  Similar to the optimal-doped, weak-ferromagnetic (WFM induced by canted
antiferromagnetism, T$_{Curie}$ = 131 K) and superconducting (T$_{c}$ = 56 K)
RuSr$_{2}$GdCu$_{2}$O$_{8}$, the underdoped RuSr$_{2}$EuCu$_{2}$O$_{8}$
(T$_{Curie}$ = 133 K, T$_{c}$ = 36 K) also exhibited a spontaneous vortex state
(SVS) between 16 K and 36 K. The low field ($\pm$20 G) superconducting
hysteresis loop indicates a weak and narrow Meissner state region of average
lower critical field B$_{c1}^{ave}$(T) = B$_{c1}^{ave}$(0)[1 -
(T/T$_{SVS}$)$^{2}$], with B$_{c1}^{ave}$(0) = 7 G and T$_{SVS}$ = 16 K. The
vortex melting transition (T$_{melting}$ = 21 K) below T$_{c}$ obtained from
the broad resistivity drop and the onset of diamagnetic signal indicates a
vortex liquid region due to the coexistence and interplay between
superconductivity and WFM order. No visible jump in specific heat was observed
near T$_{c}$ for Eu- and Gd-compound. This is not surprising, since the
electronic specific heat is easily overshadowed by the large phonon and
weak-ferromagnetic contributions. Furthermore, a broad resistivity transition
due to low vortex melting temperature would also lead to a correspondingly
reduced height of any specific heat jump. Finally, with the baseline from the
nonmagnetic Eu-compound, specific heat data analysis confirms the magnetic
entropy associated with antiferromagnetic ordering of Gd$^{3+}$ (J = S = 7/2)
at 2.5 K to be close to $\it{N_{A}k}$ ln8 as expected.
