On the Paramagnetic Impurity Concentration of Silicate Glasses from Low-Temperature Physics

Abstract

The concentration of paramagnetic trace impurities in glasses can be determined via precise SQUID measurements of the sample’s magnetization in a magnetic field. However, the existence of quasi-ordered structural inhomogeneities in the disordered solid causes correlated tunneling currents that can contribute to the magnetization, surprisingly, also at the higher temperatures. We show that taking into account such tunneling systems gives rise to a good agreement between the concentrations extracted from SQUID magnetization and those extracted from low-temperature heat capacity measurements. Without suitable inclusion of such magnetization contribution from the tunneling currents, we find that the concentration of paramagnetic impurities gets considerably over-estimated. This analysis represents a further positive test for the structural inhomogeneity theory of the magnetic effects in the cold glasses.

Appendix

Here we present our preliminary study of the SQUID magnetization data (also available from [2]) for the borosilicate glass BK7, for which however no substantial magnetic effect in the heat capacity $C_p$ has been reported [2]. This glass has a nominal Fe-impurity concentration of $\bar{n}_{Fe^{3+}} = 6$ ppm [2, 3, 9], yet our best fit in Fig. 9 with both Langevin (Eq. 15) and ATS (Eq. 19) contributions produces the concentrations and parameters given in Table 10. The best fit was carried out with knowledge of ATS parameters from our own theory [32] for the magnetic effect in the polarization-echo experiments at mK temperatures [3]. We conclude that our main contention is once more confirmed, in that the concentration of Fe in BK7 we extract in this way is only about 1.1 ppm and the bulk of the SQUID magnetization is due to the ATSs. Table 10 reports our very first estimate of $n_{ATS}P^{*}$ for BK7. Assuming $P^{*}$ to be of order 1 and about the same for all glasses, we conclude that the concentration $n_{ATS}$ of the ATSs nesting in the RERs is very similar for all of the multi-silicate glasses by us studied for their remarkable magnetic effects. From the present SQUID-magnetization best fits we have obtained 5.74$\times 10^{16}$ g$^{-1}$ (BAS glass), 8.68$\times 10^{16}$ g$^{-1}$ (Duran), and 1.40$\times 10^{16}$ g$^{-1}$ (BK7). The almost negligible magnetic effect in $C_p$ for BK7 is due, in our approach, to the low values of the cutoffs $D_{0min}$ and $D_{0max}$ for this system (these parameters appearing in the prefactor and in the integrals’ bounds determining the ATS contribution to $C_p$ [8]).

Table 10 Extracted parameters (from the magnetization data of [2]) for the concentration of ATSs and Fe-impurities of the BK7 ($\sum _i\xi _iA_i$= 63.530 g mol$^{-1}$ [2]). The vertical offset represents the residual Larmor diamagnetic contribution.