Singular points in the magnetization curve of a polycrystalline ferromagnet

Abstract

The reversible magnetization curve M(H) of a polycrystalline ferromagnet has been investigated with the objective of examining the properties of the singularities located at H = −HA, the anisotropy field, along the hard direction. Using a simple model that approximates the system as a continuous assembly of noninteracting particles, we show that the singular point becomes apparent in the successive derivatives dnM/dHn plotted as functions of H. Indeed, differentiation accentuates more and more the singularity hidden in the magnetization curve, and the minimum order n* at which it can be detected is the order for which the function dn*M/dHn* has a discontinuity in the slope at the singular point. The general formula for the dependence of n* on the symmetry properties of the hard direction is given together with the analytical expression for the shape and amplitude of the singularity in the most important cases. The same sort of phenomenon is shown to be present in the reversible transverse susceptibility, and the general expression for nt* is also given. For all the symmetry cases, nt* turns out to be lower than n*. Experimental tests of the theory have been carried out for binary axes of both uniaxial and cubic materials—namely, BaFe12O19, Fe, and CoFe2O4. The singularity appears in d2M/dH2, as expected, and position and amplitude are in good agreement with the values predicted by theory. The suggestion is made that singular point detection (SPD) could be used as a new technique for measuring the anisotropy in polycrystalline samples.

Intrinsic Magnetic Properties of Ce2Fe14B Modified by Al, Ni, or Si

“…Saturation magnetizations (M S ) and anisotropy fields (H A ) were measured using a Quantum Design physical property measurement system (PPMS-9T). The demagnetization data were taken on bulk samples in external fields of up to 50 kOe at 25 • C. H A was determined by the singular point detection (SPD) method, using second derivative of magnetization (d 2 M/dH 2 ) [34][35][36][37]. A Perkin-Elmer 7 Series thermogravimetric analyzer (TGA) was used to determine the Curie temperatures (T C ) of the materials by observing the temperature dependence of the force exerted on the sample in a small magnetic field gradient provided by a permanent magnet placed close to the sample.…”

Origin of Magnetic Anisotropy of Gd5Si2Ge2Compound

“…X-ray diraction patterns did not show any extra lines and were successfully indexed in the hexagonal P 112 1 /a space group. The magnetic anisotropy was investigated by the use of the singular point detection technique developed by Asti and Rinaldi [7] (see also review paper [8]). This powerful technique was developed for the study of singularities in magnetization process when it reaches saturation at the anisotropy eld H an .…”

On the Ising character of the quantum-phase transition in LiHoF4

“…The curve exhibits a singularity at the anisotropy field H A = 2K 1 /µ o M s . This singularity is exploited in a well-established experimental method known as single-point detection (SPD), 10 which traces the second derivative d 2 M z /dH 2 . Ideally, this derivative is a delta peak, but in practice, it is a simple maximum near H A , because sample and grain misalignments smooth the singularity (dashed line in Fig.…”