Zn $_2$ VO（PO $_4)_2$和用Ti $^{4+}$稀释）的反铁磁性
Antiferromagnetism of Zn$_2$VO(PO$_4)_2$ and the dilution with Ti$^{4+}$
摘要：
我们报告的静态和动态性质的反铁磁化合物Zn $_{2}$（VO）（PO $_{4}$）$_{2}$，和非磁性Ti $^{4+}$掺杂的V $^{4+}$网站的后果。$^{31}$ P的核磁共振谱和自旋晶格弛豫速率（$1/T_1$）一致地表明在低于$T_N= 3.8-3.9$ \，K.由9.4MHz下$^{31}$ P NMR测量的亚晶格磁化强度的温度依赖性估算的临界指数$β=0.33 \pm 0.02$与三维自旋模型的普适类一致. $^{31}$ P核和V $^{4+}$自旋之间的各向同性和轴向超精细耦合分别为$A_{\rm hf}^{\rm iso} = (9221 \pm 100)$ Oe/ $μ_{\rm B}$和$A_{\rm hf}^{\rm ax} = (1010 \pm 50)$ Oe/ $μ_{\rm B}$。用量子Monte-Carlo方法模拟了正方晶格上的Heisenberg模型，得到了6.5K以上的磁化率数据和4.5K以上的热容数据. $J$的该值与从NMR位移、$1/T_1$和电子自旋共振（ESR）强度分析获得的值一致。用非磁性Ti $^{4+}$掺杂Zn $_2$ VO（PO）$_4)_2$导致$J$值的边际增加和自旋晶格的总体稀释。与最近的\textit{ab initio}结果相反，我们既没有发现单斜结构畸变的证据，也没有发现掺杂样品的磁性一维性的签名，Ti $^{4+}$高达15\%。Néel温度$T_{\rm N}$随着非磁性掺杂剂的量的增加而线性降低。
英文摘要：
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 $β=0.33 \pm 0.02$ 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/$μ_{\rm B}$ and $A_{\rm hf}^{\rm ax} = (1010 \pm 50)$ Oe/$μ_{\rm B}$, 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 Néel temperature $T_{\rm N}$ decreases linearly with increasing the amount of the non-magnetic dopant.
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