Specific heat magnetic contribution

Electrons of the valence band, more exactly electrons in an energy interval kT near the Fermi level, bring about a specific contribution to several physical properties like electrical conductivity, specific heat, magnetic susceptibility (Pauli paramagnetism) etc. contributions which can be measured experimentally. 

Figure 4.7 Temperature dependence of the contribution to the total specific heat, reveals magnetization in 5 0e applied field of a pow- two distinct phase transitions. (Redrawn der sample of Gd(hfac)3NIT-Et n evidencing from Ref. [53] with data kindly provided by a phase transition around 1.8K. In the inset A. Lascialfari. (Published by American the magnetic contribution to the specific physical society).) heat, evaluated by subtracting the lattice...

There are several types of magnetic behaviour that affect the specific heat of a material paramagnetism, ferromagnetism, antiferromagnetism and ferrimagnetism. Diamagnetism, being independent of temperature, causes no specific heat contribution and is not considered. 

From formula (3.21), we see that the temperature at which the maximum of the magnetic contribution to the specific heat occurs is determined by the energy splitting AE of the levels ... 

An example of magnetic contributions to the specific heat is reported in Fig. 3.9 that shows the specific heat of FeCl24H20, drawn from data of ref. [35,36]. Here the Schottky anomaly, having its maximum at 3K, could be clearly resolved from the lattice specific heat as well as from the sharp peak at 1K, which is due to a transition to antiferromagnetic order (lambda peak). 

A special attention is to be devoted to copper, which is very often used in a cryogenic apparatus. The low-temperature specific heat of copper is usually considered as given by c = 10-5 T [J/g K], However, an excess of specific heat has been measured, as reported in the literature [59-69], For 0.03 K < T< 2K, this increase is due to hydrogen or oxygen impurities, magnetic impurities (usually Fe and Mn) and lattice defects [59-66], The increase of copper specific heat observed in the millikelvin temperature range is usually attributed to a Schottky contribution due to the nuclear quadrupole moment of copper [67,68],... 

The coordination numbers based on this structure work extremely well for describing the microscopic physical properties of this material, including the Mossbauer I.S.s of the surface sites and of the specific heat of the clusters below about 65 K. No linear electronic term in the specific heat is seen down to 60 mK, due to the still significant T contribution from the center-of-mass motion still present at this temperature. The Schottky tail which develops below 300 mK in magnetic fields above 0.4 T has been quantitatively explained by nuclear quadrupole contributions. 

Table 3. Density of states at the Fenni level for actinide metals from band calculations (model) from the electronic contribution y to the specific heat from magnetic susceptibility measurements. The increasing values indicate a decreasing 5 f bandwidth pinned at Ep for americium metal (not shown) there is a sudden decrease in N(np)...

A major achievement of the free-electron model was to show why the contributions of the free electrons to the heat capacity and magnetic susceptibility of a metal are so small. According to Boltzmann statistics, the contribution to the former should be nkB per unit volume. According to Fermi-Dirac statistics, on the other hand, only a fraction of order kBT/ F of the electrons acquire any extra energy at temperature T, and these have extra energy of order kBT. Thus the specific heat is of order nfcBT/ F, and an evaluation of the constant gives... 

As can be seen in fig. 47 the temperature dependence of the specific heat C(T) of TmNi2B2C shows pronounced anomalies at the critical temperature Tc as well as the magnetic ordering temperature Tn, which is different from the behaviour of HoNi2B2C where the magnetic contribution to C(T) dominates (fig. 38). 

Fig. 47. (a) Temperature dependence of the specific heat C as aC/T-vs.-T2 plot for TmNi2B2C. The maximum at 7"c indicates the transition to superconductivity and the low-temperature upturn is related to magnetic ordering. The solid line is calculated taking into account contributions from phonons and crystal field levels (b) specific heat of TmNi2B2C at low temperatures with a maximum at Tn (after Movshovich et al. 1994). 

Fig. 57. Specific heat contribution y(H) of the vortex core electrons in the mixed state (normalized by the Sommerfeld parameter /n) of the Yj[Lu jrNi2B2C samples from fig. 56 as function of the applied magnetic field (normalized by //c2(0)). The straight line y(H)

Fig. 61. Magnetic field dependence of the specific heat contribution y(H) of the vortex core electrons in the mixed state for Y(Nio.7sPto.25)2B2C. The dashed line is a fit according to eq. (8) with /) = 0.17, the solid line corresponds to the y(H)

In many cases, it is helpful to measure the specific heat as a function of temperature with and without an applied magnetic field. Like the susceptibility, the magnetic specific heat capacity Cm at a given temperature is averaged over the contributions of... 

A recent specific-heat measurement is shown in Fig. 2.31 for -(ET)2l3 [198]. At Tc = 3.4 K (3.5 K with magnetization measurements at the same crystal) a clear anomaly in C/T vs T can be seen. The height of the jump at Tc is AC sa 103 mJ/molK. In a small field applied perpendicular to the ET planes the anomaly of C becomes smaller and much broader. In an overcritical magnetic field of Bx = 0-5 T (not shown here) the normal-state specific heat was measured. Besides the usual linear electronic and cubic Debye specific heat a hyperfine contribution at low temperatures and an appreciable T phononic term had to be taken into account. Therefore, below 5K C was fitted by... 

The specific heat (C) is the amount of energy required, per unit mass or per mole, to raise the temperature of a substance by one degree. This is the derivative of its internal energy dU/dT, and since magnetic levels make a contribution to this their separations can in principle be measured from C(T) measurements. However, the magnetic contribution to the specific heat must be disentangled from that of lattice vibrational modes. 

---