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1 Mar 1965

Volume 36, Issue 3, pp. 675-1270

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Magnetostriction of Polycrystalline Aggregates

Herbert B. Callen and Norman Goldberg

J. Appl. Phys. 36, 976 (1965); http://dx.doi.org/10.1063/1.1714285 (2 pages) | Cited 14 times

Online Publication Date: 14 July 2004

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The magnetostriction constant of the polycrystal λs can be written as a linear combination of the constants of the cubic crystallites; λs = αλ100 + (1‐α)λ111. The almost universally used approximation α = ⅖ is a poor one. It is based on the assumption of uniform stress through the aggregate (analogous to the Reuss approximation for the polycrystalline shear modulus). The alternative approximation of uniform strain (analogous to the Voigt approximation of the shear modulus) gives α = 2∕(2+3c), where c = 2c44∕(c11‐c12) is a measure of the elastic anisotropy of the microcrystals. However, both approximations lie outside upper and lower bounds which have been derived by Hashin and Shtrikman for the elastic case (although the magnetostrictive analogs have not been calculated). A physically reasonable approximation (the analog of Kroner's spherical stress approximation which lies between the Hashin and Shtrikman bounds in the elastic case) was given in a little known paper by Vladimirsky. Here the local stress is approximated by that in a spherical microcrystal surrounded by a homogeneous material with the isotropic properties of the polycrystalline aggregate. We show that for physically interesting elastic constants the rather complicated Vladimirsky result can be represented simply by α = ⅖ − (lnc)∕8. The available experimental data are compared with these various approximations; they favor the latter very strongly over the more commonly used α = ⅖.

Magnetic Structure of Rare‐Earth‐Cobalt (RCo2) Intermetallic Compounds

R. M. Moon, W. C. Koehler, and John Farrell

J. Appl. Phys. 36, 978 (1965); http://dx.doi.org/10.1063/1.1714286 (2 pages) | Cited 76 times

Online Publication Date: 14 July 2004

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Saturation magnetization and neutron diffraction measurements have been performed on cubic Laves phase compounds RCo2 in which R is Nd, Tb, Ho, and Er. Neutron powder patterns obtained at room temperature and at 15°K allowed the determination of the magnetic structures. The low‐temperature patterns are of the ferromagnetic or ferrimagnetic type, with large magnetic intensities superimposed on the nuclear peaks. For the compounds of Tb, Ho, and Er, the rare‐earth atoms show nearly the full moment expected for the free tripositive ion and the cobalt moment is about one Bohr magneton. The rare‐earth moments are coupled parallel to each other, but antiparallel to all the cobalt moments. For NdCo2, the observed Nd moment of 2.6±0.2 Bohr magnetons is smaller than the free ion value of 3.27 Bohr magnetons, and it is coupled parallel to the cobalt moment of 0.8±0.2 Bohr magnetons. In the Nd ion, the spin is opposite to the moment (J = L−S), while for the heavier rare earths the spin is parallel to the total moment (J = L+S). Thus, in all cases there is antiparallel coupling between the spins of the rare‐earth and cobalt atoms. The values for the total moment per molecule based on the neutron diffraction results are in satisfactory agreement with the magnetization measurements.

Exchange Anisotropy and Long‐Range Magnetic Order in the Mixed Intermetallic Compounds, (Mn, Fe)3Sn

