Abstract
The demagnetizing factor has an important effect on the physics of ferromagnets. For cuboidal samples it depends on susceptibility and the historic problem of determining this function continues to generate theoretical and experimental challenges. To test a recent theory, we measure the magnetic susceptibility of the Ising dipolar ferromagnet LiHoF$_4$, using samples of varying aspect ratio, and we reconsider the demagnetizing transformation necessary to obtain the intrinsic material susceptibility. Our experimental results confirm that the microscopic details of the material significantly affect the transformation, as predicted. In particular, we find that the uniaxial Ising spins require a demagnetizing transformation that differs from the one needed for Heisenberg spins and that use of the wrong demagnetizing transformation would result in unacceptably large errors in the measured physical properties of the system. Our results further shed light on the origin of the mysterious `flat' susceptibility of ordered ferromagnets by demonstrating that the intrinsic susceptibility of the ordered ferromagnetic phase is infinite, regardless of sample shape.
Highlights
The demagnetizing energy of a magnetized sample presents several intriguing aspects
We present a detailed study of the role of spin symmetry in determining the demagnetizing factor of cuboids, focusing, as a model example, on the Ising dipolar ferromagnet LiHoF4
The crucial aspect of LiHoF4 for this study is its uniaxial Ising symmetry, which distinguishes it from the isotropic, multiaxial Ising spin ice compound Dy2Ti2O7 used in our previous study [3]
Summary
The demagnetizing energy of a magnetized sample presents several intriguing aspects. It plays a crucial role in the analysis of magnetic susceptibility [1,2], realizes a laboratory example of long-range interactions [3], and even mediates some exotic physics, for example, the complex nonlinear response and pattern formation in the intermediate state of type-I superconductors [4].
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