All magnets elongate and contract anisotropically when placed in a magnetic field, an effect referred to as Joule magnetostriction1. The hallmark of Joulian magnetostriction is volume conservation2, which is a broader definition applicable to self-accommodation of ferromagnetic, ferroelectric or ferroelastic domains in all functional materials3,4,5,6,7,8,9,10. Here we report the discovery of ‘giant’ non-volume-conserving or non-Joulian magnetostriction (NJM). Whereas Joulian strain is caused by magnetization rotation, NJM is caused by facile (low-field) reorientation of magnetoelastically and magnetostatically autarkic (self-sufficient) rigid micro-‘cells’, which define the adaptive structure, the origin of which is proposed to be elastic gradients ultimately caused by charge/spin density waves11,12,13. The equilibrium adaptive cellular structure is responsible for long-sought non-dissipative (hysteresis-free), linearly reversible and isotropic magnetization curves along all directions within a single crystal. Recently discovered Fe-based high magnetostriction alloys14,15 with special thermal history are identified as the first members of this newly discovered magnetic class. The NJM paradigm provides consistent interpretations of seemingly confounding properties of Fe-based alloys, offers recipes to develop new highly magnetostrictive materials, and permits simultaneously large actuation in longitudinal and transverse directions without the need for stacked composites.
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The authors appreciate the donation of single crystals by T. A. Lograsso. We thank S. Fähler for discussions. We thank S. Z. Hua for discussions, input on experimental design and help with magnetic and temperature dependent measurements. We thank J. Steiner, T. Ren, E. Gande and J. N. Armstrong for help with vibrating sample magnetometry and magnetostriction measurements, and assistance in collation of some images, experiments and sample preparation. M.W. acknowledges support from the National Science Foundation DMR-Metals grant 1206397 and H.D.C. acknowledges support from the National Science Foundation DMR-Condensed Matter Physics grants 1541236 (previously 1309712) and 0964830.
The authors declare no competing financial interests.
Extended data figures and tables
The data displays the angular dependence of magnetostriction along various directions in an as-quenched Fe73.9–Ga26.1 single crystal.
Extended Data Figure 3 Degradation of NJM characteristics in Fe73.9–Ga26.1 single crystal when cooled slowly from 1,033 K to room temperature (furnace cooled).
In comparison to volume expansion in all directions when an alloy of this composition was rapidly quenched (Fig. 1a), furnace (slow) cooling cause transverse magnetostriction to become slightly contractile. However, unlike conventional ferromagnets, the sample still exhibits a net volume increase, that is, NJM.
Extended Data Figure 4 Collage showing magnetic domains across the entire 5-mm-diameter circular single crystal sample of Fe73.9–Ga26.1, which was rapidly quenched from 1,033 K to room temperature.
The collage was prepared after polishing and etching the sample but before applying any magnetic field. Notice the existence of micromagnetic motifs along both  and  axes. Also notice the existence of APBs. The collage consists of high-resolution images and can thus be zoomed in for further analysis by the scientific community. Original magnification is ×5.
a, Demagnetized state of a thin circular plate. b, Demagnetized state of a thin ferromagnetic film, λ100 = 0. c, Angular distortion of the diagonals for λ100 < 0 and λ100 > 0. d, Stress-free rectangular demagnetized state through twinning.
Extended Data Figure 6 Zero-field micromagnetic patterns of as-quenched Fe73.9–Ga26.1 crystal after cycling in saturation magnetic field.
A, a–c, Low-magnification images. Original magnification is ×10. B, a–c, High-magnification images. The pattern’s periodicity and scale equals that shown in Fig. 3. Original magnification is ×20.
a, An apparently scratch-free Fe82.9–Ga17.1 single crystal after polishing but before etching. b, Subsequent etching in a 50:50 nitric acid and distilled water solution reveals numerous scratches.
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Chopra, H., Wuttig, M. Non-Joulian magnetostriction. Nature 521, 340–343 (2015). https://doi.org/10.1038/nature14459
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