Flux jumps, second magnetization peak anomaly, and the peak effect phenomenon in single crystals of $\mathrm{Y}{\mathrm{Ni}}_2{\mathrm{B}}_2\mathrm{C}$ and $\mathrm{Lu}{\mathrm{Ni}}_2{\mathrm{B}}_2\mathrm{C}$

We present magnetization measurements in single crystals of the tetragonal $\mathrm{Y}{\mathrm{Ni}}_2{\mathrm{B}}_2\mathrm{C}$ compound, which exhibit the phenomenon of peak effect as well as the second magnetization peak anomaly for $H>0.5\mathrm{T}$ $(H\Vert c)$. At the lower field $(50\mathrm{mT}<H<200\mathrm{mT})$, we have observed the presence of flux jumps, which seem to relate to a structural change in the local symmetry of the flux line lattice (a first-order reorientation transition across a local field in some parts of the sample, in the range of 100 to 150 mT). These flux jumps are also observed in a single crystal of $\mathrm{Lu}{\mathrm{Ni}}_2{\mathrm{B}}_2\mathrm{C}$ for $H\Vert c$ in the field region from $2\text{to}25\mathrm{mT}$, which are compatible with the occurrence of a reorientation transition at a lower field in a cleaner crystal of this compound, as compared to those of $\mathrm{Y}{\mathrm{Ni}}_2{\mathrm{B}}_2\mathrm{C}$. Vortex phase diagrams drawn for $H\Vert c$ in $\mathrm{Lu}{\mathrm{Ni}}_2{\mathrm{B}}_2\mathrm{C}$ and $\mathrm{Y}{\mathrm{Ni}}_2{\mathrm{B}}_2\mathrm{C}$ show that the ordered elastic glass phase spans a larger part of $(H,T)$ space in the former as compared to latter, thereby, reaffirming the difference in the relative purity of the two samples.

Figure 1

A portion of the five quadrant $M\text{−}H$ loop at $2.1\mathrm{K}$ in Y1221 (A) with $H\Vert c$. The presence of a peak effect bubble and flux jumps (four in the third quadrant and three in the fifth quadrant) can be noted in (a). Panel (b) shows a blow up of the $M\text{−}H$ loop highlighting the second magnetization peak anomaly. The locations of the $H_p^{\mathrm{on}}$, $H_p$, and $H_{c2}$ are marked in this panel.

Figure 2

Log-linear plots of normalized critical current density, $J_c\left(H\right)∕J_c\left(H_p\right)$ $[=\Delta M\left(H\right)∕\Delta M\left(H_p\right)]$ vs field $\left({\mu }_{0}H\right)$ in Y1221 (A) at two temperatures (2.1 and $6.5\mathrm{K}$) for $H\Vert c$. The locations of the maximum position of the SMP anomaly $\left(H_{\mathrm{smp}}\right)$ and the onset $\left(H_p^{\mathrm{on}}\right)$ and maximum $\left(H_p\right)$ positions of the PE are marked.

Figure 3

Log-log plot of normalized critical current density $\Delta M∕\Delta M_p(\propto j_c)$ vs normalized field $(h=H∕H_{c2})$ in Y1221 (A) and Lu1221 at $T=6.5\mathrm{K}$ for $H\Vert c$. The peak effect as well as the second magnetization peak anomaly are evident in the data of both the crystals. Although only one power-law region is evident for the case of Lu1221, two power-law regions, viz., PL-I and PL-II can be seen for Y1221.

Figure 4

Plot of the pinning force density $\left(J_{c}H\right)$ vs field in Y1221 (A) with $H\Vert c$. The regimes of ${\left(F_p\right)}^{\max }$, SMP, and PE have been indicated, and the positions of the flux jumps have been marked by arrows.

Figure 5

(a) Shows a five quadrant $M\text{−}H$ loop in Y1221 (A) at $T=2.1\mathrm{K}$ with $H\Vert c$ using a VSM with a scan rate of $0.25\mathrm{mT}∕\mathrm{s}$. Presence of two flux jumps in the third quadrant and three flux jumps in the fifth quadrant can be clearly noted. (b) shows the$M\text{−}H$ curve obtained after cycling the field several times between $\pm H_{\max }$ $(=\pm 300\mathrm{mT})$. Note that the number of flux jumps in third and fifth quadrant is now the same.

Figure 6

$M\text{−}H$ loop recorded using VSM (scan rate of field $0.025\mathrm{T}∕\min$) in Y1221 (B) at $T=2.1\mathrm{K}$ with $H\Vert a$.

Figure 7

Bean’s profiles [only one half section $(-D\text{to}0)$ shown] relevant for the five quadrant $M\text{−}H$ loop in Fig. 5a.

Figure 8

Bean’s profiles [only one half section ($-D$ to 0) is shown] at an applied field of ${\mu }_{0}H=-100\mathrm{mT}$ corresponding to a situation (a) just before the flux jump and (b) just after the flux jump. (c) Bean’s profiles as the field ramps upto ${\mu }_{0}H=-140\mathrm{mT}$.

Figure 9

(a) The filled square data points trace the initial magnetization curve $(0–75\mathrm{mT})$ after zero field cooling (ZFC) at $T=2.1\mathrm{K}$ in Y1221 (A) with $H\parallel c$. The open triangle and filled circle data points in different panels correspond to the minor curves traced while ramping up the field to $-500\mathrm{mT}$ from (a) $75\mathrm{mT}$ and (b) $174\mathrm{mT}$, respectively, and reversing the field from $-500\mathrm{mT}$ to (a) $75\mathrm{mT}$ and (b) $174\mathrm{mT}$, respectively.

Figure 10

(a) and (b) correspond to Bean’s profiles [only one half section ($-D$ to 0) shown] relevant for the minor curves of Fig. 9a. (c) and (d) show the same for the minor curves of Fig. 9b.

Figure 11

$M\text{−}H$ loops at $4.45\mathrm{K}$ (a), $6.45\mathrm{K}$ (b), and $8.45\mathrm{K}$ (c) in Y1221 (A) with $H\Vert c$. Inset shows temperature variation in $H^{\mathit{reor}}$ and $H_{c2}$ (see text for details).

Figure 12

Expanded portions of the $M\text{−}H$ loop obtained at $2.2\mathrm{K}$ in Lu1221 with $H\Vert c$. (a) and (b) depict the $M\text{−}H$ curves in the fifth (ramping the field from $0\text{to}{H}_{\max }=200\mathrm{mT}$) and the third (ramping the field from $0\text{to}-H_{\max }=-200\mathrm{mT}$) quadrants, respectively. The locations of the flux jumps have been marked with arrows.

Figure 13

(a) and (b) depict the plots of quadrupolar signal $Q$ (in arbitrary units) vs $H$ in Y1221 (A) for $H\Vert c$ at $T=2\mathrm{K}$ and $2.9\mathrm{K}$, respectively.

Figure 14

Vortex phase diagrams in $\mathrm{Y}{\mathrm{Ni}}_2{\mathrm{B}}_2\mathrm{C}$ (A) and $\mathrm{Lu}{\mathrm{Ni}}_2{\mathrm{B}}_2\mathrm{C}$ with $H\Vert c$. $H^{\mathit{reor}}$, $H_{\mathrm{smp}}^{\mathrm{on}}$, $H_p^{\mathrm{on}}$, and $H_{c2}$ lines have been sketched and different phases have been named.