Specific heat and magnetic susceptibility of the spinels GeNi2O4 and GeCo2O4

Specific-heat and magnetic-susceptibility measurements are reported for the polycrystalline spinel compounds GeNi(2)O(4) and GeCo(2)O(4) 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 GeNi(2)O(4) at Neel 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 similar to 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 GeNi(2)O(4) is the simultaneous presence of both gapped and ungapped spin waves in the Neel state, inferred from the specific-heat data. GeCo(2)O(4) 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 similar to 50% of the derived magnetic entropy is below the ordering temperatures, and the total magnetic entropies are only similar to 60% of that predicted for the Ni(2+) and Co(2+) 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 Neel temperatures. Fitting the GeNi(2)O(4) susceptibilities to the Curie-Weiss law yields parameters that are consistent with those found for Ni(2+) ions in a crystal-electric-field environment including octahedral and trigonal components. The application of the Curie-Weiss law to the GeCo(2)O(4) susceptibilities is not valid because of low-lying crystal-electric-field states.