Magnetism of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>S</mml:mi><mml:mo>=</mml:mo><mml:mfrac><mml:mn>1</mml:mn><mml:mn>2</mml:mn></mml:mfrac></mml:mrow><mml:mo> </mml:mo><mml:mrow><mml:msub><mml:mi>J</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mi>J</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:mrow></mml:math> square-kagome lattice antiferromagnet

Over the last decade, spin-$1/2$ Heisenberg antiferromagnet on square-kagome (SK) lattice has attracted growing attention as a model system of highly frustrated quantum magnetism. A further motivation for theoretical studies this comes from recent discovery SK spin-liquid compounds ${\mathrm{KCu}}_{6}{\mathrm{AlBiO}}_{4}{({\mathrm{SO}}_{4})}_{5}\mathrm{Cl}$ [M. Fujihala et al., Nat. Commun. 11, 3429 (2020)] and ${\mathrm{Na}}_{6}{\mathrm{Cu}}_{7}{\mathrm{BiO}}_{4}{({\mathrm{PO}}_{4})}_{4}{[\mathrm{Cl},(\mathrm{OH})]}_{3}$ [O. V. Yakubovich Inorg. Chem. 60, 11450 (2021)]. The exhibits two nonequivalent nearest-neighbor bonds ${J}_{1}$ ${J}_{2}$. One may expect that in ${J}_{2}$ are different strength. Here, we present numerical study finite systems $N=30$, 36, $N=42$ sites by means finite-temperature Lanczos method. We discuss temperature dependence Wilson ratio $P(T)$, specific heat $C(T)$, entropy $S(T)$, susceptibility $X(T)$ ${J}_{1}\ensuremath{-}{J}_{2}$ varying ${J}_{2}/{J}_{1}$ range $0\ensuremath{\le}{J}_{2}/{J}_{1}\ensuremath{\le}4$. also zero-field ground state model. find indications magnetically disordered singlet $0\ensuremath{\le}{J}_{2}/{J}_{1}\ensuremath{\lesssim}1.65$. Beyond ${J}_{2}/{J}_{1}\ensuremath{\sim}1.65$ gives way ferrimagnetic state, which becomes stable Lieb ferrimagnet with magnetization $M=N/6$ (UUD state) ${J}_{2}/{J}_{1}\ensuremath{\gtrsim}1.83$. In region $0.77\ensuremath{\lesssim}{J}_{2}/{J}_{1}\ensuremath{\lesssim}1.65$ low-temperature thermodynamics is dominated singlet-triplet gap filled low-lying excitations leading to an exponentially activated behavior $X(T)$. On other hand, singlets yield extra maximum or shoulderlike profile below main $C(T)$ curve. For ${J}_{2}/{J}_{1}\ensuremath{\lesssim}0.7$ characterized large fraction $N/3$ weakly coupled spins sizable amount at very low temperatures. applied magnetic field process features plateaus jumps wide ${J}_{2}/{J}_{1}$.