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Spinor Bose Einstein condensates (BEC) can be realized nowadays usingdifferent atomic species of several spin values, offering unprecedentedopportunities to scrutinize the underlying physics of its spin phase domainsand of its quantum phase transitions. At sufficient low temperatures, lowerthan the critical temperature, a fraction of thermally excited atoms of thecondensate can still interact with the whole system leading to spin-dependentinteractions that can modify the nature of its phase domains. In this work, wecharacterize the thermal fraction of atoms of a spinorial BEC of generalspin-$f$ value, provided that its ground state lies in a given spin phase withrotational symmetry. To that end, we use the Hartree-Fock approximation and amethod based on the Majorana stellar representation for mixed quantum statesand symmetry arguments. We consider the spin phases with usual point groupsymmetries, including those with some exotic phases associated to the platonicsolids. The method leads to useful analytical expressions of the eigenspectrumof the thermal cloud allowing us to study the admissible regions and multipolarmagnetic moments of the spin phases as a function of the temperature forgeneral spin values.

Thermal effects on the spin domain phases of high spin-f Bose-Einstein condensates with rotational symmetries