Single-crystal ³¹P NMR studies of the frustrated square-lattice compound Pb₂(VO)(PO₄)₂

Abstract

The static and dynamic properties of V⁴⁺ spins (S=1/2) in the frustrated square-lattice compound Pb₂(VO)(PO₄)₂ were investigated by means of magnetic susceptibility χ and ³¹P nuclear magnetic resonance (NMR) shift (K) and ³¹P nuclear spin-lattice relaxation rate 1/T1 measurements on a single crystal. This compound exhibits long-range antiferromagnetic order below T_N≃3.65 K. NMR spectra above T_N show two distinct lines corresponding to two inequivalent P sites present in the crystal structure. The observed asymmetry in hyperfine coupling constant for the in-plane (P1) P site directly points toward a distortion in the square lattice at the microscopic level, consistent with the monoclinic crystal structure. The nearest- and next-nearest-neighbor exchange couplings were estimated by fitting K versus temperature T by a high-temperature series expansion for the spin susceptibility of the frustrated square lattice to be J₁/kB=(−5.4±0.5) K (ferromagnetic) and J₂/kB=(9.3±0.6) K (antiferromagnetic), respectively. 1/(T₁Tχ) is almost T independent at high temperatures due to random fluctuation of spin moments. Below 20 K, the compound shows an enhancement of 1/(T₁Tχ) which arises from a growth of antiferromagnetic spin correlations above T_N. Below T_N and for the field applied along the c axis, the NMR spectrum for the P1 site splits into two satellites and the spacing between them increases monotonically with decreasing T which is a direct evidence of a columnar antiferromagnetic ordering with spins lying in the ab plane. This type of magnetic ordering is consistent with expectation from the J₂/J₁≃−1.72 ratio. The critical exponent β=0.25±0.02 estimated from the temperature dependence of the sublattice magnetization as measured by ³¹P NMR at 11.13 MHz is close to the value (0.231) predicted for the two-dimensional XY model.