Conduction electrons in aperiodic versus periodic structures: An ESR study of quasicrystalline i -Y(Gd)-Cd and its approximant Y(Gd)Cd6

Abstract

A formal description of collective electronic states in condensed-matter systems lacking long-range periodicity remains a theoretical challenge. To experimentally explore the differences in electronic and magnetic behavior between metallic quasicrystals (QCs) and their conventional crystalline analogs [quasicrystal approximants (QCAs)], we have grown single crystals of ${\mathrm{Y}}_{1\ensuremath{-}x}{\mathrm{Gd}}_{x}{\mathrm{Cd}}_{6}$ (QCA) together with their QC counterparts $i\text{\ensuremath{-}}{\mathrm{Y}}_{1\ensuremath{-}x}{\mathrm{Gd}}_{x}\text{\ensuremath{-}}\mathrm{Cd}$ for $x=0.006$, 0.01, 0.1, and 1.00, and we carried out comparative $T$-dependent electron spin resonance (ESR) measurements. On the high Gd concentration side, $x=1.00$, we confirm that ${\mathrm{GdCd}}_{6}$ adopts an antiferromagnetic ground state below ${T}_{N}\ensuremath{\sim}22\phantom{\rule{4pt}{0ex}}\mathrm{K}$, whereas $i$-Gd-Cd presents spin-glass-like behavior showing similar local and dynamical properties from the point of view of ESR. For the diluted samples, our ESR experimental results show similar local conduction electron polarization behavior at the ${\mathrm{Gd}}^{3+}$ site in all QC/QCA pairs investigated, supporting the validity of using QCAs as periodic representations of QCs in terms of short-range electronic interactions. However, there is a measurable difference in the Korringa relaxation rate (spin-flip relaxation process between the localized ${\mathrm{Gd}}^{3+}4f$ electron and the delocalized $s$-type conduction electrons at the Fermi surface) between the QC/QCA pairs probably associated with the lack of periodicity. We expect that our comparative ESR study may provide support and motivation for the development of new theoretical approaches toward a generalized band-structure theory, contemplating condensed-matter systems beyond the scope of traditional periodicity.