Theoretical Study of the Pressure Dependence of the Knight Shift in Alkali Metals

Abstract

Metals 1 Quantum Mechanics f Spectroscopy, Nuclear Magnetic Resonance f Wave FunctionsFor Li and Na metals we investigated theoretically the pressure dependence of the atomic spin susceptibility xA, the probability density PF and the Knight shift K, = (8x/3)xAPF by the spin polarized version of the scalar relativistic augmented plane wave method. The calculations were performed within the volume range V, 2 V 2 0.5 Vo, where Vo is the volume at 1 bar. Recently it was found experimentally by Bertani et al. that a) the slopes of the curves K, = Ks( V ) have different signs for lithium and sodium metals and b) for high pressures K,(V) goes through a minimum for Na metal. We found in the present investigation that this behavior can be understood in terms of a competition between the pressure dependence of xA and PF for these metals.

Pressure-dependent Knight shift in Na and Cs metal

“…Therefore, in a next step, we included the ''exchange enhancement,'' which is known to be large for alkali metals according to Stoner-like theories 23 and spin-polarized calculations. 7 In calculating the exchange-enhanced Knight shift K , we have taken linearly interpolated / 0 ratios ͑see Table I͒ from spin-polarized calculations. 7 The K value at normal pressure ͑Table I͒ is in fairly good agreement with our experimental result.…”

“…7 In calculating the exchange-enhanced Knight shift K , we have taken linearly interpolated / 0 ratios ͑see Table I͒ from spin-polarized calculations. 7 The K value at normal pressure ͑Table I͒ is in fairly good agreement with our experimental result.…”

“…In a first step, we perform spin-restricted calculations, where the magnetization is given by the net spin produced by the external magnetic field only, and the susceptibility is determined by the DOS at E F . In a second step, we take into account the exchange enhancement from the spinpolarized calculations of Leiberich et al 7 The enhancement occurs because the net spin gives rise to exchange potentials which are different for ''spin up'' and ''spin down'' electrons, thus encouraging further polarization of the electrons. The enhanced susceptibility due to s states, , is related to the unenhanced susceptibility 0 via the relation 16…”

“…It is unlikely that it is caused by a thermal rearrangements of the density of states since these vary smoothly near the Fermi energy. 7 Instead, we suggest that the temperature dependence of the lattice constant accounts for the effect. Figure 3 shows the absolute Knight shift K( p) as a function of the lattice constant d for 295 and 358 K. We have determined d(p,T) as follows.…”

“…5 Furthermore, we will present a detailed theoretical study of the volume dependence of the sodium Knight shift based on a self-consistent band structure calculation, with the scalar-relativistic linear muffin tin orbital method and the local density approximation. Finally, we will address the question why all previous theoretical examinations of this problem established a stronger volume dependence of K than found experimentally 6,7 and did not reproduce the minimum or found it at too low volume ratios.…”