Studies of the thermal expansion of solids in the temperature range 1–100 K are reviewed. Effects due to thermal vibrations of the lattice, electrons, magnetic interactions and defects are fully discussed. The survey of experimental data is intended to be comprehensive. From the large volume of theoretical work in recent years the authors have aimed to select for discussion the most significant contributions.

Thermal expansion of solids at low temperatures

The structural evolution and magnetic properties of nanostructured copper ferrite, CuFe2O4, have been investigated by x-ray diffraction, Mossbauer spectroscopy, and magnetization measurements. Nanometre-sized CuFe2O4 particles with a partially inverted spinel structure were synthesized by high-energy ball milling in an open container with grain sizes ranging from 9 to 61 nm. Superparamagnetic relaxation effects have been observed in milled samples at room temperature by Mossbauer and magnetization measurements. At 15 K, the average hyperfine field of CuFe2O4 decreases with decreasing average grain size while the coercive force, shift of the hysteresis loop, magnetic hardness, and saturation magnetization at 4.2 K increase with decreasing average grain size. At 295 K the coercive-field dependence on the average grain size is described, with particles showing superparamagnetic relaxation effects. At 4.2 K the relationship between the coercive field and average grain size can be attributed to the change of the effective anisotropy constant of the particles. The interface anisotropy of nanostructured CuFe2O4 is found to be about 1.8(1) × 105 erg cm-3. Although spin canting was present, approximately 20% enhancement of the saturation magnetization in CuFe2O4 nanoparticles was observed, which could be explained by a cation redistribution induced by milling. The high-field magnetization irreversibility and shift of the hysteresis loop detected in our samples have been assigned to a spin-disordered phase, which has a spin-freezing temperature of approximately 50 K.

https://iopscience.iop.org/article/10.1088/0953-8984/11/20/313/pdf

Magnetic properties of nanostructured CuFe2O4

Surface effects in maghemite nanoparticles

Here we report an unconventional magnetic and transport phenomenon in a layered cobalt oxide ${\mathrm{Na}}_{x}{\mathrm{CoO}}_{2}.$ Only for $x=0.75,$ a magnetic transition of the second order was clearly detected at ${T}_{m}\ensuremath{\sim}22\mathrm{K}$ where an apparent specific-heat jump, an onset of extremely small spontaneous magnetization, and a kink in resistivity came in. Moreover large positive magnetoresistance effect was observed below ${T}_{m}.$ These features of the transition strongly indicate the appearance of an unusual electronic state that may be attributed to the strongly correlated electrons in ${\mathrm{Na}}_{0.75}{\mathrm{CoO}}_{2}.$

Unconventional magnetic transition and transport behavior in Na 0.75 CoO 2

By means of thermal decomposition, we prepared single-phase spherical Ni nanoparticles (23 to 114 nm in diameter) that are face-centered cubic in structure. The magnetic properties of the Ni nanoparticles were experimentally as well as theoretically investigated as a function of particle size. By means of thermogravimetric/differential thermal analysis, the Curie temperature TC of the 23-, 45-, 80-, and 114-nm Ni particles was found to be 335°C, 346°C, 351°C, and 354°C, respectively. Based on the size-and-shape dependence model of cohesive energy, a theoretical model is proposed to explain the size dependence of TC. The measurement of magnetic hysteresis loop reveals that the saturation magnetization MS and remanent magnetization increase and the coercivity decreases monotonously with increasing particle size, indicating a distinct size effect. By adopting a simplified theoretical model, we obtained MS values that are in good agreement with the experimental ones. Furthermore, with increase of surface-to-volume ratio of Ni nanoparticles due to decrease of particle size, there is increase of the percentage of magnetically inactive layer.

/pdf/size-dependence-of-the-magnetic-properties-of-ni-44meb6da0d.pdf

Size dependence of the magnetic properties of Ni nanoparticles prepared by thermal decomposition method

The local magnetic moment at the Curie temperature in the 35 at% Ni-Fe alloy retains still a half value of the magnetic moment at 0 K. Taking into consideration this fact, new formulas are proposed, which describe reasonably the phenomena of spontaneous volume magnetostriction and forced volume magnetostriction. The magnetovolume coupling constant determined by the new formulas is approximately 1.2 ×10 -8 cm 6 /emu 2 for Fe-Ni Invar alloys, which is independent of the Ni concentration.

The Magnetovolume Effect due to the Decrease of Local Magnetic Moment in Fe-Ni Invar Alloys

Precise measurements of magnetizations for single crystals of FCC Fe–Ni alloys in the Invar region have been made at temperatures from 4.2 K to 300 K in external applied fields up to 16.9 kOe to a relative accuracy of 5×10 -5 . In an analysis of these observed results with iterative least-squares method, it is found that there exists a large Stoner-type contribution varying as T 2.00±0.05 besides the spin-wave one to the temperature change in magnetization and that the coefficient of the Stoner-type contribution increases rapidly with decreasing Ni concentration, showing a maximum at about 35 at%Ni, and decreases for the alloys containing less than 35 at%Ni. It becomes evident that ferromagnetism in FCC Fe–Ni alloys disappears at a critical concentration of about 31 at%Ni. An anomalous behavior of the magnetization at low temperatures is also shown.

Role of T^2 Term in Temperature Dependence of the Magnetization for Fe-Ni Invar Alloys

The magnetization of a single crystal of the 35.4 at% Ni–Fe Invar alloy has been investigated between 4.2 K and 280 K in external fields up to 16.9 kOe to an accuracy of about 5 parts in 10 5 . The spin-wave stiffness constant including its temperature variation and the higher-order term than the T 3/2 term due to the spin-wave excitations are determined from only the data of magnetization measurements. The observed decrease in magnetization excluding the spin-wave term depends on T 2 and seems to be associated with the Stoner-type excitations. The contribution of T 2 term is found to be as large as the spin-wave contribution.

Contribution of T 2 Term to the Magnetization of a 35.4 at% Ni-Fe Invar Alloy

Detailed magnetization measurements for single crystals of Ni-rich Fe–Ni alloys have been carried out between 4.2 K and 300 K in external magnetic fields up to 16.9 kOe to a relative accuracy of 5×10 -5 . It is found by iterative least-squares analysis of these observed values that the temperature variation of magnetization consists of two parts: one is due to the spin-wave excitations and the other due to the Stoner-type excitations. The coefficient of the latter part has a considerable value at pure Ni, decreases with addition of Fe atoms to pure Ni, vanishing around 70 at%Ni, and reappears at about 65 at%Ni. A simple picture for metallic ferromagnetism at finite temperatures is proposed.

I. Nakai

Papers

The Magnetovolume Effect due to the Decrease of Local Magnetic Moment in Fe-Ni Invar Alloys

Role of T^2 Term in Temperature Dependence of the Magnetization for Fe-Ni Invar Alloys

Contribution of T 2 Term to the Magnetization of a 35.4 at% Ni-Fe Invar Alloy

Magnetic Excitations in FCC Fe–Ni Alloys Revealed from Detailed Magnetization Measurements

Comparison of magnetic properties of Fe-Pt and Fe-Pd invar alloys with those of Fe-Ni invar alloys