Here, we employ thermoreflectance thermal imaging to directly visualise the 2D temperature field produced by localised heat sources on InGaAs with characteristic widths down to 100 nm. Experimental observations are commonly interpreted through a reduction of effective thermal conductivity, even though most measurements only probe a single aggregate thermal metric. Heat removal from small sources is well established to be severely impeded compared to diffusive predictions due to the ballistic nature of the dominant heat carriers. Understanding nanoscale thermal transport is of substantial importance for designing contemporary semiconductor technologies. This experiment demonstrates the ability to probe bulk properties of materials and paves the way for ultrafast coherent four-wave-mixing techniques using X-ray probes and involving nanoscale TG spatial periods. In bismuth germanate (BGO), the non-resonant TG excitation generates coherent optical phonons detected as a function of time by diffraction of an optical probe pulse. Here, we demonstrate TG excitation in the hard X-ray range at 7.1 keV. X-rays offer multiple advantages for TG: their large penetration depth allows probing the bulk properties of materials, their element specificity can address core excited states, and their short wavelengths create excitation gratings with unprecedented momentum transfer and spatial resolution. The newly developed coherent X-ray free-electron laser sources allow its extension to the X-ray regime. Optical-domain transient grating (TG) spectroscopy is a versatile background-free four-wave-mixing technique that is used to probe vibrational, magnetic and electronic degrees of freedom in the time domain¹. Error bars are described in “Methods” section. The inset shows the amplitude of the Fourier transform of the TG profile at 0.4 ns. The points show the normalized change in the amplitude of the first- (circles), second- (downward pointing triangles), and third- (upward pointing triangles) order Fourier components of the spatial profiles in (c). The curve for the minimum TG excitation has been multiplied by a factor of 5. (d) Non-exponential decay in X-ray diffraction intensity at various TG positions. The shading indicates the approximate locations of regions in which the FM phase occurred. (c) Diffracted intensity as a function of TG position and delay time with 1.4 mJ/cm² peak absorbed fluence. Dotted lines are separate linear fits to the AFM and FM peak centers. (b) Lattice constant and FM phase fraction as a function of absorbed laser fluence. The insets are diagrams of the cubic FeRh lattice showing Fe (red) and Rh (blue) atoms, and the directions of the magnetic moments (arrows). The vertical arrow indicates the value of θ for the measurements shown in (c,d). Dashed lines fit the contributions of the AFM (green) and FM (blue) phases to the high-fluence curve (red dashed line total). At higher fluence (triangles) there is a mixture of AFM and FM phases. The peak at low excitation fluences (circles) is in the AFM phase (solid green line fit). (a) 001 Bragg peak measured at the TG peak at t = 0. TGXD successfully characterizes mesoscopic energy transport in functional materials without relying on a specific transport model. The focused X-ray probe provides spatial resolution within the engineered optical excitation profile, resolving the spatiotemporal flow of heat through FeRh locally heated above the phase transition temperature. The strain profile of the structural grating in FeRh, in comparison, deviates from the sinusoidal excitation and exhibits both higher-order spatial frequencies and a location-dependent relaxation. In BiFeO3, structural relaxation is location independent, and the strain persists on the order of microseconds, consistent with the optical excitation of long-lived charge carriers. We demonstrate TGXD using two thin-film samples: epitaxial BiFeO3, which exhibits a photoinduced strain (structural grating) with an amplitude proportional to the optical fluence, and FeRh, which undergoes a magnetostructural phase transformation. This method adds spatial resolution and direct structural sensitivity to the established utility of a sinusoidal transient-grating excitation. Here, we introduce an optical transient grating pump and focused X-ray diffraction probe technique (TGXD) to examine the structural evolution of materials excited by modulated light with a precisely controlled spatial profile. A fundamental understanding of materials’ structural dynamics, with fine spatial and temporal control, underpins future developments in electronic and quantum materials.
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