Exchange Interactions in FexTiS2

Abstract

TiS2 crystallizes in a hexagonal CdI2 structure with repetitions of S-, Tiand S-layers. Various 3d transition metal atoms T are intercalated into van der Waals gaps between neighboring S-layers, which are called T-layers hereafter, forming TxTiS2. In the T-layers, T-atoms are located in ordered manners for x 1⁄4 1=4 and 1/3 and are randomly distributed for other values of x. As x increases in random FexTiS2 spin glass phase, then ferromagnetic phase appears. Motizuki and Suzuki performed band calculation studies of TiS2 and T1=3TiS2. 2) They found that the TiS2-band consists of, with increasing energy, a bonding band of mainly S-3p states hybridized with states, a nonbonding band of Ti-3d states and an antibonding band of mainly states. In FexTiS2 the Fe-atom supplies two conduction electrons. According to the band calculation for Fe1=3TiS2, 2) the two electrons enter into the host TiS2-band nearly in a rigid-band manner, raising the Fermi level of the host TiS2-band. The Fe-atoms form the Fe-band. Although the energy of the Fe-band is close to that of the nonbonding Ti-3d band, the degree of hybridization between the two bands is low because Tiand Fe-atoms are located in different layers. Furthermore, interaction between the Feband and the bonding TiS2-band, whose main contribution is from S-3p states, is expected to be weak because the energy of the Fe-band is much higher than that of the bonding TiS2band. Then it is expected that Fe behaves nearly as an Fe2þ ion, and the origin of the exchange interaction is expected to be the Ruderman–Kittel–Kasuya–Yosida (RKKY) interaction. These expectations may also be valid for random FexTiS2. In fact, from the values of paramagnetic effective moments of about 4:0 B/Fe in FexTiS2, Fe-atoms are presumed to be in a nearly divalent ionic state with S 1⁄4 2. Furthermore, it has been suggested that the dominant exchange interactions in Fe0:05TiS2 and Co0:1TiS2 are RKKY interactions. In the present paper, we try to explain the x-dependence of the asymptotic Curie temperature of the paramagnetic susceptibility of FexTiS2 (0 x 0:43) by the RKKY interaction. Letting Ji be the exchange interaction constant between an Fe-spin and its i-th neighbor Fe-spin, is expressed as