Thermal expansion measurements in multiferroic HoMn$_{2}$O$_{5}$

Thermal expansion measurements were done on HoMn$_{2}$O$_{5}$ along the a,b,and c axes at zero applied magnetic field. Distinctive anomalies in the linear expansivities along the principal axes were seen at T$_{N}$=44K,T$_{C}$=39K,T$_{N\mbox{'}}$=20K and T$_{C\mbox{'}}$=15K with a notable negative c-axis thermal expansivity below 100K.All three axes were observed to shrink at T$_{N}$ and T$_{N\mbox{'}}$ while a and b expand as c shrinks when it passes through T$_{C}$ and T$_{C\mbox{'}}$ upon cooling. These anomalies are intimately correlated with anomalies in the dielectric constant and the specific heat at the phase transition temperatures. Our observations suggest that the coupling of the magnetic orders with the dielectric properties are mediated by strong magnetoelastic effects and the lattice anomalies play a crucial role in understanding the ferroelectricity in the compound. The anomalies associated with the ferroelectric transitions at T$_{C}$ and T$_{C\mbox{'}}$ show a thermal hysteresis revealing the first order nature of the transitions.