Resonances in a dilute gas of magnons and metamagnetism of isotropic frustrated ferromagnetic spin chains

We show that spin-$S$ chains with SU(2)-symmetric, ferromagnetic nearest-neighbor and frustrating antiferromagnetic next-nearest-neighbor exchange interactions exhibit metamagnetic behavior under the influence of an external magnetic field for small $S$, in the form of a first-order transition to the fully polarized state. The corresponding magnetization jump increases gradually starting from an $S$-dependent critical value of exchange couplings and takes a maximum in the vicinity of a ferromagnetic Lifshitz point. The metamagnetism results from resonances in the dilute magnon gas caused by an interplay between quantum fluctuations and frustration.

Figure 1

1D scattering length $a_S/a$ ($a$ is the lattice spacing) for $S=1/2,1,3/2$ (solid, dashed, dot-dashed lines, respectively).

Figure 2

Effective bare intraspecies interaction $g_0\left(S\right)$, for $S=3$ (solid line), representative of the generic behavior for $S<S_{\mathrm{cr}}$, $S=10$ (dashed curve), representative of $S>S_{\mathrm{cr}}$ [dot-dashed line: $g_0(S=\infty )$]. Inset: $g_0$ for $S=1$ and $3/2$.

Figure 3

(a) Magnetization curves $M\left(h\right)$ for $S=1$ at $J=-2.5,-3,-3.5$. (b) $M\left(h\right)$ for $S=1$, $J=-1.$ (c) $M\left(h\right)$ for $S=3/2$ at $J=-3.5$ (all for $L=128$).

Figure 4

Magnetization profiles for $S=1$, $L=128$ at $J=-1$ (no jump, dashed lines) and $J=-3$ (jump at $S^z=97$) for $S^z=80,90,110,120$ (top to bottom).

Figure 5

DMRG results for the von-Neumann entropy $S_{vN}\left(l\right)$ in the gapless phase $h_c<h<h_{\mathrm{sat}}$ of the $S=1$ system: (a) $J=-1$, $M=1/2$, (b) $J=-2$, $M=1/2$, and (c) $J=-3$, $M=5/16$ (symbols). The lines are fits to Eq. (25), resulting in $c=1.0\pm 0.1$ in all cases (we exclude $S_{vN}\left(l\right)$ for $l<10$ and $l>54$ from the fit). In this figure, we display results for periodic boundary conditions and $L=64$ sites.

Figure 6

Phase diagram of Eq. (1) for $S=1$ (circles are the saturation field $h_{\mathrm{sat}}$, squares are the spin gap $h_c$). Inset: height $\Delta M_{\mathrm{jump}}$ of the metamagnetic jump vs $J$. The comparison of $L=64$ (open symbols) and $L=128$ (solid symbols) as well as finite-size scaling (not shown here) supports that both $\Delta M_{\mathrm{jump}}$ and $h_c$ are finite in extended regions of $J$.

Figure 7

Magnetization curves $M\left(h\right)$ for $S=1$ (a) $J=-3.5$ and (b) $J=-1$ ($L=48$), calculated with DMRG on systems with periodic boundary conditions. In panel (a), we clearly see the metamagnetic jump of height $\Delta M_{\mathrm{jump}}$, and in panel (b), the Haldane gap that defines $h_c$ shows up as a zero-field magnetization plateau.

Figure 8

Phase diagram of the frustrated ferromagnetic $S=1$ chain, comparing DMRG results from systems with OBC (open symbols) to results from systems with PBC (solid symbols). $L=64$ in all cases. Lines are guides to the eye.