Specific heat and magnetic susceptibility of the spinels GeNi₂O₄ and GeCo₂O₄

Specific-heat and magnetic-susceptibility measurements are reported for the polycrystalline spinel compounds GeNi₂O₄ and GeCo₂O₄ in magnetic fields up to 14 T and 0.5 K≤T≤400 K. Both compounds have first-order antiferromagnetic transitions. There are two sharp closely spaced magnetic-ordering anomalies for GeNi₂O₄ at Néel temperatures T_N1(0)=12.080 K and T_N2(0)=11.433 K in zero magnetic field. There is also a broad anomaly in the specific heat centered at ∼5 K, which is present for all fields. Spin waves with an average gap of 10.9 K are associated with this anomaly, which is confirmed by neutron-scattering measurements. An unusual feature of the antiferromagnetism for GeNi₂O₄ is the simultaneous presence of both gapped and ungapped spin waves in the Néel state, inferred from the specific-heat data. GeCo₂O₄ has a single anomaly at T_N(0)=20.617 K in zero magnetic field. Spin waves with an average gap of 38.7 K are derived from fitting the low-temperature specific heat and are also observed by neutron scattering. For both compounds ∼50% of the derived magnetic entropy is below the ordering temperatures, and the total magnetic entropies are only ∼60% of that predicted for the Ni²⁺ and Co²⁺ single-ion ground-state configurations. The missing entropy is not linked to magnetic disorder in the ground state or hidden ordering below 0.5 K. It is postulated that the missing entropy is accounted for by the presence of substantial magnetic correlations well above the Néel temperatures. Fitting the GeNi₂O₄ susceptibilities to the Curie-Weiss law yields parameters that are consistent with those found for Ni²⁺ ions in a crystal-electric-field environment including octahedral and trigonal components. The application of the Curie-Weiss law to the GeCo₂O₄ susceptibilities is not valid because of low-lying crystal-electric-field states.