Unconventional magnetic phase diagram of cuprate superconductor La2-xSrxCuO4 at quantum critical point x = 1/9

We propose a new magnetic phase diagram of La2-xSrxCuO4 around a quantum critical point x = 1/9 based on field-cooled magnetization measurements and critical fittings. A new phase boundary Tm2(H) is discovered which buries deeply below the first order vortex melting line in the vortex solid phase. The coupling between superconductivity and antiferromagnetism is found to be attractive below Tm2(H) while repulsive above. The attractive coupling between superconducting order and static antiferromagnetic order provides compelling experimental evidence that the antiferromagnetism microscopically coexists and collaborates with the high temperature superconductivity in cuprates.