Figure 1

(Color online) Rietveld refined neutron-diffraction patterns of ${\text{Zn}}_2\text{VO}{\left({\text{PO}}_4\right)}_2$ at (a) 300 K and (b) 1.5 K. The observed and calculated diffraction patterns are indicated by circles and solid line, respectively. Solid line at the bottom shows the difference between observed and calculated patterns. Tick marks show the positions of nuclear Bragg peaks (space group: $I4cm$) and magnetic Bragg peaks (space group: $P\overline{1}$) (bottom row corresponding to the 1.5 K pattern only). The magnetic peaks are labeled with asterisks. The upper inset in the panel (b) shows an enlarged view of the diffraction pattern at 1.5 K. The lower inset in the panel (b) shows the temperature dependence of the ordered magnetic moment of V ion. (c) Magnetic pattern at 1.5 K, after subtraction of the pattern at 15 K (paramagnetic state), along with the patterns calculated by considering either a ferromagnetic (black line) or an antiferromagnetic (red squares) coupling along the $c$ direction. Tick marks show the Bragg peak positions considering a magnetic unit cell same as chemical unit cell.Reuse & Permissions

Figure 2

(Color online) (a) Crystal structure of the quasi-2D compound ${\text{Zn}}_2\text{VO}{\left({\text{PO}}_4\right)}_2$. (b) Projection of the crystal structure in the $ab$ plane. The dimmers of ${\text{ZnO}}_5$ square pyramids are evident.Reuse & Permissions

Figure 3

(Color online) (a) Magnetic structure of ${\text{Zn}}_2\text{VO}{\left({\text{PO}}_4\right)}_2$. The origin is shifted along the positive $c$ axis by an amount of $z/c=0.1174$. (b) The Néel-type AFM ordering of the spins in a given $ab$ plane. The nearest-neighbor and next-nearest-neighbor exchange interactions are labeled $J_1$ and $J_2$, respectively.Reuse & Permissions

Figure 4

(Color online) [(a)–(d)] Magnetic-diffraction patterns at 10, 7, 4.5, and 4 K, respectively, after subtracting the nuclear background at 15 K from all patterns. The solid curves [(a)–(d)] are the profiles calculated using the Warren function expected for a purely 2D magnetic ordering.Reuse & Permissions

Figure 5

(Color online) The in-plane (V-O1-P-O1-V) and out-of-plane (V-O1-Zn-O2-P-O1-V) shortest possible magnetic exchange interaction pathways.Reuse & Permissions

Figure 6

(Color online) Magnetic-diffraction patterns at (a) 1.5 K and (b) 2 K, after subtracting out the nuclear background at 15 K. The thin curves are the 3D Bragg peaks calculated by considering a pseudo-Voigt function for the resolution profile. The open circles are the calculated profile of the spin-waves contribution to the scattering with the values of $J_1$, $J_2$, $J_{\perp }$, and $D$ of $J_1=7.9\text{K}$ (AFM), $J_2=0.2\text{K}$ (AFM), $J_{\perp }=-0.2\text{K}$ (FM), and $D=-0.1$, respectively. The thick red curves are the sum of the spin waves and pseudo-Voigt (3D) peak profiles.Reuse & Permissions

Figure 7

(Color online) Calculated spin-wave spectrum along (a) $\left(h,h,0\right)$ and (b) $\left(0,0,l\right)$ directions. (c) The powder averaged spin-wave spectrum. (d) The powder averaged $S\left(Q\right)$ vs $Q$ with the values of $J_1$, $J_2$, $J_{\perp }$, and $D$ of $J_1=7.9\text{K}$ (AFM), $J_2=0.2\text{K}$ (AFM), $J_{\perp }=-0.2\text{K}$ (FM), and $D=-0.1$, respectively.Reuse & Permissions

Figure 8

(Color online) Temperature dependence of FWHM for the 3D magnetic Bragg peak (100) and the 2D spin-spin correlation length $\left({\xi }_{2\text{D}}\right)$. Several magnetic ordering regions, 3D long range with spin waves, 3D-reduced long range with 2D short range, and pure 2D short range, are indicated.Reuse & Permissions