Direct evidence of interchange between hole doping and Curie paramagnetism in underdoped YBa${}_2$Cu${}_3$O${}_x$

We present high-accuracy magnetization measurements on YBa${}_2$Cu${}_3$O${}_x$ ceramic samples, with $x$ ranging from 6.19 to 7.00. Magnetization relaxation measurements around or above room temperature display a cooling-rate-dependent behavior, evocative of a thermally activated mechanism. Through careful simultaneous time-dependent studies of the pseudogap and Curie law contributions to the magnetic susceptibility and of the critical temperature, we are able to establish an original, quantitative relationship between the proportion of free paramagnetic Cu${}^{++}$, which is a measure of intrinsic oxygen disorder in the chains and the hole doping of the CuO${}_2$ planes. This observation paves the way to a microscopic model for the role of charge “reservoir” played by the chains in YBa${}_2$Cu${}_3$O${}_x$.

Figure 1

Magnetization between 100 and 400 K measured under 1 T in temperature sweeps of 1 K/min for the different samples. $x$ is indicated on each graph.

Figure 2

Magnetization measurements upon slow warming up (0.5 K/min) of sample YBCO6.32 after, respectively, slow (1 K/min) cooling down (blue dotted line) and fast (10 K/min) cooling down (red solid line) from 400 K. Similar data are observed for all samples with $x<7.0$. Note the crossing of the two curves circa 270 K. Inset: Same enlarged data between 250 and 380 K. Note that a linear trend has been subtracted from both curves in the inset.

Figure 3

Relative difference $(M_{\text{fast}}-M_{\text{slow}})/(M_{\text{fast}}+M_{\text{slow}})=\Delta M/M$ between the magnetic susceptibility of YBCO$x$ samples measured during slow warming up after temperature cooling down from 400 K with two different cooling rates: 10 K/min (fast) and 1 K/min (slow).

Figure 4

Top: Amplitude of the relative difference $(M_{\text{fast}}-M_{\text{slow}})/(M_{\text{fast}}+M_{\text{slow}})=\Delta M/M$ at its minimal (negative) value, giving the amplitude of the cooling rate effect in the “pseudogap” region, as a function of oxygen content $x$. Bottom: Amplitude of the relative difference $\Delta M/M$ at 100 K, giving the amplitude of the effect on the paramagnetic Curie term, as a function of the oxygen content $x$.

Figure 5

Superconducting diamagnetism under 15 G of four different YBCO$x$ samples after zero-field cooling down from 400 K with two different cooling rates. For every sample, the curve corresponding to the lower $T_C$ is obtained after the fast cooling down ($-10$ K/min, open symbols). Filled symbols: slow cooling rate ($-1$ K/min). No effect is measurable for $x=7.00$.

Figure 6

Magnetization relaxation measurements on YBCO$\mathit{6}.\mathit{43}$ sample ($x=6.43$) as a function of time. The dashed lines are the exponential fits to the data, for temperatures which allowed a reasonable fit. Inset, same data in log scale versus time for a chosen set of temperatures. $M_0$ denotes the magnetization at $t=\infty$.

Figure 7

Relaxation times assuming an exponential relaxation for four different samples, as a function of the inverse of the temperature (markers) and corresponding Arrhénius fits using Eq. (1) of text (solid lines).

Figure 8

Activation energies ($\Delta$) deduced from a fit to an Arrhenius law [Eq. (1)] of the characteristic relaxation times $\tau$ (see Fig. 7). For sample YBCO6.32, two different activation energies are observed below and above 312 K. The dashed lines are a guide for the eye.

Figure 9

Relationship between the variation of the number of free Cu $N$ per unit cell and the hole doping $p$ during a given relaxation interrupted every hour in order to measure $T_C$ and the amplitude of the Curie term for sample YBCO6.43. The amplitude of the Curie term gives $\Delta N$, while $T_C$ yields the variation of the hole doping $\Delta p$ (see Ref. 22). The solid line corresponds to 4$\Delta N=-\Delta p$. The arrow indicates the chronological order of the measurements.

Figure 10

Left axis. Light red triangles and light blue circles: measured magnetization during warming of sample YBCO6.43 after, respectively, fast and slow cooling rates. Dark red and dark blue solid lines: low-temperature fit and high-temperature extrapolation of the magnetization for, respectively, fast and slow cooling rate data. Right axis. Black dashed line: thermodynamical order parameter (explicitly chosen to reproduce the change of slope), red and blue dashed lines: realistic order parameters (blocked at low $T$, thermodynamical at high $T$), computed using the measured relaxation times, for, respectively, fast and slow cooling rates.