In this chapter, we will restrict our attention to the ferrites and a few other closely related materials. The great interest in ferrites stems from their unique combination of a spontaneous magnetization and a high electrical resistivity. The observed magnetization results from the difference in the magnetizations of two non-equivalent sub-lattices of the magnetic ions in the crystal structure. Materials of this type should strictly be designated as “ferrimagnetic” and in some respects are more closely related to anti-ferromagnetic substances than they are to ferromagnetics in which the magnetization results from the parallel alignment of all the magnetic moments present. We shall not adhere to this special nomenclature except to emphasize effects, which are due to the existence of the sub-lattices.

Ferromagnetic materials

http://boulph.free.fr/Krzysztof/2003_Recent_and_future_advances.pdf

Recent advances and future directions in magnetic materials

Most metallic elements have a crystal structure that is either body-centered cubic (bcc), face-centered close packed, or hexagonal close packed. If the bcc lattice is the thermodynamically most stable structure, the close-packed structures usually are dynamically unstable, i.e., have elastic constants violating the Born stability conditions or, more generally, have phonons with imaginary frequencies. Conversely, the bcc lattice tends to be dynamically unstable if the equilibrium structure is close packed. This striking regularity essentially went unnoticed until ab initio total-energy calculations in the 1990s became accurate enough to model dynamical properties of solids in hypothetical lattice structures. After a review of stability criteria, thermodynamic functions in the vicinity of an instability, Bain paths, and how instabilities may arise or disappear when pressure, temperature, and/or chemical composition is varied are discussed. The role of dynamical instabilities in the ideal strength of solids and in metallurgical phase diagrams is then considered, and comments are made on amorphization, melting, and low-dimensional systems. The review concludes with extensive references to theoretical work on the stability properties of metallic elements.

https://perssongroup.lbl.gov/papers/rmp2012-instabilities.pdf

Lattice instabilities in metallic elements

It is demonstrated that hysteresis in the magnetostriction k is coupled to hysteresis in the magnetization M because of the dependence of the magnetostriction on the magnetization. At the same time, when stress is present, the magnetization is in turn coupled to the behavior of the part of the magnetostriction associated with domain moment rotation. An expression for the magnetostriction is formulated, and numerical modeling results for magnetostriction hysteresis are compared to experimental results. Although some features of the magnetostriction in iron and steel still need additional explanation, the main features of the magnetostriction are accounted for. These include liftoff (failure of the magnetostriction to return to its value in the demagnetized state as the hysteresis loop is cycled) and a magnetostriction increase after flux density B reaches its maximum and starts to decrease. A macromagnetic, multidomain formulation that yields zero magnetostriction in the demagnetized specimen is used. >

/pdf/coupled-magnetoelastic-theory-of-magnetic-and-41bfs4mwzq.pdf

Coupled magnetoelastic theory of magnetic and magnetostrictive hysteresis

The main magnetic characteristics regarding the domain structure and magnetization processes (axial, circular and Matteucci and inverse Wiedemann effects) of amorphous wires and glass-coated microwires are analysed. Magnetic bistability, spontaneously observed in samples with large enough ratio magneto-elastic anisotropy with axial easy axis to shape anisotropy, is the main source for a number of sensor applications in pulse generators, position and field sensors, encoded security tags, rotational counters, magnetostrictive delay lines, and so on. The relevant perspectives of the novel giant magneto-impedance effect recently reported and observed in non-magnetostrictive samples are also introduced.

https://iopscience.iop.org/article/10.1088/0022-3727/29/4/001/pdf

A soft magnetic wire for sensor applications

Extraordinary magnetostrictive behavior has been observed in Fe-Ga alloys with concentrations of Ga between 4% and 27%. λ100 exhibits two peaks as a function of Ga content. At room temperature, λ100 reaches a maximum of 265 ppm near 19% Ga and 235 ppm near 27% Ga. For compositions between 19% and 27%, λ100 drops sharply to a minimum near 24% Ga and exhibits an anomalous temperature dependence, decreasing by as much as a factor of 2 at low temperatures. This unusual magnetostrictive behavior is interpreted on the basis of a single maximum in the magnetoelastic coupling |b1| of Fe with increasing amounts of nonmagnetic Ga, combined with a strongly temperature dependent elastic shear modulus (c11−c12) which approaches zero near 27% Ga. λ111 is significantly smaller in magnitude than λ100 over this composition range, and has an abrupt change in sign from negative for low Ga concentrations to positive for a concentration of Ga near 21%.

https://lib.dr.iastate.edu/cgi/viewcontent.cgi?article=1027&context=ameslab_conf

Extraordinary magnetoelasticity and lattice softening in bcc Fe-Ga alloys

This paper presents a comparative study on the tetragonal magnetostriction constant, λγ,2, [ = (3/2)λ100] and magnetoelastic coupling, b1, of binary Fe100-xZx (0 < x < 35, Z = Al, Ga, Ge, and Si) and ternary Fe-Ga-Al and Fe-Ga-Ge alloys. The quantities are corrected for magnetostrains due to sample geometry (the magnetostrictive form effect). Recently published elastic constant data along with magnetization measurements at both room temperature and 77 K make these corrections possible. The form effect correction lowers the magnetostriction by ∼10 ppm for high-modulus alloys and by as much as 30 ppm for low-modulus alloys. The elastic constants are also used to determine the values of the magnetoelastic coupling constant, b1. With the new magnetostriction data on the Fe-Al-Ga alloy, it is possible to show how the double peak magnetostriction feature of the binary Fe-Ga alloy flows into the single peak binary Fe-Al alloy. The corrected magnetostriction and magnetoelastic coupling data for the various alloys...

