EXCITON SCATTERING ON SPIN WAVES IN QUASI-ONE-DIMENSIONAL ANTIFERROMAGNET

Abstract

Exciton absorption bandwidths have been measured in quasi-onedimensional antiferromagnet CsMnC13.2 Hz0 and three-dimensional MnF2 in magnetic fields oriented along crystal easy axes. In one-dimensional antiferromagnets exciton-magnon interaction is shown to result in considerable broadening of exciton bands in the vicinity of the critical field of the spin-flop transition. In one-dimensional (Id) antiferromagnetic (AFM) dielectrics the spin wave dispersion has strong anisotropy: at the wave vector k oriented along the strong exchange interaction direction, the magnon energy changes from EO (a slit in the spectrum, i.e. the spin wave energy in the Brillouin zone center) to E, , (the maximum energy at the zone boundary); for transverse directions the energy dispersion is too small. It leads to additional peculiarities in the energy distribution of density of magnon states, p (E) : besides the peak near the band Yap , p (srnax) , there appears the peak near its bottom , p (E) . In the present work the exciton absorption bandwidth has been studied in Id AFM CsMnCl3.2 H20. It is shown that its behavior near the orientational phase transition induced by an external magnetic field (the spin-flop transition, H,=1.8 T at T = 1:96 K) is due to exciton scattering on spin waves. In this case the high density of magnon states near the band bottom in Id AFM plays predominant role. For comparison similar studies of the exciton bandwidth were performed in threedimensional (3d) AFM MnF2. In order to study experimentally the broadening mechanism of light absorption bands, the temperature dependences of their half-widths are generally investigated [I]. However, for such an experiment, it is difficult to distinguish contributions to the bandwidth from both the interaction of excitons with magnons and their interaction with acoustic phonons. In the present work we fixed temperature (as low as possible, in order to diminish the phonon effect of the bandwidth) and varied the number of thermally excited magnons, thereby decreasing a slit in the spinwave spectrum by an external field H oriented along the crystal easy axes. pendences of band half-widths in CsMnCl3.2 Hz0 (0) and MnFz (a) on the magnetic field strength oriented along the easy axes of these AFM crystals. In the case of manganese fluoride the exciton band half-width increases by about 10 % in field H Hc as compared with the initial value. For CsMnCl3.2 Hz0 the band broadens approximately by factor of 3.5 near the Hc field,. In the spin-flop phase (H > Hc) the exciton band half-width in CsMnCl3.2 Hz0 takes again its initial value in the absence of an applied field. Objects of investigation were the exciton band of the Fig. 1. Relative broadening of exciton bands in 6 ~ 1 g ( 6 ~ ) + 4 ~ 2 g ( 4 ~ ) transition in CsMnCls.2 HzO ~ s ~ n ~ 1 3 . 2 HzO (o) and MnF2 (;) due to exciton scattering on spin waves versus magnetic field strength; H // b, crystal in field H // b at 1.96 K, and the exciton band = for CsMnC13.2 HzO; H // C4, = 14 of the 6At (6S) -j 4Tlg (4p) transition in MnF2 in for MnF2. Solid curves are calculated for a) Id AFM; field H // C4 at T = 14 K. Figure 1 gives the deb) 2d AFM. Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19888681 C8 1482 JOURNAL DE PHYSIQUE The exciton-magnon interaction operator responsible for the exciton scattering on magnons can be represented in the form J S z H e r n , p = ~ C x k 1 ... k3 x [@I, (k2, kg) B: (ki k2 + k3) Bp (ki) b'(k2) 6 (k3) +62p (k2, k3) B: (ki + k2 k3) Bp (ki) b (k2) b+ (k3)] (1) Here J is the exchange integral along the a-direction of strong interaction, z = 2 the number of nearest neighbours along the c B: (k) and B, (k) exciton creation and annihilation operators, respectively, in the p band, and b+ (k) and b (k) those of magnons of the low frequency branch; N the number of crystal lattice sites, S the spin of the ground state. The interaction amplitudes a;, are of the form @ll (k2r k3) = ( ~ V j c ~ U k ~ ~ k ~ + eU 2 Uk,; @12 (k2r k3) = -pVk2 Uk3x3 + pUk2 Uk3~k2-k3 ; (k2~ k3) = -pVk2 Uk3x2 + pVk2 Vk3Yk2 -k3 ; @22 (k2, k3) = -pVk2 Uk3x3 + eVk2 Vk3;