gap.Usually, gaps in the excitation spectrum directly reflect the structure of the primitive cell of the lattice according to the commensurability condition [2] ℓS(1 − m) = integer (1) where S is the magnitude of the spin, m the magnetization per site in units of gµ B S (i.e., the average onsite spin component parallel to the magnetic field), and ℓ the number of spins in the primitive cell. Some evidence for a m = 1/3 plateau has been proposed for the triangular lattice, [9,10] while in the square lattice, the m = 0 properties of the J 1 −J 2 model are still debated. Indeed, although for J 2 /J 1 ∼ 1/2 the ground state is believed to be disordered, the existence of a finite triplet gap is much less clear, [11,12] casting some doubt as to the possibility of having an m = 0 plateau. The interest in the J 1 −J 2 model has grown due to the recent discovery of two materials well described by a two-dimensional (2D) quantum antiferromagnet, i.e., Li 2 VOSiO 4 and VOMoO 4 . [13,14] Although the experimental magnetization curve of these compounds has not yet been considered, the magnetization properties of the J 1 −J 2 model have been recently considered by using exact diagonalization calculations, leading to some evidence in favor of a magnetization plateau at m = 1/2. [15] This outcome has been interpreted as a consequence of the emergence of a 2 × 2 super-cell. According to this scenario, inside each cell the magnetic moments acquire a preferential orientation along the direction of the magnetic field, lea...

Fractional Magnetization Plateaus and Magnetic Order in the Shastry-Sutherland MagnetTmB4

“…For an understanding of the rich superstructures and of the fractional plateaus observed in the regime intermediate between afm and ferrimagnetic order, the Ising limit is not sufficient (the spatial period in this regime is just doubled compared to the period of the Néel phase) and in fact several higher order corrections may contribute to the observed features such as additional exchange interactions between further neighbors resulting from RKKY interactions and magnetoelastic effects [18].…”

Topological solitons and bulk polarization switch in collinear type-II multiferroics

“…A most important example is the spin-Peierls mechanism that promotes the formation of spin singlets at the cost of dimerized distortions [61,62], either in the non-frustrated case J 2 = 0 or the frustrated one [58]. This has been studied not only in one dimensional spin chains but also in higher dimensions [63][64][65][66][67]. The spinlattice coupling also provides mechanisms for the opening of plateaus at different magnetization fractions, either for quantum S = 1/2 spins [68] or classical spins [69].…”

Lattice distortions in a sawtooth chain with Heisenberg and Ising bonds

“…It was also demonstrated than spin-lattice coupling in zigzag ladder gives rise to a novel type on magnetic excitations carrying fractional spin 3 . In twodimensional both classical and quantum spin models with spin-lattice coupling the enhancement of magnetization plateau stabilization as well as appearance of new ordered phases due to biquadratic interaction have been also reported for the J 1 − J 2 − J 3 -model 5 as well as for ShastrySutherland lattice 6 and pyrochlore antiferromagnet 1 . In this paper we consider an exactly solvable onedimensional spin model with Ising and Heisenberg bonds and spin-lattice interaction between the spins connectedhighly frustrated lattices.…”

“…Magnetic lattices of few class of materials, such as delafossite YCuO 2. 5 13,14 and olivines with structure ZnL 2 S 4 (L=Er,Tm,Yb) 15 have been found to be of sawtooth chain type. In addition to that, recently much attention has been paid to the problem of localized magnon states or dispersionless excitation bands, which have been found in various frustrated spin and electron systems, particularly, in the Heisenberg and Hubbard models on sawtooth chain [16][17][18][19][20][21][22] .…”

“…The lift of the ground state degeneracy in frustrated magnets and magnetization plateaus stabilization mechanisms have been investigated intensively in various lattice spin systems with spin-lattice coupling [1][2][3][4][5][6] . The concept of adiabatic phonos 7 yielding the effective spin Hamiltonian with additional biquadratic interaction is one of the main approximations using to gain inside into the properties of strongly correlated spin systems, interacting with lattice vibrations.…”