Temperature and field dependence of the flux-line-lattice symmetry in ${\mathrm{V}}_3\mathrm{Si}$

In ${\mathrm{V}}_3\mathrm{Si}$, a first-order structural phase transition from hexagonal to square flux-line lattice occurs at approximately 1 T with $H\Vert$ to the $a$ axis. In this paper, we demonstrate the reentrant structural transition in the flux-line lattice, which reverts to hexagonal symmetry as the magnetic field approached $H_{c2}\left(T\right)$. This behavior is described very well by a nonlocal London theory with thermal fluctuations. The phase diagram of the flux lattice topology is mapped out for this geometry.

Figure 1

(Color) The observed diffraction pattern in ${\mathrm{V}}_3\mathrm{Si}$ with the field $H=1\mathrm{T}$ parallel to the $a$ axis at (a) $T=11\mathrm{K}$, (b) $T=12.5\mathrm{K}$, and (c) $T=14\mathrm{K}$. The fraction of the rhombic FLL at 11 K is less than 10% (the intensity is on a logarithmic scale). The neutron wavelength was 8 Å, the sample to detector $\text{distance}=10\mathrm{m}$, and the effective divergence of the beam at the sample was 0.2°. The pattern was obtained by summing over a rocking curve of $+∕-1°$ in 0.1° steps in order to get the different reflections on the Bragg condition.

Figure 2

(Color) A schematic explaining the origin of the multiple peaks visible in a region of phase space that has coexisting square and hexagonal FLL domains. Since the $a$ and $b$ axes are equivalent in this cubic system, two hexagonal domains could be expected to exist. The two square FLL coincide with each other.

Figure 3

(Color online) The opening angle $\left(\beta \right)$ as a function of applied field at base $\text{temperature}=2\mathrm{K}$.

Figure 4

(Color online) The intensities of rhombic and square FLL intensities as a function of applied field at 2 K are shown. Since the Bragg intensity is proportional ${(B∕q^2)}^2$ from the form factor and further, has a $1∕q$ term from the Lorentz factor, $I{q}^5∕B^2$ should be constant if all other factors (such as lattice perfection, Debye-Waller factor, for example) remain the same.

Figure 5

(Color) The phase diagram of the FLL topology obtained from the diffraction patterns shows that a rhombic FLL (green triangles) dominates at low fields and near $H_{c2}\left(T\right)$ curve (black line), while a square FLL (blue squares) is stable at lower temperatures above $\approx 1.1\mathrm{T}$. The theoretical transition curve $B_{◻}\left(T\right)$ (Ref. 9), is indicated by the solid red line. The shaded region indicates the observed coexistence of both rhombic and square phases.