J. S. Kouvel

J. Appl. Phys. 36, 980 (1965); http://dx.doi.org/10.1063/1.1714287 (2 pages) | Cited 7 times

Online Publication Date: 14 July 2004

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Magnetization and neutron diffraction results are reported for hexagonal (DO19) pseudo‐binary compounds of compositions intermediate between antiferromagnetic Mn3Sn and ferromagnetic Fe3Sn. Both Mn2.5Fe0.5Sn and Mn2FeSn exhibit a complex magnetization‐field‐temperature behavior that is suggestive of a finely mixed ferro‐antiferromagnetic state of the type previously proposed for Cu☒Mn and other disordered alloys. This exchange anisotropy state is further demonstrated by displaced hysteresis loops produced by cooling to low temperatures in a magnetic field; unidirectional anisotropies of about 106 erg∕g are computed from these loops. However, unlike Cu☒Mn, these compounds also give neutron diffraction evidence for some long‐range periodic magnetic order. The magnetic structure for Mn2.5Fe0.5Sn is basically that for Mn2Sn, in which three equivalent sublattice moments add vectorially to zero by describing a closed equilateral triangle, whereas Mn2FeSn probably has a ferrimagnetic variant of this structure.

Study of the Magnetic Properties of the Actinide Metals: Th1−xUxPd3

J. H. Wernick, H. J. Williams, D. Shaltiel, and R. C. Sherwood

J. Appl. Phys. 36, 982 (1965); http://dx.doi.org/10.1063/1.1714288 (2 pages) | Cited 11 times

Online Publication Date: 14 July 2004

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ThPd3, with UPd3, forms a continuous series of solid solutions. These two intermetallic compounds have the hexagonal DO24 structure. We have studied the magnetic susceptibilities of eleven Th1−xUxPd3 alloys (0≤x≤1) at temperatures from 1.4° to 300°K in fields up to 15 kOe and at 4.2°K in fields up to 80 kOe. ThPd3 is diamagnetic and shows a temperature‐independent susceptibility, but the addition of U, even in small amounts, gives rise to a strongly temperature‐dependent paramagnetic susceptibility. The data analyzed in terms of T against 1∕χ−χ∞ gives a Curie‐Weiss behavior in the high‐temperature region with 3.35 μB∕U atom at low U concentrations; decreasing to 2.6 μB for UPd3. It appears that the U‐5f electrons form a localized moment for low U concentrations. A deviation from a Curie law at around 100°K for all U concentrations is suggested to be due either to crystal field splitting of the U‐5f levels or to the presence of a narrow 5f band. The lack of any indication of an antiferromagnetic transition in the temperature behavior of the susceptibility at high U concentrations and the linearity of the magnetic moment with magnetic field up to 80 kOe for the same alloys, favors the formation of a very narrow 5f band as the U concentration increases and lends support to previous EPR experiments of Gd in UPd3, where a similar conclusion was reached.

Magnetic Characteristics of Gadolinium, Praseodymium, and Thulium Nitrides

David P. Schumacher and W. E. Wallace

J. Appl. Phys. 36, 984 (1965); http://dx.doi.org/10.1063/1.1714289 (2 pages) | Cited 18 times

Online Publication Date: 14 July 2004

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Bulk magnetic measurements were made on GdN, PrN, and TmN over the range 4.2° to 300°K. GdN is ferromagnetic with Tc = 69°K and a saturation moment of 7.03 μB (gJ = 7.00). Results obtained in the paramagnetic region give: for GdN μeff = 7.86 μB {g[J(J+1)]☒ = 7.94}, Θp = 75°K; for PrN 3.57 μB (3.58), −11°K; for TmN 7.32 μB (7.56), −21°K. These nitrides all occur in the NaCl structure. Under the influence of the cubic crystal field the 2J+1‐fold degenerate multiplet is decomposed so that Pr and Tm have singlet (nonmagnetic) ground states. Thus if the crystal field splitting exceeds the exchange interaction, no cooperative magnetic phase is expected at low temperatures. The measurements indicate this to be the case for TmN, supporting recent neutron diffraction work, and apparently this is also true for PrN. The possibility cannot be excluded, however, the PrN is a weak ferromagnet. If so, its saturation moment is estimated as 0.27 μB (gJ = 3.2 μB), indicating considerable crystal field quenching of the orbital contribution to the moment.

