Competing Interactions and the Effects of Uniaxial Out-of-plane Perturbations in the Honeycomb Antiferromagnet Na$_2$Co$_2$TeO$_6$

TL;DR

This study investigates how uniaxial out-of-plane perturbations affect the magnetic and elastic properties of Na$_2$Co$_2$TeO$_6$, revealing competing energy scales and field-induced phase transitions relevant to Kitaev physics.

Contribution

It provides the first high-resolution capacitance dilatometry analysis of out-of-plane magnetic field effects on Na$_2$Co$_2$TeO$_6$, highlighting uniaxial strain effects and complex phase behavior.

Findings

Antiferromagnetic order is stabilized by out-of-plane pressure at 0.28 K/GPa.

Failure of Gr"uneisen scaling indicates competing energy scales below 7.5 K.

Field induces a sharp peak at T_cr and a kink in magnetization at 4.6 T.

Abstract

Despite exhibiting magnetic long-range order below $T_\mathrm{N} = 26.7\,\mathrm{K}$, the honeycomb cobaltate Na$_2$Co$_2$TeO$_6$ is predicted to enter a Kitaev spin liquid state when subjected to small external perturbations. While most of the reported literature investigates the effects of magnetic fields applied parallel to the honeycomb layers, we present high-resolution capacitance dilatometry studies for fields perpendicular to the Co-planes up to $15\,\mathrm{T}$. Gr\"uneisen analysis reveals the effect of uniaxial out-of-plane strain and shows that antiferromagnetic order in Na$_2$Co$_2$TeO$_6$ is stabilized at a rate of $\partial T_\mathrm{N}/\partial p_\mathrm{c} = 0.28(5)\,\mathrm{K/GPa}$. Further, failure of the Gr\"uneisen scaling at low temperatures around $T_\mathrm{cr} \simeq 7.5\,\mathrm{K}$ demonstrates the presence of competing energy scales. In contrast to an only weak field dependence of the anomaly at $T_\mathrm{N}$, a broad hump at $T_\mathrm{cr}$ ($B=0\,\mathrm{T}$) evolves into a sharp peak at high fields applied $B \parallel c$. Our magnetostriction data show that a kink in the magnetisation at $B_\mathrm{C} \simeq 4.6\,\mathrm{T}$ is accompanied by an inflection point in the field-induced length changes, which is likely related to weak unequal spin canting. All observed phenomena leave their signatures in the magnetoelastic phase diagram as constructed by our experimental results.