High-Resolution Capacitance Dilatometry of Microscopically Thin Samples Using a Miniature Dilatometer

TL;DR

This work addresses the mounting limitations of high-resolution capacitive dilatometry for ultrathin, platelet-shaped quantum materials. It introduces a slot-based mounting stamp that preserves sample orientation and provides full-length contact, enabling accurate thermal expansion measurements along in-plane directions for thicknesses below 500 μm. Validation on a 300 μm silver platelet, 50 μm EuB6 platelets, and a 40 μm AgCrS2 platelet demonstrates reliable data, agreement with literature, and high-resolution features such as sharp anomalies near phase transitions. The approach significantly widens the applicability of capacitance dilatometry to reduced-dimensional systems and anisotropic studies of emergent quantum phenomena.

Abstract

We present a novel application of our high-resolution capacitance dilatometer, specifically engineered for the precise characterization of quantum materials. These materials, which often appear as ultrathin, platelet-shaped crystals, are known for exotic phenomena such as superconductivity, topological order and quantum spin liquid. However, these crystals seldom reach macroscopic dimensions, making them unsuitable for conventional dilatometry techniques. By introducing a modified sample-mounting configuration, our design enables high-resolution measurements of thermal expansion and magnetostriction along in-plane crystallographic directions in samples with thicknesses well below 500 $μ$m. Validation measurements using a Quantum Design PPMS system confirm reliable performance for a 300 $μ$m-thick silver platelet, relatively hard ferromagnetic EuB$_6$ single crystals down to 50 $μ$m, and a 40 $μ$m-thin, soft AgCrS$_2$ single crystal. This advancement significantly broadens the applicability of capacitance dilatometry, providing a powerful platform for investigating emergent phenomena in reduced-dimensional quantum systems.

Figures (16)

• Figure 1: Main panel displays the measured length change $\Delta L(T)$ of the mounted 10 $\mu$m-thick AgCrS$_2$ sample (black curve), along with the background signal from the empty cell (red curve) for comparison. Inset A) shows an expanded view of both curves in between 36 K $\leqq T \leqq$ 37.25 K, illustrating detailed changes near the phase transition. Inset B) presents $\alpha(T)$ of AgCrS$_2$, obtained after subtraction of the background signal from the empty cell. Note that the pronounced background noise for the very thin sample ($L_0$ = 10 $\mu$m) results essentially from the $1/L_0$ scaling of $\alpha(T) = (1/L_0) dL/dT$, which amplifies the effect of any length fluctuations. For such a small absolute expansion, these instrumental noise sources appear much larger in $\alpha(T)$ than for thicker samples. Inset C) shows a comparison of $\alpha(T)$ measured in zero magnetic field and under an applied magnetic field of 9 T.
• Figure 2: Left: Common sample mounting procedure with cube-shaped stamp (indicated by a red arrow). Dilatometer consists of three main parts: (A) main body with sample (dark red) positioned in its center, (B) cover, and (C) sample-adjusting tool. Right: Sample mounting procedure using a slotted cube-shaped stamp, shown here with a mounted sample of 50 $\mu$m thickness (dark red).
• Figure 3: A) Standard cube-shaped mounting stamp commonly used for sample mounting. B) Slotted cube-shaped stamp with an ultra-thin sample (red) mounted. Two 30 $\mu$m-thick PTFE-coated silicon threads are looped around the sample.
• Figure 4: (a) A 300 $\mu$m thin rectangular silver plate mounted within the narrow slot of our custom-made cubic mounting stamp. Figures (b) and (c) show the top and side views of the mounted silver platelet, respectively.
• Figure 5: Comparison of the relative length change, $\Delta L(T)/L_0$, and the thermal expansion coefficient, $\alpha(T)$, as a function of temperature for the 300 $\mu$m silver plate measured while mounted in the narrow slot, alongside literature data from Ref.Kuechler2012. Very good agreement is observed across the entire temperature range, confirming the reliability of the measurement setup.