We have theoretically designed the half-metallic (HM) antiferromagnets (AFMs) in thiospinel systems, Mn(CrV)S4 and Fe0.5Cu0.5(V0.5Ti1.5)S4, based on the electronic structure studies in the local-spin-density approximation (LSDA). We have also explored electronic and magnetic properties of parent spinel compounds of the above systems; CuV2S4 and CuTi2S4 are found to be HM ferromagnets in their cubic spinel structures, while MnCr2S4 is a ferrimagnetic insulator. We have discussed the feasibility of material synthesis of HM-AFM thiospinel systems.PACS numbers: 71.20. Be, 75.25.+Z, 75.50.Ee Since the first theoretical report of Heusler halfmetallic (HM) ferromagnet NiMnSb by de Groot et al.[1], much effort has been devoted to developing the HM magnetic materials, in which the conduction electrons at the Fermi level E F are 100% spin-polarized [2]. Especially, the HM antiferromagnet (AFM) attracts great attention because it is a non-magnetic metal but its conduction electrons are 100% spin-polarized. It can be used as a probe of the spin-polarized scanning tunneling microscope without perturbing the spin-character of samples. Further, the HM-AFM is expected to play a vital role in the future spintronic devices that utilize the spin polarization of the carriers.The first HM-AFM, V 7 MnFe 8 Sb 7 In, which is a derivative of the Heusler compound, was proposed by van Leuken and de Groot [3]. Anther possibility was suggested by Pickett [4] in the double perovskite system such as La 2 VMnO 6 . In this case, V and Mn have antiferromagnetically aligned magnetic moments that exactly cancel each other. To date, there has been no successful experimental realization of the HM-AFM.The thiospinel FeCr 2 S 4 in its metallic phase has the HM ferrimagnetic state with nominal valence configurations of Fe 2+ (d 6 ) and Cr 3+ (d 3 ) [5][6][7]. The magnetic moments of Fe and Cr are 4µ B and −3µ B , respectively, which produce the integer total magnetic moment of −2µ B per formula unit. From this, one can expect that FeV 2 S 4 becomes a HM-AFM, since V has one less electron than Cr and so the magnetic moment of two V 3+ (d 2 : S=1) ions would cancel that of Fe 2+ (d 6 : S=2), still possessing the HM property. Indeed the local-spindensity approximation (LSDA) band calculation yields the HM-AFM electronic structure of FeV 2 S 4 [8]. Unfortunately, FeV 2 S 4 does not exist in the cubic spinel structure but in the hexagonal NiAs structure (Cr 3 S 4 -type) with a complicated magnetic configuration [9]. So the above expectation does not work for FeV 2 S 4 in nature.Motivated by the above expectation, we attempt to search for the HM-AFM in other thiospinel compounds. Most of the thiospinel compounds of AB 2 S 4 -type (A, B: transition metals) with cubic structure have a ferrimagnetic ground state. Usually, the magnetic moment of the A ion in the tetrahedral site is antiferromagnetically polarized with that of the B ion in the octahedral site. Under this circumstance, there are some pairs of A and B which give rise to the exactly cancelled ma...