Iron-gallium alloy (galfenol) is a body centered cubic (BCC) magnetostrictive alloy that, like many other BCC metals, is auxetic in the h110i{100} directions. For compositions of 12-33 at.% gallium, Poisson ratio (n) values as low as À0.7 are observed along these directions in response to a uniaxial elastic force (tensile tests, resonant ultrasound spectroscopy, etc.). In 2014, Raghunath and Flatau first reported that galfenol also exhibits positive strain in both these directions when the uniaxial force applied along the h110i{100} directions is provided solely by a magnetic field, i.e., with no external mechanical/elastic force or stress being applied to the alloy [Raghunath and Flatau, IEEE Trans. Magn. 50(11), 1-4 (2014)]. The observed response is a result of the intrinsic, atomic-scale, bi-directionally coupled magnetoelastic properties of these alloys. In this paper, we advance the understanding of the intrinsic atomic-scale magnetoelastic coupling of the alloy that leads to the observed magnetoelastic auxetic-like behavior by presenting simulations developed based on density functional theory, which we show match the experimental findings and energy-based simulations. The elastic anisotropy and the electronic mechanisms that lead to magnetoelastic auxetic-like behavior in galfenol are discussed.

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Galfenol (Fe x Ga100À x ), a magnetostrictive alloy (3/2k 110-400 ppm) of Iron and Gallium exhibits an in-plane auxetic response in the h110i crystallographic direction. Negative Poisson's ratios have been observed in response to application of stress fields, where values of as low as À0.7 have been reported for compositions of greater than roughly 20% Ga [Zhang et al., J. Appl. Phys. 108(2), 023513 (2010)] and in response to application of magnetic fields, where values of as low as À2.5 have been reported to be expected for compositions of less than roughly 20% Ga [G. Raghunath and A. B. Flatau, IEEE Trans. Magn. (in press)]. Several models have been proposed to understand these two distinct phenomena. Galfenol samples with less than 20% Ga also exhibit an unusual response to an increasing magnetic field applied along the h110i direction. The longitudinal strain which increases initially with applied field experiences a dip (until $10 mT) before increasing again to reach saturation. The transverse strain increases and reaches a maximum value (at the same field of $10 mT) and then drops from the maximum by 5%-10% as magnetic saturation is approached [G. Raghunath and A. B. Flatau, IEEE Trans. Magn. (in press)].This work deals with discussing the evolution of magnetic domains in a 16 at. % Ga single crystal Galfenol sample when subjected to magnetic fields in the h110i direction in the (100) plane. The magnetic domains on the surface of mechanically polished Galfenol samples were imaged using Magneto-Optic Kerr Effect microscopy. Simultaneously, the strains along the longitudinal and transverse h110i directions were recorded using a bi-directional strain gauge rosette mounted on the unpolished bottom surface of the planar samples. The energy from the applied magnetic field is expected to grow the h110i oriented domains at the expense of domains oriented along all other directions. But since the plane has an easy h100i axis, we expect the domains to orient along the easy direction before saturating along the applied magnetic field direction. A correlation between the images recorded and the strains observed will be used to understand this shift of domains and bump in strain at low fields. V C 2015 AIP Publishing LLC. [http://dx.