Magnetization of underdoped ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_y$ above the irreversibility field

Torque magnetization measurements on ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_y$ (YBCO) at doping $y=6.67$ $\left(p=0.12\right)$, in dc fields ($B$) up to 33 T and temperatures down to 4.5 K, show that weak diamagnetism persists above the extrapolated irreversibility field $H_{\mathrm{irr}}(T=0)\approx 24$ T. The differential susceptibility $dM/dB$, however, is more rapidly suppressed for $B\gtrsim 16$ T than expected from the properties of the low field superconducting state, and saturates at a low value for fields $B\gtrsim 24$ T. In addition, torque measurements on a $p=0.11$ YBCO crystal in pulsed field up to 65 T and temperatures down to 8 K show similar behavior, with no additional features at higher fields. We offer two candidate scenarios to explain these observations: (a) superconductivity survives but is heavily suppressed at high field by competition with charge-density-wave (CDW) order; (b) static superconductivity disappears near 24 T and is followed by a region of fluctuating superconductivity, which causes $dM/dB$ to saturate at high field. The diamagnetic signal observed above 50 T for the $p=0.11$ crystal at 40 K and below may be caused by changes in the normal state susceptibility rather than bulk or fluctuating superconductivity. There will be orbital (Landau) diamagnetism from electron pockets and possibly a reduction in spin susceptibility caused by the stronger three-dimensional ordered CDW.

Figure 1

Black dots: high temperature anisotropic susceptibility ${\chi }_D\left(T\right)$ of the OVIII crystal at 10 T. Blue solid line: fit to this data above 120 K using Eq. (1). The parameters $A=11.09$ A/m/T, $T_F=680$ K are taken from Ref. [19], while the fit gives ${\chi }^{VV}=5.84$ A/m/T, $T^{*}=330$ K and ${\chi }^R\left(0\right)=1.26$ A/m/T; Red dashed line: Linear fit with $\chi \left(T\right)=1.22\times {10}^{-2}\times (T+948)$, following Ref. [6] but with different parameters. Note that $1\times {10}^{-4}\mathrm{emu}/\mathrm{mol}=9.73$ A/m/T.

Figure 2

(a) Magnetization $\left(M_c\right)$ of the OVIII crystal vs $B_z$, the field parallel to the $c$ axis. Here $M_c(T,H)=M_{\mathrm{obs}}(T,H)-M_{BG}(T,H)$, where $M_{BG}={\chi }_D{B}_z$ and ${\chi }_D$ is the blue line in Fig. 1. Dashed line: $M_{BG}$ at 4.5 K. Diamagnetism is present even at our highest field of 33 T. (b) Differential susceptibility $dM/dB$ of the OVIII crystal vs $B_z$ at selected temperatures. The lines are guides to the eye. We call the characteristic field at which $dM/dB$ departs from linearity $H_d$. Red: calculated mean field $dM/dB$ near $H_{c2}$ with $\kappa =50$, with $\kappa =41$ (purple) and with $\kappa =150$ (blue).

Figure 3

(a) Magnetization $\left(M_c\right)$ of the OII crystal measured in pulsed magnetic field up to $B_z=63$ T, where $M_c=M_{\mathrm{obs}}-M_{BG},M_{BG}={\chi }_D{B}_z$, and ${\chi }_D$ is the blue line in Fig. 1. For clarity only the falling-field sweeps are shown. Diamagnetism is present though extremely weak at high field (inset). The small offset in $M_c$ between the $T\le 40$ K and $T\ge 50$ K curves may be due to the transition to long-range CDW order near 40 K in high fields as observed in both sound velocity [14] and NMR [13]. (b) Differential susceptibility for the OII crystal in pulsed field. $dM/dB$ is seen to be small and constant up to the highest field of 63 T. Blue: calculated mean field $dM/dB$ near $H_{c2}$ with $\kappa =50$.

Figure 4

$H_d$ for both OII and OVIII crystals show similar temperature dependencies. Exponential fits to $H_{\mathrm{irr}}$ of OII $[23.2exp(-T/13.5\left)\right]$ and OVIII $[23.7exp(-T/20.5\left)\right]$ give extrapolated values $H_{\mathrm{irr}}\left(0\right)=23.2$ and 23.7 T. These values are close to the low temperature $H_d$ for both crystals. Note that $H_{c2}$ from GL fits (see main text) connects smoothly to $H_d$.

Figure 5

Magnetization data of the OVIII crystal at 16 K. The blue dashed line shows the MF behavior near $H_{c2}$ for an $s$-wave superconductor with $\kappa =41$. The stronger (3D) CDW sets in above 15 T for OVIII YBCO. At higher fields the data are consistent with $\kappa =145$ (solid line).