Quantum critical scaling of specific heat in a quasicrystal

In strongly correlated systems, interactions give rise to critical fluctuations surrounding the quantum critical point (QCP) of a quantum phase transition. Quasicrystals allow the study of quantum critical phenomena in aperiodic systems with frustrated magnetic interactions. Here, we study the magnetic field and temperature scaling of the low-temperature specific heat for the quantum critical Yb-Au-Al quasicrystal. We devise a scaling function that encapsulates the limiting behaviors as well as the area where the system goes from a temperature-limited to a field-limited quantum critical region, where the magnetic field acts as a cutoff for critical fluctuations. The zero-field electronic specific heat is described by a power-law divergence, <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:msub><a:mi>C</a:mi><a:mtext>el</a:mtext></a:msub><a:mo>/</a:mo><a:mi>T</a:mi><a:mo>∝</a:mo><a:msup><a:mi>T</a:mi><a:mrow><a:mo>−</a:mo><a:mn>0.54</a:mn></a:mrow></a:msup></a:mrow></a:math>, aligning with previously observed ac-susceptibility and specific-heat measurements. The field dependence of the electronic specific heat at high magnetic fields shows a similar power law <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mrow><b:msub><b:mi>C</b:mi><b:mtext>el</b:mtext></b:msub><b:mo>/</b:mo><b:mi>T</b:mi><b:mo>∝</b:mo><b:msup><b:mi>B</b:mi><b:mrow><b:mo>−</b:mo><b:mn>0.50</b:mn></b:mrow></b:msup></b:mrow></b:math>. In the zero-field and low-field region, we observe two small but distinct anomalies in the specific heat, located at 0.7 and 2.1 K.