Persistence of Metastable Vortex Lattice Domains in ${\mathrm{MgB}}_2$ in the Presence of Vortex Motion

Recently, extensive vortex lattice metastability was reported in ${\mathrm{MgB}}_2$ in connection with a second-order rotational phase transition. However, the mechanism responsible for these well-ordered metastable vortex lattice phases is not well understood. Using small-angle neutron scattering, we studied the vortex lattice in ${\mathrm{MgB}}_2$ as it was driven from a metastable to the ground state through a series of small changes in the applied magnetic field. Our results show that metastable vortex lattice domains persist in the presence of substantial vortex motion and directly demonstrate that the metastability is not due to vortex pinning. Instead, we propose that it is due to the jamming of counterrotated vortex lattice domains which prevents a rotation to the ground state orientation.

Figure 1

${\mathrm{MgB}}_2$ vortex lattice phases for $\mathit{H}\parallel \mathit{c}$. (a) Ground state phase diagram. Diffraction patterns in (b) and (c) were measured at 2 K and 0.5 T, indicated by the red star. The metastable VL (b) is formed by cooling across the $F\mathrm{\text{−}}L$ phase boundary as shown by the arrow. A 50 mT damped field oscillation drives the VL to the ground state configuration (c). Crystalline axes are shown in (c).

Figure 2

Resolving the MS to GS transition. (a)–(c) Diffraction patterns at 2 K: As-prepared MS VL state at 0.5 T (a); coexistence of MS and GS obtained after decreasing the field by 22 mT (b); GS VL obtained after decreasing field by 65 mT (c). (d)–(f) Azimuthal intensity distribution in counts per standard monitor (${10}^7$) corresponding to the diffraction patterns in (a)–(c). Solid lines are fits to the data as described in the text.

Figure 3

VL transition from MS to GS. (a) Relative intensity of the MS (squares) and GS (circles) VL Bragg peaks measured at 2 K as the applied field was decreased from 0.5 T. The solid, black line is an exponential fit to the data with a characteristic field $H^{*}=18\mathrm{mT}$, and the dashed, red line is a Bean model fit with a critical field $H^{*}=50\mathrm{mT}$. (b) Solid symbols correspond to an initial decrease of 14 mT followed by an increase of the applied magnetic field. Open symbols same as in (a). (c) Same as (b) but with solid symbols reflected about the reversal field of 0.486 T.

Figure 4

Magnetic induction calculated from the measured VL scattering vector as a function of applied magnetic field, corresponding to the data in Fig. 3b. The dashed, red line shows a linear fit to the data and the solid, black line is $B={\mu }_{0}H$. The schematic shown in the inset illustrates the proposed jamming of counterrotated VL domains. For the center domain, rotation to the ground state orientation is prevented, as it would lead to overlapping domains in the shaded regions.