We report neutron diffuse scattering measurements on highly magnetostrictive Fe 1Àx Ga x alloys (0:14 < x < 0:20) with different thermal treatments. This diffuse scattering scales with magnetostriction and exhibits asymmetric peaks at the (100) and (300) reciprocal lattice positions that are consistent with the coexistence of short-range ordered, coherent nanometer-scale precipitates embedded in a long-range ordered, body-centered cubic matrix. A large peak splitting is observed at (300) for x ¼ 0:19, which indicates that the nanoprecipitates are not cubic and have a large elastic strain. This implies a structural origin for the enhanced magnetostriction. DOI: 10.1103/PhysRevLett.102.127201 PACS numbers: 75.80.+q, 61.05.fg, 64.70.Nd, 75.50.Bb Mechanically strong and malleable Galfenol alloys (Fe 1Àx Ga x ) exhibit enhanced and extremely large magnetostriction coefficients along [100] of up to 3 100 =2 ¼ 400 ppm at low saturation fields [1,2]. The addition of Ga into the body-centered cubic (bcc) -Fe phase is known to produce a diversity of crystal structures including chemically disordered bcc A2 (Fe), ordered bcc DO 3 (Fe 3 Ga), ordered bcc B 2 (FeGa), and face-centered cubic L1 2 (Fe 3 Ga) phases [3,4]. Previous studies of Fe 1Àx Ga x alloys cooled (postgrowth) at 10 C= min have shown the presence of two anomalous peaks in the magnetostriction. The first peak at x % 0:19 has been attributed to an increase in the magnetoelastic coupling, resulting from the formation of short-range ordered (SRO) Ga pairs along the [100] axis of the A2 structure [5], and the second at x % 0:27 to a softening of the shear modulus c 0 ¼ ðc 11 -c 12 Þ=2 [6,7]. Of special note is the fact that both 3 100 =2 and the presence of a two-phase region (A2 þ DO 3 ) depend sensitively on thermal history; this suggests that the enhanced magnetostriction is due to an underlying heterogeneity rather than a conventional homogeneous ferromagnetic phase.A structurally heterogeneous model [8] has been proposed to explain the enhanced magnetostriction and elastic softening for such Fe 1Àx Ga x alloys. This model assumes that the heat treatment produces a structurally and chemically heterogeneous state consisting of coarseningresistant, nanometer-scale DO 3 precipitates within an A2 matrix. Theoretically, heterogeneity has been predicted to result from the following sequence of transformations: (i) bcc ! bcc 0 þ DO 3 decomposition, followed by (ii) a diffusionless Bain strain that transforms the DO 3 nanoprecipitates into a face-centered tetragonal (fct) structure. Recently, nanometer-scale (<2 nm) DO 3 precipitates [9] have been identified in an A2 matrix of Fe 0:81 Ga 0:19 using high-resolution transmission electron microscopy (HRTEM), consistent with the theoretical prediction of step (i) in the transformational sequence. However, all prior structural investigations have shown that both the DO 3 and A2 phases are cubic. There have been no reports of lower-symmetry phases, as predicted by step (ii) in the transformational sequence. This is a ke...