First model-independent measurements of the hydrogen diffusivity D in lanthanum trihydrides LaH x ͑2.00 # x # 3.0͒ have been performed by PFG-NMR. At a fixed concentration x # 2.92, D͑T ͒ shows single Arrhenius behavior over wide temperature ranges. The activation enthalpy decreases with increasing x from 0.55 ͑x 2.00͒ to 0.17 eV ͑x 2.92͒, resulting in a strong increase in D. The formation of a hydrogen superstructure associated with the semiconductor-to-metal transition results in a strong reduction in D. It was also observed for the first time that in the stoichiometric limit D depends on the thermal history of the sample. 76.60.Lz Recent experiments demonstrating the switchable optical properties of yttrium, lanthanum, and other rare-earth hydride films have again focused interest on these unusual systems [1][2][3]. An important factor underlying the switching speed is the diffusivity of hydrogen in the hydride. But in spite of intensive investigations over the years [4], the mechanisms of hydrogen diffusion in these systems are not yet understood.Lanthanum forms nonstoichiometric homogeneous hydrides LaH x with the fluorite structure in the concentration range from x ഠ 1.9 to x 3.0. The hydrogen atoms occupy predominantly the tetrahedral ͑T ͒ interstitial sites at low concentrations, and with increasing concentration, the octahedral ͑O͒ sites are also filled.Nuclear magnetic resonance (NMR) offers unique capabilities to measure the diffusion on both macroscopic and microscopic scales [5,6]. The pulsed-field-gradient technique (PFG-NMR) permits model-independent measurement of the long-range diffusivity D. We report here the first PFG measurements of hydrogen diffusivity in lanthanum hydrides, LaH x ͑2.0 # x # 3.0͒, over a wide range of temperatures, 235 # T # 800 K, as well as the discovery of unusual hysteresis effects accompanying an order-disorder transition in stoichiometric LaH 3 .The six samples of the present work with 2.0 # x # 2.92 are those used in previous NMR studies [7-9]. They were prepared from the highest-purity Ames Laboratory lanthanum available, having a total magnetic rare-earth impurity content, determined by mass spectroscopy, below 4.5 ppm. The LaH 3 sample has a higher magnetic rare-earth impurity content of 25 ppm. The uncertainties in the hydrogen concentrations x are about 1% of the quoted values.The PFG measurements were performed by using the stimulated-echo sequence [10]. Typical operating parameters were gradient pulse length d 1 ms and diffusion time D 10 ms. Within D the hydrogen atoms diffuse over a distance of the order of 1 mm. The diffusivities were determined from the variation of the echo attenuation with the amplitude of the gradient pulses up to 25 Tm 21 .