Magnetization Plateaus Induced by a Coupling to the Lattice

We present a novel mechanism for the appearance of magnetization plateaus in quasi-one-dimensional quantum spin systems, which is induced by the coupling to the underlying lattice. We investigate in detail a simple model of a frustrated spin-$1/2$ Heisenberg chain coupled to adiabatic phonons under an external magnetic field, but the present mechanism is expected to be more general. Using field theoretic methods complemented by extensive density matrix renormalization group techniques, we show that magnetization plateaus at nontrivial rational values of the magnetization can be stabilized by the lattice coupling. We suggest that such a scenario could be relevant for some low dimensional frustrated spin-Peierls compounds.

Figure 1

$M(H)$ for the 36, 60, and 84 sites for $J_2=0.4$ and $\tilde{A}{\delta }_0=0.4$ in the case of fixed modulation and OBC. The inset shows the finite size scaling of the width of the different plateaus.

Figure 2

$M(H)$ for 36, 48, and 60 sites for $J_2=0.5$ and ${\tilde{A}}_1=0.8$ in the case of an adaptive modulation and PBC. The solid line is an extrapolation to the thermodynamical limit.

Figure 3

Region of stability of the $1/3$ and $1/2$ plateaus obtained from a finite size scaling of the critical fields as a function of $\frac{J_2}{J_1}$ in the interval $[0.5,0.7]$ and for $A_1=0.8$. Stability of the other plateau phases is not excluded.