Small-angle neutron scattering and magnetic decoration both demonstrate a topological transition in the flux line lattice (FLL) in ErNi 2 B 2 C. The high-field square lattice slowly transforms into a hexagonal lattice via an area preserving [100] rhombohedral distortion below roughly 500 Oe. The square FLL is aligned with the [110] direction of the tetragonal crystal, while the two domains of the hexagonal FLL are aligned with [100] and [010]. The differences in pinning for the two FLL

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... s are reflected in the rf kinetic inductance. [S0031-9007(97)02526-X] PACS numbers: 74.60.Ge The nominal incompatibility between superconducting and magnetic ground states requires that a system in which both occur develops novel strategies to allow microscopic coexistence. Studies of the magnetic ground states and their structures in such systems have, historically, prevailed [1] . Only recently has the flux line lattice (FLL) in these systems come under scrutiny despite the fact that all known materials in this class are strongly type-II superconductors which form a FLL in the mixed state. Small-angle neutron scattering (SANS) studies [2] of the FLL in the magnetic superconductor ErNi 2 B 2 C found a square FLL at high fields, contradictious to the hexagonal FLL typically found in strongly type-II superconductors. In this paper we report on SANS, magnetic decoration, and rf kinetic inductance studies which clearly show how the square FLL undergoes a smooth structural transformation to a hexagonal lattice below roughly 500 Oe at 3.5 K. The monodomain square lattice is aligned with the [110] direction of the host crystal, while the hexagonal lattice has domains aligned along [100] and [010]. This transformation proceeds via an area preserving rhombohedral distortion along the [100] axis. Previous observations of FLL symmetry transformations were limited to the marginally type-II superconductor niobium in the intermediate mixed state, where a field independent transformation from a distorted hexagonal to a square lattice was seen by lowering the temperature [3, 4] . Our experiments used single crystals of ErNi 2 B 2 C, grown using Ni 2 B flux [5] and, to increase penetration of thermal neutrons, isotopically enriched B 11 . Platelet samples, with the c axis perpendicular to the flat surface, were typically 8 3 12 3 1 mm 3 with masses in the 300 500 mg range. ErNi 2 B 2 C has a superconducting transition ͑T c 10.5 K͒ [5,6] and an antiferromagnetic transition ͑T n 6.0 K͒ [5,7,8]. It is a strongly type-II superconductor, with k ϳ 5. Our experiments were performed in the antiferromagnetic superconducting regime. The SANS experiments, performed at the cold neutron guide hall at Risø National Laboratory, employed magnetic fields between 200 and 3000 Oe applied parallel to both the c axis of the crystal (to within 4 ± ) and the incident neutron beam. In this orientation, the upper critical field is H c2 ͑2 K͒ 1.8 T [5] and there is no field dependence to T n [5] . The neutrons had a wavelength, l n , between 9 and 15.3 Å, a wavelength spread Dl n ͞l n 18%, and angular divergences of ϳ0.15 ± and ϳ0.18 ± in the horizontal and vertical directions, respectively. An area detector at the end of a 6 m long evacuated chamber counted neutrons Bragg scattered from the magnetic field pattern due to the FLL. Shown in Fig. 1 are SANS data as a function of applied field for a field cooled experiment. This figure shows the scattered intensity, after zero field background subtraction, in the plane of the detector at 3.5 K for 1000, 750, and 500 Oe. The data are shown for a single point on the rocking curves, centered relative to all four Bragg reflections. All the peaks remain essentially at the Bragg condition for this condition, since the rocking curve width is greater than the scattering angle. The data at high fields clearly show both the square symmetry of the FLL and its alignment with the [110] crystal direction [2] . In addition to the (10) peaks, the well ordered FLL shows strong (11) reflections. As the field is reduced, two effects are obvious. The first is the reduction in the scattering vector due to the field dependence of the flux line density. The second effect, the subject of this paper, is the azimuthal broadening which occurs as the field is reduced below 500 Oe. In contrast to the azimuthal width, the radial width remains roughly constant and resolution limited as the field is reduced. Further, broadening of the rocking curve is smooth and continuous through this region and is 1968 0031-9007͞97͞78(10)͞1968(4)$10.00