In two recent papers [1, 2] we have shown how measurements of the static magnetic susceptibility of YBa₂Cu₃O_6+x single crystals, χ_c(T) for magnetic fields applied along the c-axis and χ_ab(T) for fields in the ab-plane, can give useful information about their thermodynamic properties which are still being hotly debated. SQUID magnetometry above the superconducting (s/c) transition temperature T_c is used for larger crystals while piezolever torque magnetometry gives χ_c(T)- χ_ab(T) for tiny crystals [2]. We briefly review the main results of this work - the T-dependent anisotropy well above T_c arises from the pseudogap and the g-factor anisotropy while at lower T there are Gaussian s/c fluctuations with a strong cut-off above 1.1 T_c. Appropriate analysis allows the relatively small, but still important, Curie terms to be separated from other contributions to the susceptibility. Our data support a picture in which the Curie terms arise from oxygen disorder in the Cu-O chains. This agrees with published work on polycrystalline samples where the sample cooling rate was varied [3], but here we show that the Curie plots flatten out above 200 K. We identify small effects of charge density wave (CDW) instabilities in the temperature (T) derivative of the in-plane susceptibility dχ_ab(T)/dT and discuss their x dependence. We discuss some of these results in connection with a study [4] at higher magnetic fields up to 33 T. We then present some new data for heavily under-doped crystals with hole concentrations per CuO₂ plane, from p =0.058 up to 0.073. This is the region where neutron scattering studies [5, 6] give evidence for competition between incommensurate magnetic short-range order and superconductivity. We have studied crystals with three values of x, measuring χ_c(T) and χ_ab(T) immediately after fixing x by quenching on to a copper block and again after allowing sufficient time at room temperature for the Cu-O chains to order. In this doping range, ordering the Cu-O chains increases Tc and substantially reduces the Curie term. The χ_D(T)= χ_c(T)- χ_ab(T) data show a weakly T-dependent linear region at higher T where χ_D(0) is 1-2 x10^-4emu/mol. We also discuss deviation from this linear behavior in terms of 2D or 3D Gaussian superconducting fluctuations at lower T.

References
[1] I. Kokanović and J. R. Cooper, Phys. Rev. B 94, 075155 (2016).
[2] I. Kokanović, et al., Phys. Rev. B 88, 060505(R) (2013).
[3] J. Biscaras, et al., Phys. Rev. B 85, 134517 (2012).
[4] Jing Fei Yu, et al., Phys. Rev. B 92, 180509(R) (2015).
[5] D. Haug, et al., Phys. Rev. Lett. 103, 017001 (2009).
[6] D. Haug, et al., New J. Phys. 12, 105006 (2010).

Keywords: Superconductivity, Magnetic properties, Strongly correlated systems