Magnetic order and crystal structure in the superconducting RNi 2 B 2 C materials

Neutron-diffraction measurements have been carried out to investigate the crystal structure, magnetic structures, and magnetic phase transitions in ${\mathrm{RNi}}_{2}$${\mathrm{B}}_{2}$C (R= Y, Ce, Pr, Nd, Tb, Dy, Ho, Er, Tm, and Yb). The materials that order magnetically exhibit a wide variety of both commensurate and incommensurate magnetic structures, which argues strongly that the dominant exchange interactions are of the indirect Ruderman-Kittel-Kasuya-Yosida type. The Nd system exhibits a commensurate antiferromagnetic ordering at 4.8 K, with wave vector \ensuremath{\delta}=(1/2,0,1/2) and moment direction along a (or equivalently with \ensuremath{\delta}=(0,1/2,1/2) and moment direction along b in this tetragonal system). For Dy (${\mathrm{T}}_{\mathrm{N}}$=10.6 K), Pr (${\mathrm{T}}_{\mathrm{N}}$=4.0 K), and the low-temperature phase of Ho, the magnetic structure is also a commensurate antiferromagnet that consists of ferromagnetic sheets of rare-earth moments in the a-b plane, with the sheets coupled antiferromagnetically along the c axis [\ensuremath{\delta}=(0,0,1)]. Pr is not superconducting, while for Dy (${\mathrm{T}}_{\mathrm{c}}$=6 K) and Ho (${\mathrm{T}}_{\mathrm{c}}$=8 K) this magnetic order coexists with superconductivity. For Ho, though, the magnetic state that initially forms at ${\mathrm{T}}_{\mathrm{N}}$\ensuremath{\approx}8.5 K is an incommensurate spiral antiferromagnetic state along the c axis in which the direction of these ferromagnetic sheets are rotated in the a-b plane by \ensuremath{\sim}17\ifmmode^\circ\else\textdegree\fi{} from their low-temperature antiparallel configuration [\ensuremath{\delta}=(0,0,0.91)]. The intensity for this spiral state reaches a maximum near the reentrant superconducting transition (\ensuremath{\sim}5 K); the spiral state then collapses at lower temperature in favor of the commensurate antiferromagnetic state. An incommensurate a-axis modulation, with \ensuremath{\delta}=(0.55,0,0), is also observed above the spiral-antiferromagnetic transition, but it exists over a narrower temperature range than the spiral state, and also collapses near the reentrant superconducting transition. The Er system forms an incommensurate, transversely polarized spin-density wave (SDW) state at ${\mathrm{T}}_{\mathrm{N}}$=6.8 K, with \ensuremath{\delta}=(0.553,0,0) and moment direction along b (or with \ensuremath{\delta} along b and the moment direction along a). The SDW squares up at low T, and coexists with the superconducting state (${\mathrm{T}}_{\mathrm{c}}$=11 K) over the full temperature range where magnetic order is present. Tb, which does not superconduct, orders with a very similar wave vector, but the SDW is longitudinally polarized in this case and again squares up at low T. Tm orders at ${\mathrm{T}}_{\mathrm{N}}$=1.5 K in a transversely polarized SDW state, but with the moments along the c axis and \ensuremath{\delta}=(0.093,0.093,0). This state is coexistent with superconductivity (${\mathrm{T}}_{\mathrm{c}}$=11 K). No significant magnetic moment is found to develop on the Ni site in any of the materials, and there is no magnetic ordering of any kind in the Y, Yb, or Ce materials. Profile refinements have also been carried out on these same samples to investigate the systematics of the crystallography, and the crystal structure is I4/mmm over the full range of compositions and temperatures investigated. The area of the a-b plane and the volume of the unit cell both decrease smoothly with either decreasing lanthanide radius or decreasing temperature, but the strong boron-carbon and nickel-carbon bonding then forces the c axis to expand.