Precursor to quantum criticality in Ce-Au-Al quasicrystal approximants

Rare-earth elements containing aperiodic quasicrystals and their related periodic approximant crystals can exhibit nontrivial physical properties at low temperatures. Here, we investigate the 1/1 and 2/1 approximant crystal phases of the Ce-Au-Al system by studying the ac susceptibility and specific heat at low temperatures and in magnetic fields up to 12 T. We find that these systems display signs of quantum criticality similar to the observations in other claimed quantum critical systems, including the related Yb-Au-Al quasicrystal. In particular, the ac-susceptibility at low temperatures shows a diverging behavior <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:mi>χ</a:mi><a:mo>∝</a:mo><a:mn>1</a:mn><a:mo>/</a:mo><a:mi>T</a:mi></a:mrow></a:math> as the temperature decreases as well as cutoff behavior in magnetic field. Notably, the field dependence of <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mi>χ</b:mi></b:math> closely resembles that of quantum critical systems. However, the ac susceptibility both in zero and nonzero magnetic fields can be understood from the splitting of a ground state Kramers doublet of <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:msup><c:mrow><c:mi>Ce</c:mi></c:mrow><c:mrow><c:mn>3</c:mn><c:mo>+</c:mo></c:mrow></c:msup></c:math>. The high-temperature Curie-Weiss fit yields an effective magnetic moment of approximately <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mrow><d:mn>2.54</d:mn><d:msub><d:mi>μ</d:mi><d:mi mathvariant="normal">B</d:mi></d:msub></d:mrow></d:math> per Ce for both approximant systems, which is reduced to <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"><f:mrow><f:mo>∼</f:mo><f:mn>2.0</f:mn><f:msub><f:mi>μ</f:mi><f:mi mathvariant="normal">B</f:mi></f:msub></f:mrow></f:math> at temperatures below 10 K. The low-temperature specific heat is dominated by the Schottky anomaly originating from the splitting of the <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"><h:msup><h:mrow><h:mi>Ce</h:mi></h:mrow><h:mrow><h:mn>3</h:mn><h:mo>+</h:mo></h:mrow></h:msup></h:math> Kramers doublet, resulting in an entropy of <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"><i:mrow><i:mi>R</i:mi><i:mo form="prefix">ln</i:mo><i:mn>2</i:mn></i:mrow></i:math> at around 10 K.