Collinear Spin-density-wave Order and Anisotropic Spin Fluctuations in the Frustrated $J_1$--$J_2$ Chain Magnet NaCuMoO${}_4$(OH)

The phase diagram of the quasi-one-dimensional magnet NaCuMoO${}_4$(OH) is established through single-crystal NMR and heat-capacity measurements. The ${}^{23}$Na and ${}^1$H NMR experiments indicate a spiral and a collinear spin-density-wave (SDW) order below and above $B_c$ = 1.5-1.8 T, respectively. Moreover, in the paramagnetic state above the SDW transition temperature, the nuclear spin-lattice relaxation rate $1\mathrm{/}{T}_1$ indicates anisotropic spin fluctuations that have gapped excitations in the transverse spectrum but gapless ones in the longitudinal spectrum. These static and dynamic properties are well described by a theoretical model assuming quasi-one-dimensional chains with competing ferromagnetic nearest-neighbor interactions $J_1$ and antiferromagnetic next-nearest-neighbor interactions $J_2$ ($J_1$-$J_2$ chains). Because of the excellent crystal quality and good one dimensionality, NaCuMoO${}_4$(OH) is a promising compound to elucidate the unique physics of the frustrated $J_1$-$J_2$ chain.