The residual entropy of Shastry-Sutherland lattice of rare-earth tetraborides

Abstract The experimental temperature dependence of thulium tetraboride specific heat C p (T) and other heat capacity data for other RE-tetraborides were investigated in the 2–300 K temperature interval. Anomalies of C p (T) dependence of TmB 4 at T N1  = 9.6 K and T N2  = 11.4 K due to the antiferromagnetic ordering have been revealed. The ground state of the ion Tm 3+ was confirmed as a doublet. The diffuse anomaly of C p (T) is attributed to the Schottky contribution to the specific heat of the tetraboride, which is caused by the influence of the crystal electric field (CEF). The presence of the residual (zero-point) entropy S 0 of the magnetic moments system of Tm 3+ ions, due to frustration of the Shastry-Sutherland lattice, is detected. As a measure of the frustration of the system, a new characteristic of frustrated systems, the entropy frustration figure of merit, the value of which depends on the zero-point entropy of the system, is introduced: f S  =  S 0 /ΔS m max , where ΔS m max is the maximum value of entropy change of the boride magnetic subsystem. For TmB 4 and tetraborides of Gd, Tb, Dy, Ho, and Er, f s values determined from thermal measurements, and f  =  Ө c-w /T N ( Ө c-w denotes the Curie-Weiss temperature; T N is Neel temperature), calculated according to the magnetic measurement data, are practically identical.