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We report results of magnetization and $^{31}$P NMR measurements under highpressure up to 6.4~GPa on RbMoOPO$_4$Cl, which is a frustrated square-latticeantiferromagnet with competing nearest-neighbor and next-nearest-neighborinteractions. Anomalies in the pressure dependences of the NMR shift and thetransferred hyperfine coupling constants indicate a structural phase transitionat 2.6~GPa, which is likely to break mirror symmetry and triggers significantchange of the exchange interactions. In fact, the NMR spectra in magneticallyordered states reveal a change from the columnar antiferromagnetic (CAF) orderbelow 3.3~GPa to the N\'{e}el antiferromagnetic (NAF) order above 3.9~GPa. Thespin lattice relaxation rate $1/T_1$ also indicates a change of dominantmagnetic fluctuations from CAF-type to NAF-type with pressure. Although the NMRspectra in the intermediate pressure region between 3.3 and 3.9 GPa showcoexistence of the CAF and NAF phases, a certain component of $1/T_1$ showsparamagnetic behavior with persistent spin fluctuations, leaving possibilityfor a quantum disordered phase. The easy-plane anisotropy of spin fluctuationswith unusual nonmonotonic temperature dependence at ambient pressure getsreversed to the Ising anisotropy at high pressures. This unexpected anisotropicbehavior for a spin 1/2 system may be ascribed to the strong spin-orbitcoupling of Mo-4$d$ electrons.

Pressure-induced phase transition in the $J_1$-$J_2$ square lattice antiferromagnet RbMoOPO$_4$Cl