Dynamic Reorganization of Vortex Matter into Partially Disordered Lattices

We report structural evidence of dynamic reorganization in vortex matter in clean ${\mathrm{NbSe}}_2$ by joint small-angle neutron scattering and ac susceptibility measurements. The application of oscillatory forces in a transitional region near the order-disorder transition results in robust bulk vortex lattice configurations with an intermediate degree of disorder. These dynamically originated configurations correlate with intermediate pinning responses previously observed, resolving a long-standing debate regarding the origin of such responses.

Figure 1

Scattering geometry: Both the dc field $\mathbf{H}$ and the ac field ${\mathbf{h}}_{\mathrm{a}\mathrm{c}}$ are aligned with the $\mathbf{c}$ axis of the single crystal, in the $\mathbf{x}\mathbf{z}$ plane. As the whole system is rocked around the $\mathbf{y}$ axis, the distribution of the scattered intensity $I$ is measured by the position-sensitive detector, which spans the $\mathbf{xy}$ plane, for each angle $\theta$ between the field direction and incoming neutron beam wave vector $\mathbf{K}$. The maximum intensity is expected at ${\theta }_0=Q_0/K$, for the corresponding reciprocal lattice vector ${\mathbf{Q}}_0$.

Figure 2

(a) Linear ac susceptibility ${\chi }^{\prime }(T)$ measured down to $T_0=1.9\mathrm{K}$ during a FC cooling procedure (black squares) and after shaking the VL at two different temperatures $T_{\text{sh}}^{(1,2)}$ (red circles and violet triangles) below the onset of the PE ($T_{\mathrm{p}\mathrm{o}}$). Shaking temperatures are indicated by vertical lines and arrows indicate temperature evolution. Reversibility is observed in the warming from $T_0$ of the VL shaken at $T_{\text{sh}}^{(1)}$ (dark yellow triangles). The area enclosed by the rectangular box is magnified in Fig. 3. (b) RC after FC; the black curve is the fit of a Lorentzian peak convoluted by the resolution kernel. (c) RCs after shaking the VL at $T_{\text{sh}}^{(1)}$ (red circles) and $T_{\text{sh}}^{(2)}$ (violet triangles); the curves are Gaussian fits with FWHM equal to the instrumental resolution $w_{\text{res}}=0.107°$.

Figure 3

${\chi }^{\prime }(T)$ for different thermal and dynamic histories [labeled (b)–(e) in panel (a)] and the corresponding detector intensity distributions for one VL BP at the Bragg condition [panels (b)–(e)]. Arrows in (a) indicate temperature evolution and the hatched area shows the transitional region. Data from Fig. 2 (black and red lines) is included for comparison. The application of a shaking field at $T_{\text{sh}}^{(3)}\approxeq 6.29\mathrm{K}>T_{\mathrm{p}\mathrm{o}}$ results in a unique response (full blue and green symbols) independent of whether the initial state was a disordered FC VL (open blue symbols) or an ordered VL (open green symbols). Both intensity distributions (c) and (d) indicate partial disorder as compared to the FC intensity distribution (b). Simply warming an ordered VL (magenta squares) up to $T\approxeq T_{\text{sh}}^{(3)}$ shows moderate pinning enhancement during cooling, but the corresponding BP (e) is still sharp and intense. The red boxes in (b)–(e) enclose the detector area included in the RCs in Fig. 4.

Figure 4

(a) Rocking curves measured after different field-temperature histories: FC [black, same as in Fig. 2], after shaking at $T_{\text{sh}}^{(3)}$ a FC (blue) and an ordered (green) VL, and after warming an ordered VL to $T=T_{\text{sh}}^{(3)}$ without shaking at this temperature (magenta). Curves are fits of Lorentzian peaks convoluted by the resolution. (b) Calculated profile likelihood ratio ${\mathcal{L}}_r$ as a function of ${\zeta }_L$ up to the sample thickness $d$ for each experimental RC. Symbols above the curves indicate the maximum (${\mathcal{L}}_r\equiv 1$) and error bars, the 68% confidence interval. For the ordered VL, ${\zeta }_L>L_{\text{res}}\sim 40\mu \mathrm{m}\sim 570a_0$ and is beyond our resolution. The profile likelihood of replicate RCs of the FC (black dashed line) and the one shaken at $T_{\text{sh}}^{(3)}\pm 3\mathrm{mK}$ (green dashed line) are reproducible within the error bars.