Nonlinear phononics in rare-earth orthoferrites

Harnessing nonlinear interactions between phonon modes in condensed matter presents a powerful avenue for tailoring material properties for innovative applications in future information devices. Here we report a study of nonlinear coupling between infrared (IR) active and Raman-active phonon modes in rare-earth orthoferrites <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:mi>ErFe</a:mi> <a:msub> <a:mi mathvariant="normal">O</a:mi> <a:mn>3</a:mn> </a:msub> </a:mrow> <a:mo>,</a:mo> <a:mo> </a:mo> <a:mrow> <a:mi>TmFe</a:mi> <a:msub> <a:mi mathvariant="normal">O</a:mi> <a:mn>3</a:mn> </a:msub> </a:mrow> </a:math> , and <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:mrow> <d:mi>TbFe</d:mi> <d:msub> <d:mi mathvariant="normal">O</d:mi> <d:mn>3</d:mn> </d:msub> </d:mrow> </d:math> . To reveal the nonlinear phonon interactions, we resonantly excite IR-active phonons with an ultrashort midinfrared pulse, with its central wavelength tunable in the 3–18 µm (16.5–100 THz) range, and trace the phonon modes in the time domain after the excitation. We identify two main coupling mechanisms: quadratic linear and trilinear, which stand for a nonlinear coupling of the Raman-active phonon with either one or two distinct IR-active modes, respectively. The origin of driving each Raman-active phonon mode is identified and analyzed with polarization-dependent pump-probe spectroscopy. Our results show a strong dependence of the trilinear coupling mechanism on the crystallographic orientation of the sample, thus revealing that only specific phonon modes can exhibit this coupling.