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 $A_{\rm hf}^{\rm iso} = (9221 \pm 100)$ Oe/$\mu_{\rm B}$ and $A_{\rm hf}^{\rm ax} = (1010 \pm 50)$ Oe/$\mu_{\rm B}$, 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 N\'eel temperature $T_{\rm N}$ decreases linearly with increasing the amount of the non-magnetic dopant.
Highlights
Square lattice of antiferromagnetically coupled Heisenberg spins is the simplest spin model in two dimensions (2D).[1,2] Its properties are nowadays well established by extensive numerical studies.[3,4,5]The case of spin-1 2 entails strong quantum effects that reduce the sublattice magnetization[4] and have an impact on the correlation length[6] and spin dynamics.[7,8] The ideal 2D model lacks long-range order (LRO) above zero temperature, following the Mermin-Wagner theorem.[9]
The integrated electron spin resonance (ESR) intensity [IESR(T )] increases with decreasing temperature and exhibits a broad maximum at about 7 K as observed in χ(T ) (Fig. 2) and K(T )
The total hyperfine coupling constant at the P site is the sum of transferred hyperfine (Atrans) and dipolar (Adip) couplings produced by V4+ spins, i.e., Ahf = z′ Atrans + Adip, where z′ = 2 is the number of nearestneighbor V4+ spins of the P site
Summary
Square lattice of antiferromagnetically coupled Heisenberg spins is the simplest spin model in two dimensions (2D).[1,2] Its properties are nowadays well established by extensive numerical studies.[3,4,5]. 1 2 entails strong quantum effects that reduce the sublattice magnetization[4] and have an impact on the correlation length[6] and spin dynamics.[7,8] The ideal 2D model lacks long-range order (LRO) above zero temperature, following the Mermin-Wagner theorem.[9] any real material features a non-negligible interplane coupling that triggers the LRO at a non-zero temperature TN .10. When interplane couplings are frustrated and inactive, the LRO is driven by anisotropy terms in the spin Hamiltonian.[11] Any real material features a non-negligible interplane coupling that triggers the LRO at a non-zero temperature TN .10 When interplane couplings are frustrated and inactive, the LRO is driven by anisotropy terms in the spin Hamiltonian.[11]
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