Quasi-one-dimensional uniform spin-$\frac{1}{2}$ Heisenberg antiferromagnet KNaCuP${}_2$O${}_7$ probed by ${}^{31}$P and ${}^{23}$Na NMR

Abstract

We present the structural and magnetic properties of KNaCuP${}_2$O${}_7$ investigated via x-ray diffraction, magnetization, specific heat, and ${}^{31}$P NMR and ${}^{23}$Na NMR measurements and complementary electronic structure calculations. The temperature dependent magnetic susceptibility and ${}^{31}$P NMR shift could be modeled very well by the uniform spin-$1/2$ Heisenberg antiferromagnetic chain model with nearest-neighbour interaction $J/k_{\mathrm{B}}\simeq 58.7$ K. The corresponding mapping using first principles electronic structure calculations leads to $J^{\mathrm{DFT}}/k_{\mathrm{B}}\simeq 59$ K with negligibly small inter-chain couplings ($J^{\prime }/k_{\mathrm{B}}$, $J^{\prime \prime }/k_{\mathrm{B}}<0.1$ K), further confirming that the system is indeed an one-dimensional uniform spin-$1/2$ Heisenberg antiferromagnet. The temperature-dependent unit cell volume could be described well using the Debye approximation with a Debye temperature of ${\Theta }_{\mathrm{D}}\simeq 294$ K, consistent with the heat capacity data. The diverging trend of the NMR spin-lattice relaxation rates (${}^{31}1/T_1$ and ${}^{23}1/T_1$) imply the onset of a magnetic long-range-ordering at very low temperatures supporting the anticipated $T_{\mathrm{N}}\simeq 0.38$ K from the inter-chain couplings. Moreover, the NMR spin-lattice relaxation rates show the dominant contributions from uniform ($q=0$) and staggered ($q=\pm \pi /a$) spin fluctuations in the high and low temperature regimes, respectively mimicking one-dimensionality of the spin-lattice. We have also demonstrated that ${}^{31}1/T_1$ in high temperatures varies linearly with $1/\sqrt{H}$ reflecting the effect of spin diffusion on the dynamic susceptibility. Further, the inter-chain frustration also substantially impede the magnetic ordering rendering the spin-lattice a perfect one-dimensional uniform spin-$1/2$ Heisenberg antiferromagnet over a wide temperature range.

arXiv comment15 pages, 13 figures, 1 table

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