We present the results of an optical method of quantitatively estimating the spin exchange interactions in hexagonal manganites RMnO3 (R=Tb, Dy, Ho, Er) epitaxial thin films. The two in-plane (a-b plane) spin exchange integrals J1 (intratrimer Mn-Mn interaction) and J2 (intertrimer Mn-Mn interaction) are deduced from the magnon scattering peak wavenumbers. We found that J2 decreases systematically when the R ionic radius increases, while J1 is nearly independent of R ionic radius, contrary to the expectation in single crystals. We show that the R dependence of J1 could be understood in terms of the stress in the thin films. Our result indicates that the stress has stronger effect on the atomic displacement of the intratrimer Mn-Mn distance than the intertrimer Mn-Mn distance.
Bibliographical noteFunding Information:
We thank the National Research Foundation of Korea Grant Nos. 2009-0063320 and 2010-0022857. The work at Seoul National University was supported by the National Research Foundation of Korea Grant Nos. 2009-0080567 and 2010-0020416.