Magnetic Anisotropy in Antiferromagnetic α‐(Cr1−fAlf) 2O3

J. O. Artman, J. C. Murphy, and S. Foner

J. Appl. Phys. 36, 986 (1965); http://dx.doi.org/10.1063/1.1714290 (2 pages) | Cited 3 times

Online Publication Date: 14 July 2004

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In antiferromagnetic crystals the results of AFMR, when combined with other data, yield the anisotropy K. By subtracting the magnetic dipolar anisotropy KMD from K, the fine structure anisotropy KFS is found. For Cr2O3, the KMD computation of Tachiki and Nagamiya, 0.059 cm−1∕ion, had been accepted as a basis for further analyses. However, in the course of computing KMD by modern machine methods for various sesquioxide antiferromagnets, we have found this value to be inappropriate. The Shull magnetic structure (c) to which Cr2O3 belongs is one in which the magnetic geometry effectively is almost cubic! The computed KMD value thus is sensitive to small changes in lattice geometry. Presently accepted room‐temperature crystal parameters yield KMD = 0.0088 cm−1∕ion, ⅙ the former result; consequently Cr2O3 AFMR data have been reanalyzed. The temperature behavior of KFS and KMD in pure Cr2O3 and in (Cr1−fAlf)2O3 crystals is discussed. Similar KMD calculations have been made for the Ti, V, and Fe sesquioxides. In the case of α‐Fe2O3 we have been able to predict, with the use of AFMR data, the spin‐flip near 263°K. The experimentally found decrease of this spin‐flip temperature with increasing f in the α(Fe1−fAlf)2O3 system is discussed in the light of existing information.

Magnetic Studies at the Research Institute for Iron, Steel and Other Metals

Tokutaro Hirone

J. Appl. Phys. 36, 988 (1965); http://dx.doi.org/10.1063/1.1714291 (5 pages) | Cited 9 times

Online Publication Date: 14 July 2004

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A brief survey of several investigations is presented. (1) Spin‐flopping magnetization measurements up to 80 kOe in α Fe2O3 in the low‐temperature state are reported. The temperature dependence of the uniaxial anisotropy constant is obtained therefrom. Its magnitude is of the order of 104 erg∕cc and increases with decreasing temperature. Measurements with the field perpendicular to the trigonal axis reveal that at a temperature in the transition region (240°K), the magnetic state moves first toward the high‐temperature behavior with weak ferromagnetism, but above 60 kOe it returns to the antiferromagnetic low‐temperature state. (2) Thermomagnetic measurements on CaFeO2.5 and CaFe4O7 indicate that a weak ferromagnetism appears at 400°C. From the crystal structure, a Dzyaloshinsky‐Moriya canting is suggested to account for the weak moment. (3) High‐field measurements of MnAu2 extend to low temperatures the previous data on its transition field (screw‐type antiferromagnetism to ferromagnetism). The screw angle appears to be changing slowly even below 80°K. Longitudinal and transverse magnetostriction measurements in MnAu2 are reported through the transition and up to 80 kOe. Relative length changes of about 10−4 are observed and significant volume contractions during the screw‐flopping and rotation stages are inferred. (4) Saturation moment and Curie point measurements of Pd‐Fe alloys (near 30 at. % Pd) are reported and compared with similar Invar‐type behavior in Ni‐Fe alloys.

Magnetization of the Rare‐Earth Manganese Compounds R6Mn23

B. F. DeSavage, R. M. Bozorth, F. E. Wang, and E. R. Callen

J. Appl. Phys. 36, 992 (1965); http://dx.doi.org/10.1063/1.1714292 (2 pages) | Cited 14 times

Online Publication Date: 14 July 2004

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Measurements have been made of the magnetic moments of compounds of the type R6Mn23, where R is a rare‐earth ion. Determination of the saturation moments of Mn with nine of the rare earths (Sm, Nd, Gd, Tb, Dy, Ho, Er, Tm, and Lu) show that, with one exception, the rare‐earth and manganese moments are antiparallel; only in the gadolinium manganese compound is there complete ferromagnetic coupling. From the moment of Lu6Mn23 one derives the moment of 0.4μB per manganese atom. The measured moments of the other compounds agree closely with those calculated assuming a moment of 0.4μB for Mn and the normal moment of gJ for the appropriate rare‐earth atom.

