Anisotropic magnetoelastic coupling in the honeycomb magnet Na$_3$Co$_2$SbO$_6$

Abstract

We present magnetization and dilatometry measurements on the honeycomb cobaltate Na$_3$Co$_2$SbO$_6$ and map out its detailed field-temperature phase diagram down to sub-Kelvin temperatures. Our data for in-plane magnetic fields show a strongly anisotropic $c^{*}$-axis lattice response, which is dominated by the variation of Co--O--Co bond angles according to \textit{ab initio} calculations. At $T = 0.4$~K, the magnetization $M(B)$ exhibits step-like features that are also highly anisotropic. In the case of $B \parallel b$, a small hysteresis observed around the second field-induced magnetic transition ($B_{c2}$) indicates its first-order character, whereas divergence of the magnetic Grüneisen parameter at $B_{c2}$ is suppressed upon cooling and signals the absence of quantum critical behavior upon entering the field-polarized state. None of our thermodynamic measurements provide evidence for a field-induced quantum spin liquid state near or above $B_{c2}$.

Figures (16)

• Figure 1: (a) Crystal structure of Na$_3$Co$_2$SbO$_6$. The honeycomb network formed by CoO$_6$ octahedra spread in the $ab$-plane. (b) Fisher's heat capacity and magnetic specific heat vs. $T$ under zero magnetic field in the left and right $y$-axes respectively. (c) Left half: Reflections from the Laue pattern taken on a twin-free crystal, Right half: Simulation (red spots) of the Laue pattern using the CRYSTAL MAKER program. (d) Zero-field thermal expansion of NCSO.
• Figure 2: (a, c) Temperature dependence of the relative length changes for $B\parallel a$ and $B \parallel b$, respectively (warming curves are shown). The upward arrows indicate the position of the $T_N$. The downward arrows mark the position of the crossover temperature $T^*$ above $B_{c2}$. (b, d) The corresponding plots of the linear TE coefficient, $\alpha_{c^*}$ vs. $T$ for $B\parallel a$ and $B \parallel b$, respectively. The insets show the data measured above $B_{c2}$. The arrows indicate the position of the broad maximum/minimum in $\alpha_{c^*}$.
• Figure 3: (a,c) Field dependence of relative length changes at constant temperature for $B\parallel a$ and $B \parallel b$, respectively (the data are measured upon increasing the field). The curves are shifted vertically for clarity. The arrows indicate the positions of $B_{c1}$ and $B_{c2}$. (b,d) Their corresponding coefficients of magnetostriction vs. field.
• Figure 4: (a,b) Total energy depending on the interlayer distance $c^*$ for different spin configurations of NCSO. The positions of the energy minima are indicated by arrows. (c) Deformation of the CoO$_6$ octahedra gauged by $\Delta_{\rm O-Co-O}$, the average deviation of O--Co--O angles from the median value of $90.0^{\circ}$. (d) Co--O--Co bond angles. The color codes for the zigzag and double-$q$ states correspond to the different oxygen atoms, as depicted in panels (e) and (f), respectively. Only the bond angles at the position of the energy minimum are shown in each case.
• Figure 5: Magnetic field dependence of $\Gamma_B$ for (a) $B\parallel a$ and (b) $B\parallel b$. The inset in (a) shows the hysteresis around $B_{c1}$. The dashed lines are the fit as described in the text.