https://lib.dr.iastate.edu/cgi/viewcontent.cgi?article=1114&context=ameslab_pubs

Tetragonal magnetostriction and magnetoelastic coupling in Fe-Al, Fe-Ga, Fe-Ge, Fe-Si, Fe-Ga-Al, and Fe-Ga-Ge alloys

Binary iron-gallium (Galfenol) alloys have large magnetostrictions over a wide temperature range. Single crystal measurements show that additions of 2at.% or greater of 3d and 4d transition elements with fewer (V, Cr, Mo, Mn) and more (Co, Ni, Rh) valence electrons than Fe, all reduce the saturation magnetostriction. Kawamiya and Adachi [J. Magn. Magn. Mater. 31–34, 145 (1983)] reported that the D03 structure is stabilized by 3d transition elements with electron∕atom ratios both less than iron and greater than iron. If D03 ordering decreases the magnetostriction, the maximum magnetostriction should be largest for the (more disordered) binary Fe–Ga alloys as observed. Notably, addition of small amounts of C (0.07, 0.08, and 0.14at.%) increases the magnetostriction of the slow cooled binary alloy to values comparable to the rapidly quenched alloy. We assume that small atom (C, B, N) additions enter interstitially and inhibit ordering, thus maximizing the magnetostriction without quenching.

https://lib.dr.iastate.edu/cgi/viewcontent.cgi?article=1015&context=ameslab_conf

Magnetostriction of ternary Fe–Ga–X (X=C,V,Cr,Mn,Co,Rh) alloys

Investigations were made into the effect of small additions of Ni, Mo, Sn, as well as larger additions of Al on the magnetostriction of single crystal Fe100−xGax alloys (x≅13). The Fe–Ga and Fe–Al systems are seemingly unique among the Fe-based alloys in having very large magnetostrictions in spite of Ga and Al being nonmagnetic. In this paper, we show how additions of Ni, Mo, Sn, and Al affect λ100 and λ111 of the binary Fe–Ga alloys. We substituted small amounts of Ni into a binary Fe–Ga alloy in an attempt to reduce the magnitude of the negative λ111, as Ni does in Fe, in order to improve the magnetostriction of polycrystals. The measured λ111’s were reduced to a very small value, ∼3 ppm, but λ100 fell dramatically to +67 ppm for Fe86Ga11Ni3. Mo was substituted for Ga to determine the effect of a partially filled 4d shell on the magnetostriction. Here |λ111| is affected the most, increasing to a value greater than all known α-Fe-based alloys (λ111=−22 ppm for Fe85Ga10.2Mo4.8). We find that the addition of Sn, with its very large atomic radius, makes only small changes in both λ100 and λ111. For Fe86.1Ga12.4Sn1.5 at room temperature, λ100=+161 ppm and for Fe86.7Ga12.0Sn1.3, λ111=−15 ppm. The decrease of λ100 in Fe87(GayAl1−y)13 was approximately linear, going from 67 ppm at y=0 to 154 ppm at y=1.

https://lib.dr.iastate.edu/cgi/viewcontent.cgi?article=1131&context=ameslab_pubs

Magnetostriction of ternary Fe–Ga–X alloys (X=Ni,Mo,Sn,Al)

The temperature dependence of the lowest order magnetic anisotropy constant K1 and the lowest order saturation magnetostriction constant, (3∕2)λ100, were measured from 4 K to 300 K for Fe91.4Ga8.6,Fe83.4Ga16.6, and Fe71.5Ga28.5 and were compared to the normalized magnetization power law, ml(l+1)∕2. Fe91.4Ga8.6 maintains the magnetostriction anomaly of Fe (dλ100∕dT>0) and K1 is a reasonable fit to the ml(l+1)∕2 power law with K1(0K)≅90kJ∕m3. Fe83.4Ga16.6 does not show a magnetostriction anomaly, but fits the power law remarkably well. Fe71.5Ga28.5 possesses a small K1(∼1kJ∕m3) at all temperatures and a large temperature dependent magnetostriction, reaching ∼800ppm at low temperature.

https://lib.dr.iastate.edu/cgi/viewcontent.cgi?article=1021&context=ameslab_conf

J. B. Restorff

Papers

Extraordinary magnetoelasticity and lattice softening in bcc Fe-Ga alloys

Tetragonal magnetostriction and magnetoelastic coupling in Fe-Al, Fe-Ga, Fe-Ge, Fe-Si, Fe-Ga-Al, and Fe-Ga-Ge alloys

Magnetostriction of ternary Fe–Ga–X (X=C,V,Cr,Mn,Co,Rh) alloys

Magnetostriction of ternary Fe–Ga–X alloys (X=Ni,Mo,Sn,Al)

Temperature dependence of the magnetic anisotropy and magnetostriction of Fe100−xGax (x=8.6, 16.6, 28.5)