Magnetic states of lightly hole-doped cuprates in the clean limit as seen via zero-field muon spin spectroscopy

We have performed extensive zero-field $\mu \text{SR}$ experiments on pure ${\text{YBa}}_2{\text{Cu}}_3{\text{O}}_{6+y}$ and diluted Y-rare-earth substituted ${\text{Y}}_{0.92}{\text{Eu}}_{0.08}{\text{Ba}}_2{\text{Cu}}_3{\text{O}}_{6+y}$ and ${\text{Y}}_{0.925}{\text{Nd}}_{0.075}{\text{Ba}}_2{\text{Cu}}_3{\text{O}}_{6+y}$ at light hole doping. A common magnetic behavior is detected for all the three families, demonstrating negligible effects of the isovalent Y-substituent disorder. Two distinct regimes are identified, separated by a crossover, whose origin is attributed to the concurrent thermal activation of spin and charge degrees of freedom: a thermally activated and a re-entrant antiferromagnetic regime. The peculiar temperature and hole density dependence of the magnetic moment $m\left(h,T\right)$ fit a model with a (spin) activation energy for the crossover between the two regimes throughout the entire investigated range. The magnetic moment is suppressed by a simple dilution mechanism both in the re-entrant regime $\left(0\le h\le 0.056\right)$ and in the so-called cluster spin glass state coexisting with superconductivity $\left(0.056<h\lesssim 0.08\right)$. We argue a common magnetic ground state for these two doping regions and dub it frozen antiferromagnet. Conversely either frustration or finite-size effects prevail in the thermally activated antiferromagnetic state, that vanishes at the same concentration where superconductivity emerges, suggesting the presence of a quantum critical point at $h_c=0.056\left(2\right)$.

Figure 1

(Color online) Temperature dependence for three ${\text{YBa}}_2{\text{Cu}}_3{\text{O}}_{6+y}$ samples of (a) the magnetization [Eq. (1)] and (b) the magnetic volume fraction defined in Sec. 3. Vertical arrows indicate the magnetic transition.

Figure 2

(Color online) Common phase diagram of ${\text{YBa}}_2{\text{Cu}}_3{\text{O}}_{6+y}$, ${\text{Y}}_{0.92}{\text{Eu}}_{0.08}{\text{Ba}}_2{\text{Cu}}_3{\text{O}}_{6+y}$, and ${\text{Y}}_{0.925}{\text{Nd}}_{0.075}{\text{Ba}}_2{\text{Cu}}_3{\text{O}}_{6+y}$: transition temperatures $T_N$ and $T_f$ from the fits to Eq. (2); experimental moment $m$ from fit and Eq. (1), encoded in the nonlinear color mapping (see right bar); hole density $h$, see Sec. 2 for details. The phase boundaries are best fits with $h_c=h_s=0.056\left(2\right)$ (see text) and $T_A$ labels the guide for the eye of Fig. 5. Inset: zoom of the superconducting $T_c$ from magnetic susceptibility.

Figure 3

(Color online) Dependence on hole doping of: (a) Re-entrant moment $m_F$ and activated moment $m_A$ from the fit to Eq. (2) (plus and cross, same quantities from the preliminary fit, see text); (b) Width of the moment distribution measured by muons above and below $T_A$. Squares for Y100%, circles for Eu8% and triangles for Nd7.5%.

Figure 4

(Color online) Temperature dependence of the moment $m$ with the best fit to Eq. (2), for the three families.

Figure 5

(Color online) Dependence on hole doping of the activation temperature $T_A$ from the best fits to Eq. (2). The line is a guide for the eye and the data for $h>h_C$ represent the transition temperature $T_f$.

Figure 6

(Color online) Magnetic moments $m_F$ and $m_A$ (same as Fig. 3) compared with theory (Ref. 50) (dotted line) and experiments (Ref. 51) on ${\text{La}}_{2-x}{\text{Sr}}_x{\text{Cu}}_{1-z}{\text{Zn}}_z{\text{O}}_4$(crosses).

Figure 7

(Color online) Scaling of the moment in the activated regime, $m_A$, with $T_N$ (for the solid line see the text).

Figure 8

(Color online) ${\text{YBa}}_2{\text{Cu}}_3{\text{O}}_{6+y}$, $y=0.27$, and $h=0.023$: FFT amplitude of the precessing asymmetry a three temperatures, vertically shifted for clarity. Inset: muon AO site with apical oxygen and the ${\text{CuO}}_2$ plaquette.

Figure 9

(Color online) Lattice parameter $c$ from XRD versus hole density from thermopower. The solid line is the calibration from Ref. 66.

Figure 10

(Color online) Muon asymmetry above $T_N$, just below and for $T⪡T_N$. Left: three ${\text{YBa}}_2{\text{Cu}}_3{\text{O}}_{6+y}$ samples, right: three corresponding ${\text{Y}}_{0.925}{\text{Nd}}_{0.075}{\text{Ba}}_2{\text{Cu}}_3{\text{O}}_{6+y}$ samples, from nearly undoped (top) to above the onset density for superconductivity.