The putative Kitaev material ${\mathrm{Na}}_2{\mathrm{Co}}_2{\mathrm{TeO}}_6$ has recently been proposed to enter a quantum spin disordered state when magnetic fields are applied in parallel to the honeycomb layers. In this Letter we uncover signatures of a quantum critical endpoint (QCEP) associated with the assumed order-disorder transition by means of high-resolution capacitance dilatometry. At the critical field $B_{\mathrm{C}}$ $\simeq 6 \mathrm{T}$, a sign change of the out-of-plane thermal expansion coefficient ${\alpha }_{\mathrm{c}}$ indicates the accumulation of entropy upon crossing the phase boundary. The proportional relationship between isothermal magnetization and magnetostriction signals that the QCEP can be tuned by magnetic field and pressure simultaneously. The presented results expand the material classes that exhibit metamagnetic quantum criticality to honeycomb antiferromagnets with possible Kitaev interactions.

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• Magnetic phase transitions
• Magnetostriction
• Phase diagrams
• Quantum criticality
• Quantum phase transitions
• Quantum spin liquid
• Antiferromagnets
• Honeycomb lattice
• Single crystal materials
• DC susceptibility measurements
• Magnetization measurements
• Thermodilatometry