Zero-point entropy of the spinel spin glasses CuGa₂O₄and CuAl₂O₄

Abstract

Abstract. The zero-point entropy of a spin glass is a difficult property to experimentally determine and interpret. Spin glass theory provides various predictions, including unphysical ones, for the value of the zero-point entropy, however experimental results have been lacking. We have investigated the magnetic properties and zero-point entropy of two spinel Cu 2+ based spin glasses, CuGa2O4 and CuAl2O4. Dc-and ac-susceptibility and specific heat measurements show many characteristic spin glass features for both materials. The spin glass freezing temperature is determined to be T f = 2.89 ± 0.05 K for CuGa2O4 and T f = 2.30 ± 0.05 K for CuAl2O4. By integrating the specific heat data we have found that CuGa2O4 and CuAl2O4 have zero-point entropies of S0 = 4.96 JK −1 mol −1 and S0 = 4.76 JK −1 mol −1 respectively. These values are closest to the prediction for a Sherrington-Kirkpatrick XY spin glass, however they are notably higher than all of the theoretical predictions. This indicates that CuGa2O4 and CuAl2O4 have a greater degeneracy in their ground states than any of the spin glass models.

Synthesis and magnetic properties of nano-dimensional Fe1−xCuxAl2O4 (0.3 ≤ x ≤ 0.8)

“…From the magnetic point of view CuAl 2 O 4 exhibits spin glass behavior. 21 Though we could not get pure CuAl 2 O 4 in our synthetic strategy like FeAl 2 O 4 , we have been able to synthesize the solid solutions of Fe 1Àx Cu x Al 2 O 4 at 700 C in nanodimensional scale in a limited range of x ¼ 0.3 to 0.8 by sol-gel method. We have observed some interesting magnetic features in Fe 1Àx Cu x Al 2 O 4 (x ¼ 0.3, 0.4, 0.5 and 0.7) samples.…”

Spin glass behavior in frustrated quantum spin system CuAl2O4with a possible orbital liquid state

“…Of several Cu-based spinel compounds, CuGa2O4 is reported to have an inverse spinel structure and to exhibit a spin-glass state below 2.5 K [17,18]. A brief report [18] was also made about the non-zero values of a zero-point entropy for both CuGa2O4 and CuAl2O4, indicative of unusual ground state properties. We also note that nanostructured CuAl2O4 has been studied for possible photocatalytic applications [19].…”

“…Therefore, it will 5 be interesting to examine the ground state of the Cu-based S=1/2 systems in detail. Of several Cu-based spinel compounds, CuGa2O4 is reported to have an inverse spinel structure and to exhibit a spin-glass state below 2.5 K [17,18]. A brief report [18] was also made about the non-zero values of a zero-point entropy for both CuGa2O4 and CuAl2O4, indicative of unusual ground state properties.…”

Unveiling the Hidden Entropy in ZnFe ₂O ₄

“…Most of the results on NPD report on broad peaks that suggest lack of long-range order; Fe magnetic moment smaller than 5.9 µ B at the octahedral sites; a positive Curie-Weiss temperature and a magnetic entropy which is half that of the theoretical one. This reduced entropy has been observed in other spinel structures [15,19,20], and has been described as a "hidden" entropy, an entropy different from 0 at the zero point entropy [19]. Since in most of the experimental works on normal spinel, it is assumed δ ≈ 0 [21][22][23][24], the main question is: how critical is it to have δ ≈ 0 instead δ = 0.…”

“…In the absence of an applied field, the theoretical value of the magnetic entropy increment from the spin ordered state at 0 K to the paramagnetic (PM) state at temperatures well above the magnetic transition is 2R ln(2J + 1) = 29.7 J/mol•K, where J is the total quantum moment, with J = 5/2 for Fe 3+ . The difference between the theoretical and the experimental value contains information about additional contributions to the entropy, and it is defined as the zero-point entropy at 0 K [19,20]. It is important to remark that for (Zn 1-δ Fe δ ) A [Zn δ Fe 2-δ ] B O 4 , the parameter δ remains constant in the whole temperature range for each sample.…”