WIGNER-CRYSTAL PHASES IN BILAYER QUANTUM HALL SYSTEMS

Electrons in double-layer quantum-well systems behave like pseudospin 1/2 particles where the up and down ''spin'' represent localized state s in each of the layers. The magnetically induced Wigner-crystals in t hese systems are therefore crystals of these pseudospin 1/2 particles. We have calculated the phase diagram of the bilayer Wigner-crystals u sing a variational scheme which explores a continuum of lattice and sp in structure. Five stable crystal phases are found. For the given tunn eling strength and layer separation, one typically encounters the foll owing sequence of transitions as the filling factor is increased from zero (the same sequence also occurs if one increases the ''effective'' layer separation starting from zero, with the tunneling strength and filling factor held fixed): (I) (One-component) hexagonal structure -- > (II) centered rectangular structure --> (III) centered square struct ure --> (IV) centered rhombic structure --> (V) staggered hexagonal st ructure. Crystal I is a ferromagnet in pseudospin space. All other cry stals (II-V) have mixed ferromagnetic and antiferromagnetic orders, wh ich are generated by layer tunneling and interlayer repulsion, respect ively. The relative strength of these two magnetic orders vary continu ously with external parameters (i.e., the ratio of layer separation to magnetic length, the tunneling gap to Coulomb interaction, etc). The lattice structures I, III, and V are ''rigid'' whereas II and IV are ' 'soft,'' in the sense that the latter two vary with external parameter s and the former three do not. Another important feature of the phase diagram is the existence a multicritical point and a critical end poin t, which allows all crystals (except V) to transform into one another continuously. While our findings are based on a variational calculatio n, one can conclude on physical grounds that the mixed ferromagnetic-a ntiferromagnetic order as well as the pseudospin-lattice coupling shou ld be general features-of most bilayer Wigner-crystals.