Microscopic fluctuations in a material at thermal equilibrium can be as important as static properties to understanding and controlling its properties, so measuring them over a wide range of time scales has been of growing interest among materials researchers. A collaboration headed by Joshua Turner of the SLAC National Accelerator Laboratory and Sujoy Roy of the Lawrence Berkeley National Laboratory has recently reported a major advance toward this goal in Physical Review Letters. The group used SLAC’s x-ray free-electron laser to conduct x-ray photon correlation spectroscopy (XPCS) measurements of spontaneous magnetic fluctuations in iron/gadolinium multilayers at nanosecond time scales. Previously, XPCS had been limited to microsecond or longer time scales.

“This paper is a significant step forward in applying XPCS to investigate a wide range of complex dynamics in thermodynamic systems from liquids to strongly correlated electronic and magnetic materials,” says Karl Ludwig of Boston University, who was not part of the collaboration.

In XPCS, researchers measure how the material scatters coherent x-rays. In disordered materials, for example, the scattered x-rays form a speckle pattern. The time dependence of the speckle pattern yields information about the dynamics of the disorder. In particular, if the disorder is undergoing random thermal fluctuations, then it reveals details about the temporal behavior of these fluctuations. According to Turner, theorists can calculate fundamental quantities such as the dynamic susceptibility from a complete set of measurements over a range of scattering vectors and times, leading to models for material properties and behavior. “XPCS will now not only be widely applicable but also able to connect with theory, so we are excited about the future,” he says about the advance into the nanosecond and faster range.

The iron/gadolinium system chosen for the experiment hosts magnetic domains called skyrmions, which can be produced in a non-centrosymmetric bulk or in a planar ferromagnetic material by means of an external magnetic field. In a planar material with the spins normal to the plane (perpendicular magnetic anisotropy), they can be visualized as spiral vortices in which the spin orientation at the circumference matches that of the ferromagnetic matrix but on moving inward gradually rotates until at the center, it has reversed. Skyrmions have been of interest both for the fundamental physics involved in their formation, stability, and motion and for their possible future application in low-power, high-capacity computer memories such as racetrack memories in which a bit of information would correspond to the presence or absence of a skyrmion at the read head.

The experiment was the happy confluence of several factors that united groups from SLAC, Berkeley Lab, and the University of California at San Diego (UCSD) into the collaborative effort. For starters, Eric Fullerton’s group at UCSD had been studying ways to generate stable skyrmions at room temperature, a requirement for useful applications, when he was asked to synthesize skyrmion-containing samples suitable for soft x-ray scattering measurements by Roy and others at Berkeley Lab. The result, recounts Fullerton, was the amorphous iron/gadolinium multilayer comprising 100 repetitions of alternating iron (0.34 nm) and gadolinium (0.4 nm), in which the many layers served to magnify the scattered signal. According to Berkeley Lab’s Roy, the x-ray scattering and companion transmission electron microscopy imaging demonstrated the existence of skyrmions around 100 nm in diameter arrayed in a hexagonal lattice. With no magnetic field, the iron/gadolinium multilayer exhibited a stripe structure in which there were alternating ferromagnetic regions of out-of-plane polarizations. With a perpendicular applied magnetic field between about 150 mT and 250 mT, skyrmions appeared in the ferromagnetic matrix.

Because of its much higher coherent flux crammed into ultrashort femtosecond pulses, an x-ray free-electron laser (X-FEL) like SLAC’s Linac Coherent Light Source (LCLS) would be a natural tool for studying rapid fluctuations in the iron/gadolinium sample through high-speed XPCS measurements, but X-FELs typically have uniform pulse spacing so there is no way to measure the time evolution of a speckle pattern by recording patterns as a function of delay time. Dividing a pulse into two and controllably delaying the interval between their arrivals at the sample with optics had been considered for some time but this has technical difficulties. As it happened, SLAC accelerator scientists had developed a two-pulse (two-bucket) mode of operation by using separate lasers to excite from a photocathode, pairs of electron pulses that became the sources for two X-FEL pulses with controllable intervals between them. When Turner with the knowledge of the source developments and Roy with the pre-characterized UCSD sample connected, the collaboration was completed.

Lead author Matthew Seaberg of SLAC described hurdles that had to be surmounted before the experiment could begin. First, with two pulses from separate sources there was no guarantee they would have the same intensity, so pulses had to be measured and only pairs with equal intensity selected. Second, an intense x-ray beam would either heat or damage the iron/gadolinium multilayer sample, thereby disturbing the thermal equilibrium requirement. But after reducing the flux on the sample, the scattered signal was so small that the group had to resort to counting individual photons in each pixel of the speckle pattern. The group then determined the sum of the scattered signal from each pixel due to the two pulses as a function of delay time and reconstructed the change in the speckle pattern from these measurements. At short intervals, there would be little time for fluctuations to act and change the speckle pattern, so the sum would be at a maximum, whereas at long intervals, the speckle pattern would shift and the sum would decrease. A time-dependent contrast function for the speckle pattern computed using a photon statistical method was the final result.

Because researchers want to measure skyrmion fluctuations throughout the magnetic-field range where they exist, measurements were made at room temperature in two magnetic fields, 210 mT and 200 mT. At the higher field, the group determined a decay time of 4 ns, whereas at the lower one the decay time dropped precipitously to 300 ps, possibly reflecting the influence of the stripe phase from which the skyrmions emerge. As for what it is that fluctuates, the group cited spin fluctuations, random motion of the skyrmions within the lattice, and lateral domain wall changes as possibilities. More experiments will be necessary to explore skyrmion fluctuations in detail.

Read the article in Physical Review Letters.