Field-induced decay dynamics in square-lattice antiferromagnets

Dynamical properties of the square-lattice Heisenberg antiferromagnet in applied magnetic field are studied for arbitrary value $S$ of the spin. Above the threshold field for two-particle decays, the standard spin-wave theory yields singular corrections to the excitation spectrum with logarithmic divergences for certain momenta. We develop a self-consistent approximation applicable for $S\ge 1$, which avoids such singularities and provides regularized magnon decay rates. Results for the dynamical structure factor obtained in this approach are presented for $S=1$ and $S=5/2$.

Figure 1

(Color online) Canted spin structure of the square-lattice Heisenberg antiferromagnet in external magnetic field.

Figure 2

(Color online) The lowest-order normal self-energies generated by the decay (left) and by the source (right) vertex.

Figure 3

(Color online) Magnon energy of the spin-1/2 square-lattice antiferromagnet below the decay threshold. Dashed lines show the harmonic spin-wave energy ${ϵ}_{\mathbf{k}}$ and solid lines represent the spectrum with the lowest-order quantum correction. The inset in (a) defines the chosen path in the Brillouin zone.

Figure 4

(Color online) Magnon energy and decay rate of the spin-1/2 square-lattice antiferromagnet above the decay threshold. Upper panels: dashed lines show the harmonic spin-wave energy ${ϵ}_{\mathbf{k}}$ and solid lines represent the spectrum with the lowest-order quantum correction ${\overline{ϵ}}_{\mathbf{k}}$. Lower panels: the decay rate ${\Gamma }_{\mathbf{k}}$ in the Born approximation.

Figure 5

(Color online) Field evolution of the decay region of the SAFM in the Born approximation. Numbers correspond to values of $H/H_s$.

Figure 6

(Color online) Decay region and associated singularities for $H=0.9H_s$. Line’s type represents the decay channel: solid is for a pair of magnons with equal momenta, dashed is for a pair of magnons with different momenta, and dotted is for emission of an acoustic magnon. Line’s color indicates the type of singularity in the continuum: blue (thick solid and dotted lines) is for the minimum and red (thin solid and dashed lines) is for the saddle point.

Figure 7

(Color online) Magnon decay rate ${\Gamma }_{\mathbf{k}}$ at $H=0.9H_s$ calculated in the Born approximation (dashed line) and in the iSCBA scheme for $S=1$ (thin solid line, red) and for $S=5/2$ (bold solid line, blue). Dots in $\Gamma \text{M}$ panel are $-\text{Im}{\Sigma }_{\mathbf{k}}\left({\overline{ϵ}}_{\mathbf{k}}\right)$ for $S=1/2$ from Ref. 16.

Figure 8

(Color online) Intensity maps of the magnon decay rate ${\Gamma }_{\mathbf{k}}$ calculated within the iSCBA for several values of external magnetic field and for the two values of the spin: $S=1$ (upper panels) and $S=5/2$ (lower panels).

Figure 9

(Color online) Transverse part of the dynamical structure factor (gray scale) computed using the iSCBA for $S=1$ and for the two values of external magnetic field. Dashed lines (blue) enclose the region ${ϵ}_{\mathbf{k}}\pm {\Gamma }_{\mathbf{k}}$ corresponding to the full width at half maximum of the corresponding quasiparticle peaks.

Figure 10

(Color online) Same as Fig. 9 for $S=5/2$.

Figure 11

(Color online) Phase diagram of the $XXZ$ model in applied field as a function of anisotropy parameter $\epsilon$. The field range where spontaneous magnon decays are allowed is shown in gray.