Theory of Magnetoelastic Effects in Ferromagnetism

William Fuller Brown

J. Appl. Phys. 36, 994 (1965); http://dx.doi.org/10.1063/1.1714293 (7 pages) | Cited 25 times

Online Publication Date: 14 July 2004

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Standard magnetostriction theory constructs a free energy from three terms: the energy of a rigid magnetized body, the energy of a nonmagnetic elastic body, and the volume integral of an interaction energy‐density linear in the strains. This procedure is open to three criticisms. First, strains invalidate the magnetic calculation; in particular, the magnetostatic self‐energy is strain‐dependent. Second, magnetization invalidates the elastic calculation; the stresses (whose definition is somewhat arbitrary) need not be symmetric or even constitute a tensor. Third, small‐strain formulas, valid only to the first order of small quantities, are being used in energy terms that must be correct to the second order and that are linear in the strains. Previous studies make possible a rigorous treatment, by finite‐strain theory, and a small‐strain approximation with assumptions explicitly stated. The mechanical equilibrium equations contain the usual terms plus others; the ``form effect'' is a special case. The theory is easily related to microscopic models and is suited to nucleation‐field calculations.

Magnetic Anisotropy of an Fe‐Ge Alloy

J. J. Becker and E. M. Symes

J. Appl. Phys. 36, 1000 (1965); http://dx.doi.org/10.1063/1.1714070 (2 pages) | Cited 3 times

Online Publication Date: 14 July 2004

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The Fe‐Ge β phase extends from about 34 to 45 at. % Ge and has a modified NiAs structure. Previous investigations have established the saturation magnetization and Curie temperature, and have shown that the c axis is the hard direction of magnetization, but have not established the easy axis within the base plane. In the present experiments, an alloy of 57% Fe+43% Ge by weight (36.7 at. % Ge) was prepared, found to be a single phase, and ground into a powder consisting of individual single crystallites. These were aligned in a field and held in a binder. It was then established by x‐ray diffraction that the a axis was aligned parallel to the field. A lower limit to K3 can be arrived at by ascribing the observed coercive force of further subdivided material entirely to coherent rotation in the base plane. On this basis, ∣K3∣≥1.5×104 erg∕cm3 at 77°K.

Investigation of the Magnetic Structure of ErMn2, TmMn2, TbNi2 by Neutron Diffraction

G. P. Felcher, L. M. Corliss, and J. M. Hastings

J. Appl. Phys. 36, 1001 (1965); http://dx.doi.org/10.1063/1.1714071 (2 pages) | Cited 25 times

Online Publication Date: 14 July 2004

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Magnetic measurements by H. J. Williams (ErMn2 and TmMn2), and W. E. Wallace (TbNi2) have shown that these compounds are magnetically ordered at low temperature with a net moment per formula unit lower than that of the free rare‐earth ion. Neutron diffraction powder patterns have been used to determine the actual magnetic structure. ErMn2 and TmMn2 crystallize with the hexagonal Laves phase structure (C‐14 type). ErMn2 is ferromagnetic, with a moment of 7.72 μB∕Er atom at 4.2°K aligned along the c axis. No detectable moment on Mn is observed. TmMn2 is almost completely ferromagnetic, with a moment of 4.95 μB∕TM atom at 2.1°K aligned along the c axis, and essentially zero moment for Mn. A faint additional line at low angle seems to indicate a weak antiferromagnetic contribution. TbNi2 crystallizes with the cubic Laves phase structure (C‐15 type). At 4.2°K, ferromagnetic lines as well as additional peaks appear in the diffraction pattern, but the magnetic scattering is rather sensitive to sample preparation.
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