Antiferromagnetism of Zn${}_2$VO(PO${}_4{)}_2$ and the dilution with Ti${}^{4+}$

Abstract

We report static and dynamic properties of the antiferromagnetic compound Zn${}_2$(VO)(PO${}_4$)${}_2$, and the consequences of non-magnetic Ti${}^{4+}$ doping at the V${}^{4+}$ site. ${}^{31}$P nuclear magnetic resonance (NMR) spectra and spin-lattice relaxation rate ($1/T_1$) consistently show the formation of the long-range antiferromagnetic order below $T_N=3.8-3.9$\,K. The critical exponent $\beta =0.33\pm 0.02$ estimated from the temperature dependence of the sublattice magnetization measured by ${}^{31}$P NMR at 9.4\,MHz is consistent with universality classes of three-dimensional spin models. The isotropic and axial hyperfine couplings between the ${}^{31}$P nuclei and V${}^{4+}$ spins are $A_{\mathrm{hf}}^{\mathrm{iso}}=(9221\pm 100)$ Oe/${\mu }_{\mathrm{B}}$ and $A_{\mathrm{hf}}^{\mathrm{ax}}=(1010\pm 50)$ Oe/${\mu }_{\mathrm{B}}$, respectively. Magnetic susceptibility data above 6.5\,K and heat capacity data above 4.5\,K are well described by quantum Monte-Carlo simulations for the Heisenberg model on the square lattice with $J\simeq 7.7$\,K. This value of $J$ is consistent with the values obtained from the NMR shift, $1/T_1$ and electron spin resonance (ESR) intensity analysis. Doping Zn${}_2$VO(PO${}_4{)}_2$ with non-magnetic Ti${}^{4+}$ leads to a marginal increase in the $J$ value and the overall dilution of the spin lattice. In contrast to the recent \textit{ab initio} results, we find neither evidence for the monoclinic structural distortion nor signatures of the magnetic one-dimensionality for doped samples with up to 15\% of Ti${}^{4+}$. The Néel temperature $T_{\mathrm{N}}$ decreases linearly with increasing the amount of the non-magnetic dopant.

13 pages, 12 figures, 2 tables

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