Quantum Heisenberg antiferromagnets in a uniform magnetic field: Nonanalytic magnetic field dependence of the magnon spectrum

Abstract

We re-examine the 1/S-correction to the self-energy of the gapless magnon of a D-dimensional quantum Heisenberg antiferromagnet in a uniform magnetic field h using a hybrid approach between 1/S-expansion and non-linear sigma model, where the Holstein-Primakoff bosons are expressed in terms of Hermitian field operators representing the uniform and the staggered components of the spin-operators [N. Hasselmann and P. Kopietz, Europhys. Lett. 74, 1067 (2006)]. By integrating over the field associated with the uniform spin-fluctuations we obtain the effective action for the staggered spin-fluctuations on the lattice, which contains fluctuations on all length scales and does not have the cutoff ambiguities of the non-linear sigma model. We show that in dimensions D ≤ 3 the magnetic field dependence of the spin-wave velocityc−(h) is non-analytic in h 2 , withc−(h)−c−(0) ∝ h 2 ln |h| in D = 3, andc−(h) −c−(0) ∝ |h| in D = 2. The frequency dependent magnon self-energy is found to exhibit an even more singular magnetic field dependence, implying a strong momentum dependence of the quasi-particle residue of the gapless magnon. We also discuss the problem of spontaneous magnon decay and show that in D > 1 dimensions the damping of magnons with momentum k is proportional to |k| 2D−1 if spontaneous magnon decay is kinematically allowed.

Dynamical structure factor of quasi-two-dimensional antiferromagnet in high fields

“…17,18 Generally, non-collinearity leads to an enhanced interaction among spin excitations 19,20 and results in stark differences from conventional theory for magnons in the highfield regime. [21][22][23][24] In increasing field, spins gradually cant toward the field direction until they reach the saturation field, H s , where quantum fluctuations are fully suppressed and ferromagnetic alignment achieved. For fields above a certain threshold value, H * , but below saturation, coupling of the transverse and longitudinal spin fluctuations provides a channel for decays, through cubic terms in the spin-wave expansion.…”

Field-induced decay dynamics in square-lattice antiferromagnets

“…Other theoretical aspects of the behavior of the quantum square-lattice antiferromagnet (SAFM) in applied field have also been addressed. [19][20][21] In this paper, we extend previous work of two of us 16 and provide a comprehensive theoretical investigation of the dynamics of the nearest-neighbor Heisenberg SAFM including detailed calculation of the 1/S correction to the energy spectrum in external field, kinematic analysis of the field-induced two-magnon decays, and self-consistent treatment of magnon decay rates for systems with S ≥ 1. …”

“…Although, our focus in Sec. IV is on the large-S model, we now present numerical data for the spectrum renormalization (19) in the S = 1/2 case. Similar results for the other values of spin can be obtained by rescaling quantum corrections in Figs.…”

“…Their decay rate has a universal form Γ k ∝ k 2D−1 , in agreement with previous results for D = 2 and 3. 19,26 A more detailed discussion of the decay rate of low-energy magnons in the SAFM is provided in Appendix A.…”

Spectral Function and Quasiparticle Damping of Interacting Bosons in Two Dimensions

“…Because of the upward curvature of the dispersion, a momentum-and energyconserving decay of quasiparticles into pairs of quasiparticles is allowed. A second order perturbative analysis [21] shows that in D dimensions this damping at small momenta and for weak coupling has the form…”