Masao Shimizu

Calculations of Electronic Specific Heat and Paramagnetic Susceptibility of Chromium

Electronic specific heats for various transition metals at higher temperature are deduced from experimental results. It is pointed out that the transition metals with small values of paramagnetic susceptibility and coefficient of low temperature specific heat, γ 0 , have larger values of the electronic specific heat than the extrapolation of γ 0 T , and the metals with large values of these have smaller values of the electronic specific heat than the extrapolation of γ 0 T , at higher temperatures. With use of electronic state density determined from the data of γ 0 , for Cr-Fe and Cr-V alloys, the temperature variations of electronic specific heat and spin susceptibility of Cr are calculated at arbitrary temperatures. The calculated electronic specific heats satisfactorily agree with the experimental results, whereas the calculated spin susceptibilities are smaller than the experimental results. It is pointed out that the main difference is attributable to the orbital paramagnetic susceptibility.

Magnetic Properties of Pd Metal and Pd-Rh and Pd-Ag Alloys Containing Co and Fe Atoms

Magnetic properties of Pd metal and Pd-Rh and Pd-Ag alloys with the addition of Co and Fe atoms are analyzed by the itinerant model of 4d-electrons. It is assumed that dissolved atoms have localized magnetic moments and are distributed at random. Spin quantum number of the localized moment of the dissolved atom and a molecular field coefficient between 4d-electron and dissolved atom are estimated from the comparison between our theory and experiments. The values of spin quantum number for localized magnetic moments are estimated as 1 and 3/2 for Co and Fe atoms in these alloys. Making use of these values and the value of molecular field coefficient among 4d-electrons and the density of states curve, which were obtained before for Pd metal, the composition dependences of the magnetic moment and the Curie temperature and the temperature dependences of paramagnetic susceptibility for these alloys are numerically calculated. The obtained results can explain almost all experiments satisfactorily.

Magnetic Susceptibility and Electronic Specific Heat of Transition Metals and Alloys III. Ni Metal and Ni-Cu Alloys

Electronic Specific heat of Ni metal is deduced from the experimental data. It is shown that above the Curie temperature the electronic specific heat coefficient decreases with temperature. The density of electronic states for Ni metal and Ni–Cu alloys is determined as a function of energy from the low temperature specific heat data of Ni and Cu metals and Ni–Fe and Ni–Cu alloys on the basis of the rigid band model. The temperature variations of electronic specific heat and spin paramagnetic susceptibility of paramagnetic Ni metal are calculated. The calculated result on electronic specific heat agrees with experimental result. Whereas the calculated result on spin paramagnetic susceptibility is considerably smaller than the observed susceptibilities. The difference is attributed to the effect of the molecular field and the orbital paramagnetism. Similar calculations are performed for Ni–Cu alloys. The fact that magnetic susceptibilities of Ni–Cu alloys with less than 20 at. % Ni increase with temperature...

NMR, MAGNETIC SUSCEPTIBILITY, AND ELECTRONIC SPECIFIC HEAT OF Nb AND Mo METALS AND Nb-Tc AND Nb-Mo ALLOYS

Magnetic susceptibility and nuclear magnetic resonance measurements have been made in Nb-Tc alloys. Calculations on the temperature variations of electronic specific heats and magnetic susceptibilities are performed for Nb and Mo metals and Nb-Mo alloys by making use of the density of states determined from low temperature specific heat data for 4 d transition metals and their alloys. Temperature variations of the electronic specific heats for Nb and Mo metals are well explained by the present numerical calculations. Temperature variations of the magnetic susceptibilities of these metals and their alloys are explained by taking account of the effect of the temperature independent orbital paramagnetism and the effects of the negative (for Nb metal) and the positive (for Nb 0.75 Mo 0.25 alloy) molecular fields. The Knight shifts of Nb 93 and Tc 99 in Nb-Tc and Nb-Mo alloys are discussed. It is shown that the main contribution to these Knight shifts appear to arise from the orbital paramagnetism of the d ele...

Electronic Properties for Pd Metal and Its Ferromagnetic Alloys –On the Number of Holes in the 4d-Band of Pd Metal–

By making use of a new experimental fact that the number of electrons in the 5 s -band or the number of holes in the 4 d -band is 0.36 per atom for Pd metal, the composition dependence of the magnetization of Pd-Fe and Pd-Co alloys is discussed, and residual electric resistivities for Ni-Pd alloys are calculated. Using the density of states curve which has been determined. from the low temperature specific heat data and modified by taking account of this new fact, the temperature dependence of the electronic specific heat and the paramagnetic susceptibility of Pd metal is calculated. The new value of the number of holes or electrons can give better interpretation of the experimental results than the value 0.6 per atom, which has so far been believed to be most probable.

