Deviations from the Curie-Weiss law at temperatures below T$_{C}$ are apparently due to CF splitting of the ground-state multiplet $^{7}$, which is also reflected in the Schottky anomaly observed in specific-heat data collected for CePd$_{2}$Al$_{3}$ and PrPd$_{2}$Al$_{3}$ $^{8}$. CePd$_{2}$Al$_{3}$ exhibits heavy-fermion behavior at low temperatures ( γ = 380 mJ K $^{$_{−}$2}$mole$^{$_{−}$1}$) with a Kondo effect; 9 nevertheless, it becomes antiferromagnetic below 2.8 K 10 , $^{11}$. PrPd$_{2}$ Al$_{3}$ remains paramagnetic down to 1.5 K. Saturation of susceptibility below 15 K has been attributed to the CF effect yielding the ground-state singlet $^{12}$. NdPd$_{2}$ Al$_{3}$ becomes antiferromagnetic at T$_{N}$ = 6.5 K as reported in $^{8}$. The value of T$_{N}$ of NdPd$_{2}$Al$_{3}$ has been found to be varying in the interval from 5.2 to 7.7 K for various samples, following a linear dependence on the lattice parameter a , not on c , which may be understood with the exchange interactions inside the ab plane dominating the magnetism in this compound $^{11}$. The most intriguing case in the RE Pd$_{2}$Al$_{3}$ family seems to be SmPd$_{2}$Al$_{3}$. Results published so far on SmPd$_{2}$Al$_{3}$ have been obtained by measuring only polycrystals and point to a complex magnetic phase diagram with several magnetic phase transitions below 12 K $^{4}$. The CF interaction in SmPd$_{2}$ Al$_{3}$ can be reasonably estimated by considering the well-determined CF parameters for the NdPd$_{2}$Al$_{3}$ compound 13 , 14 or by using CF calculations as obtained from first principles, as will be presented in this paper. 

Specific-heat measurements of SmPd$_{2}$Al$_{3}$ have been reported revealing anomalies at 3, 6 and 12 K, indicating magnetic phase transitions $^{8}$. From susceptibility data three magnetic phase transitions at 4, 4.3 and 12 K $^{4}$, respectively, have been proposed whereas the electrical resistivity reflects strongly a magnetic phase transition at 12 K $^{4}$, typical for a transition to ferromagnetic ordering, the peak-like anomaly around 3.5 K resembles a transition to a low-temperature antiferromagnetic phase $^{10}$. The magnetization curve measured at 2.5 K indicated two magnetic phase transitions (at approximately 0.3 and 2 T) $^{10}$. It is clear that SmPd$_{2}$Al$_{3}$ presents unique case of 4f magnetism and we attempt here to put this context together with previous results and Sm magnetism generally. 

## II. EXPERIMENTAL AND COMPUTATIONAL DETAILS 

The single crystal of SmPd$_{2}$Al$_{3}$ was grown in a triarc furnace by the Czochralski pulling method from stoichiometric amounts of elements. The single crystal was a 20-mm long cylinder with a diameter of 3 - 4 mm. Crystal quality was checked by the Laue technique. 

A small part of the crystal was pulverized in an agate grinding mortar and X-ray powder 

