Complementing volume‐conserving Joule magnetostriction (JM), the non‐Joulian magnetostriction (NJM) phenomenon has recently been discovered whose hallmark is change in volume of the crystals in magnetic fields. This article reviews the unique set of non‐Joulian properties that are so non‐conforming relative to conventional magnets that they merit the designation of a distinctly new class of (functional) magnets. This review distils key aspects of non‐Joulian magneto‐elasticity and magnetism, including the sign of volume change (contracting or expanding); the orientation dependence of volume change that is key to realizing large volume changes (remarkably, this volume‐anisotropy coexists with a seemingly isotropic magnetization response for all crystal axes); and a digital coercivity landscape unlike that seen in conventional magnets. NJM lay undiscovered for nearly two decades because prior literature assumed, without experimental foundation, that iron‐based alloys obeyed volume‐conserving JM. Measurements now show that volume change is inherent across wide composition ranges, occurring in both quenched, metastable, and inexorably slow‐cooled, equilibrated crystals. While not essential, quenching promotes long‐range periodicity of magneto‐elastic gradients with enhanced NJM. Another objective is to “frame” Joulian‐to‐non‐Joulian behavior within a single framework of magnetically responsive, wave‐like elastic medium in which approach to homogeneity yields the limiting case of JM; in fact, gradient magnet‐elasticity is indispensable to describing non‐Joulian magnetism. A consequential auxiliary finding is the large differences in intrinsic magneto‐elastic constants for seemingly equivalent crystal axes, consistent with gradient magneto‐elasticity. Consequentially, a sizeable literature that previously characterized these crystals using volume‐conserving assumption and framework of phenomenological magnetostriction theory of homogeneous cubic crystals is rendered moot, and unreliable for high‐fidelity applications.

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The cover image shows the microscopic magnetic structure of newly discovered magnets called ‘non‐Joulian magnets’ as presented by Harsh Deep Chopra and co‐workers in their Feature Article no. http://doi.wiley.com/10.1002/pssb.201800214. This remarkable cellular magnetic structure, the ability to balloon in magnetic fields to change volume, and non‐noticeable energy losses, all originate from imperceptible variations in the atomic structure of non‐Joulian magnets. Such properties cannot exist in conventional magnets, hence, the designation as a new class of functional magnets.