Magnetic Susceptibility and Electronic Specific Heat of Transition Metals and Alloys IV. V and Ti Metals and V-Cr and V-Ti Alloys

Calculations on temperature variations of electronic specific heats and magnetic susceptibilities are performed for V and Ti metals and V-Cr and V-Ti alloys by making use of the density of states determined from low temperature specific heat data for the iron group transition metals and their alloys. Temperature variations of electronic specific heats for V and Ti metals are explained by the present numerical calculations. Temperature variations of magnetic susceptibilities are well explained by taking account of the effect of the temperature independent orbital paramagnetism for V and Cr metals and V-Cr alloys and by taking account of the effects of the temperature independent orbital paramagnetism and the positive and the negative molecular fields for Ti metal and V-Ti alloys. The Knight shifts of V 51 in V metal and V-Cr alloys are discussed and are considered to be composed of a large positive contribution due to the orbital motion of conduction electrons, a large negative one due to the exchange pola...

Theory of Spin Waves in Ferromagnetic Metals with Multiple Bands

Dispersion relations of spin waves in ferromagnetic metals with multiple bands are obtained by the method of normal mode within the random phase approximation and a certain approximation for the Coulomb interaction. It is found that spin wave spectra consist of one acoustical branch, some optical branches and other branches due to inter-band transitions. The inter-band transitions have an important effect on the dispersion relation of an acoustical spin wave at larger momentum. The coefficient of the square of momentum in the dispersion relation of the acoustical spin wave is found to be the sum of D B and D H which are derived from the intra-atomic Coulomb and inter-atomic exchange interactions, respectively. For nickel, the value of D B is estimated as about 0.1 eVA 2 by using the model of two overlapping bands, and it is concluded that (D_{B}{lesssim}D_{H}).

Effects of s – d Exchange Interaction and Temperature-Independent Paramagnetism on Susceptibilities of Nickel, Palladium and Platinum

The well-known discrepancy between the number of the Bohr magneton obtained from the saturation magnetization at 0°K and that obtained from paramagnetic susceptibilities for Ni is explained by taking into account the s – d exchange interaction, instead of the s – d electron transfer, and the temperature-independent paramagnetism due to the orbital moments of d electrons. The similar discrepancy between the number of magnetic carriers obtained from the paramagnetic susceptibility measurement at lower temperatures and that at higher temperatures for Pd is explained in the same way. The same discussion is applicable to Pt. It is concluded that the temperature-independent paramagnetism is important to understand the temperature variations of susceptibilities of transition metals. The paramagnetic susceptibilities for Ni, Pd, and Pt at higher temperatures are expressed in the form, C /( T -θ p )+χ c . The temperature-independent susceptibility, χ c , is the sum of the paramagnetic susceptibility of the conduct...

Ferromagnetism of an Electron Gas

Magnetism, especially ferromagnetism, of an electron gas is studied on the basis of the Bohm-Pines collective description of electron interactions. Exchange interactions are derived from the screened Coulomb interaction, the interaction obtained from the second-order perturbation of the screened Coulomb interaction, and the weak interaction coming from the interaction between plasma and individual electrons. We assume effective mass for the electron mass. The total energy of the electron gas in the ferromagnetic state is compared with that in the non-ferromagnetic state, and the conditions of ferromagnetism for the electron gas are discussed. The one-electron approximation being adopted, the effective number of magnetic carriers in the electron gas is expressed as a function of temperature and magnetic field. Using the Weiss approximation, we express the spontaneous magnetization at an arbitrary temperature in terms of this effective number and the molecular field obtained from the proper average of the e...

A Calculation on the Temperature Variation of the Magnetization for Iron Metal

A calculation on the temperature variation in magnetization for iron metal is performed based on the band model, by making use of the density of states curve which was determined from the experimental data for the low temperature specific heat. The effective exchange energy is expanded in a power series of magnetization and the values of coefficients are estimated by comparing the calculated and experimental results of the temperature variation in magnetization. In order to explain the experimental results for the temperature variation, the terms of higher powers of magnetization than the quadratic must be taken into account. Above the Curie temperature, the temperature variation in the molecular field coefficient is estimated from the comparison between the calculated and experimental results of the temperature dependence of the magnetic susceptibility.