Origin of the unusual strong suppression of low-frequency antiferromagnetic fluctuations in underdoped ${\mathrm{HgBa}}_2$${\mathrm{CuO}}_{4+\delta }$

Generally strong charge and magnetic inhomogeneities are observed in NQR/NMR experiments on underdoped cuprates. It is not the case for the underdoped ${\mathrm{HgBa}}_2$${\mathrm{CuO}}_{4+\delta }$, the most symmetric and highest $T_c$ single layer cuprate, whose magnetic inhomogeneity is strongly suppressed. Also neutron scattering experiments reveal a unique pair of weakly dispersive magnetic modes in this material. We propose that these special properties stem from the symmetric positioning of the O dopants between adjacent ${\mathrm{CuO}}_2$ layers that lead to a strong superexchange interaction between a pair of hole spins. In this Rapid Communication we present a theoretical model, which gives a consistent explanation to the anomalous magnetic properties of this material.

Figure 1

Projected DOS of a single supercell with the chemical potential set to zero for $\delta =0.125$ with the oxygen dopant O${}^d$ at the O(4) site. Top panel: ${\mathrm{CuO}}_2$ layer contribution to DOS, O(1) planar, O(2) apical O sites. Midpanel: Projected DOS of Hg atoms in the unit cell containing O${}^d$. Hg${}^1$ (Hg${}^3$) are the nearest to (furthest from) to O${}^d$, Hg${}^{2,4}$ remaining Hg sites at the corners of the ${\mathrm{Hg}}_4$ square. Bottom panel: Projected DOS at the dopant O${}^d$ located at the O(4) site. See Ref. [9] for the results for the case O${}^d$ is at the O(3) site.

Figure 2

The superexchange paths coupling a pair of hole spins on the CuO$-2$ layers through states of the intervening oxygen dopant. (a) O(4): antibonding Hg1-O(4) state and (b) O(3): $2p$-O(3) states weakly hybridized with (Hg1-Hg3) and (Hg2-Hg4) ions.

Figure 3

Occupation of holes in the ${\mathrm{CuO}}_2$ plane for the O(4) defect in Hg1201 as a function of the antibonding state energy ${\epsilon }_p$.

Figure 4

(a) O(4) dopant site: ${\epsilon }_p$-dependent low energy levels for O(4) defects in the ${\mathrm{Cu}}_4$-O-${\mathrm{Cu}}_4$ cluster. (b) O(3) dopant site: $J_H$ dependence of the energy levels for O(3) defect with the parameter set in Eq. (8). A solid red circle denotes a singlet state, a solid blue square a triplet, and a solid green star a spin $S=2$ state. The energy of the reference singlet state is shown in the inset.