Vortexlike excitations in a nonsuperconducting single-layer compound ${\mathrm{Bi}}_{2+x}{\mathrm{Sr}}_{2-x}{\mathrm{CuO}}_{6+\delta }$ single crystal in high magnetic fields

The in-plane ${\rho }_{ab}(H,T)$ and the out-of-plane ${\rho }_c(H,T)$ magnetotransport in magnetic fields up to 28 T has been investigated in high-quality nonsuperconducting (down to 20 mK) La-free ${\mathrm{Bi}}_{2+x}{\mathrm{Sr}}_{2-x}{\mathrm{CuO}}_{6+\delta }$ single crystal. By measuring the angular dependence of the in-plane and out-of-plane magnetoresistivities at temperatures from 1 K down to 30 mK, we present evidence for the presence of vortexlike excitations in a nonsuperconducting cuprate in the insulating state. Such excitations have previously been observed by the detection of a Nernst signal in superconducting cuprates at $T>T_c$ in magnetic fields.

Figure 1

Scanning electron micrograph of the investigated crystal between voltage contacts where the composition measurement points are denoted by crosses.

Figure 2

Temperature dependence of the in-plane ${\rho }_{ab}$ (a) and out-of-plane ${\rho }_c$ (b) resistivities for the investigated Bi2201 single crystal. Note the log scale for the vertical axis. The insets plot ${\rho }_{ab}\left(T\right)$ and ${\rho }_c\left(T\right)$ with the horizontal axis plotted using a logarithmic scale in order to emphasize the low-temperature behavior.

Figure 3

Transverse in-plane magnetoresistance for Bi2201 sample at various temperatures from 55 mK to 1 K with the magnetic field perpendicular to the $ab$ plane. The inset is the magnetic field position of the maxima ${\rho }_{ab}\left(H\right)$ (squares) vs the temperature. The solid line is a fit to the experimental points using the expressioner (1) in Ref. 18 for an irreversibility line of our low-$T_c$ Bi2201 single crystals that corresponds to the melting of a three-dimensional vortex lattice (see text below).

Figure 4

In-plane resistivity as a function of applied field for various magnetic-field orientations relative to the $ab$ plane of the crystal, measured at (a) 0.25 and (b) 0.5 K.

Figure 5

Angular dependence of the field position of the maximum of ${\rho }_{ab}\left(H\right)\left(H_{\mathit{\text{peak}}}\right)$ at the temperatures 0.25 and 0.5 K extracted from the magnetoresistance curves in Fig. 4. Dashed lines are fits to experimental data using Tinkham’s relation with anisotropy parameter $\gamma =H_{c2}^{\Vert ab}∕H_{c2}^{\perp ab}$ equals to 5.5 at $T=0.25\mathrm{K}$ and 7.4 at $T=0.5\mathrm{K}$.

Figure 6

The resistive upper critical field $H_{c2}^{*}$ as a function of the angle between the magnetic-field and $ab$ plane at $T=0.7\mathrm{K}$ extracted from the magnetic-field-induced transitions of our superconducting slightly underdoped Bi2201 single crystal with $T_c=6\text{–}7.5\mathrm{K}$. The different symbols are the experimental $H_{c2}^{*}$ values obtained from the fields at which the resistivity of the sample has reached 1%, 10%, and 50% of it normal-state value ${\rho }_n$.

Figure 7

(Main panel) ${\rho }_c$ vs magnetic field for Bi2201 single crystal at various temperatures from 30 mK to 1 K for magnetic field perpendicular to the $ab$ plane $(\mathbf{H}\Vert \mathbf{c}\Vert \mathbf{J})$. The inset is ${\rho }_c\left(H\right)$ curves at temperatures 0.1 and 0.25 K for the longitudinal $\mathbf{H}\Vert \mathbf{c}\Vert \mathbf{J}$ (solid lines) and transverse $\mathbf{H}\perp \mathbf{c}\Vert \mathbf{J}$ (dashed lines) configurations.

Figure 8

Orbital components of the transverse out-of-plane magnetoresistance at temperatures 0.1 and 0.25 K extracted from the data in the inset of Fig. 7. The inset displays the field dependence of the out-of-plane resistivity ${\rho }_c$ in the transverse configuration for our optimaly doped Bi2201 single crystal with $T_c=9.5\mathrm{K}$ (midpoint).[32]