A short Introduction to Hexaborides

The cubic Hexaborides XB₆ have been in the focus of many research activities for several decades. In the Hexaborides metal atoms X are inserted into a network of boron cages which are interconnected by covalent B-B bonds. They all crystallize in the very simple CaB₆ structure and may be synthesized with either divalent or trivalent cations. The CaB₆ structure type is shown in figure . It can be considered as a CsCl structure with the Cs replaced by the metal X and the Cl by the boron octahedra. The boron atoms are therefore situated in +(x, , ) where the coordinate x denotes the distance from the cell face.

  

Figure: The CaB₆ structure.

The averaged structural parameters are well known from x-ray diffraction experiments and theoretical computations (local density approximation, see [#!rene!#]) which agree very good.

The trivalent Hexaborides have been supposed to be understood as metals for a long time. The divalent ones were supposed to be polar semiconductors with a complete transfer of the two valence electrons to the B₆ octahedra. This conclusion was in accordance with early transport and specific heat measurements. But already in 1979 there were some doubts about this crude interpretation [#!Hasegawa!#]. Recent calculations for SrB₆ and CaB₆ which were performed within the local density approximation showed a very small band overlap at the X point in the Brillouin zone which leads to a semimetallic behaviour. According to these calculations the cation influences the band structure only very small whereby the structural parameter x affects the band overlap in a way that the material is an insulator for x larger than [#!rene!#].

In spite of the very simple crystallographic structure the Hexaborides have very complex physical properties. First of all the Hexaborides with divalent and trivalent Rare-Earth elements on the cation sites have already attracted a broad interest for a long time. Some trivalent Rare-Earth Hexaborides, such as YB₆ and LaB₆ are well understood as metallic systems. Some others, such as CeB₆ or SmB₆ show very interesting properties, namely quadrupole ordering or Kondo insulation. SmB₆ shows the intermediate valence of Sm with metallic properties at high and semiconducting features at low temperatures. A famous, in our group well investigated example, is the divalent Rare-Earth Hexaboride EuB₆ with a ground state involving two magnetically similar but electronically inequivalent phases (conf. [#!eub6_phys_rev_letters!#,#!eub6_lt_nmr!#,#!magn_order_eub6!#,#!eub6_physica_b!#]).

But also the divalent Alkaline-Earth Hexaborides are not less interesting. Their electronic structure is -- as we mentioned above -- much more complex than one would expect. The 6 2s and the 18 2p atomic orbitals of the B₆ octahedra give rise to 10 bonding and 14 antibonding molecular orbitals. 18 of the 20 electrons needed to fill the valence bands come from the 6 borons and the remaining two come from the cation. This leads to bands with the slight band overlap in X already mentioned.

The maybe most puzzeling discovery was a weak ferromagnetism with a Curie temperature of almost 600K -- of the order of the Fermi temperature of the electron gas -- made in CaB₆ doped with 0.5% La (conf. figure and ). The doping with trivalent La brings one extra electron per La to the conduction band. Since the Fermi level is located in a region of a low density of states, the additional electrons will occupy the strongly dispersed conduction band. Electron doping with a very low concentration will therefore lead to a gas of almost free electrons with a very low density given by the La concentration. Figure shows the concentration dependence of the ferromagnetic moment. Other evidence that the magnetic moment is a function of the carrier concentration and that it might be a matter of an itinerant ferromagnetism is given by the comparison with Th doped CaB₆ where the magnetic moment peaks at -- half of the concentration it peaks in Ca_1-xLa_xB₆ -- as Th is a tetravalent cation. Up to now there is not much theoretical work done on this itinerant ferromagnetism. For further reading we suggest for example [#!mike!#] where an approach similar to the one in superconductivity is given.

  

Figure: The temperature dependence of the magnetization of Ca₀.995La₀.005B₆ in a fixed field of 0.1 T. (image source [#!ott_nature!#])

  

Figure: The saturation moment per mol La at T = 5K as a function of the La concentration. (image source [#!ott_nature!#])

We performed our measurements on SrB₆ and CaB₆. They were grown in Aluminium flux [#!lowtempSRB6!#]. After the thermal treatment the crystals were separated from the Al in a hot NaOH-solution. These Hexaborides have been showed to be of a very high structural perfection and of a high quality in their chemical composition [#!lowtempSRB6!#]. We used powdered crystals for our measurements.