${}^{17}\mathrm{O}$ and ${}^{51}\mathrm{V}$ NMR for the zigzag spin-1 chain compound $\mathrm{Ca}{\mathrm{V}}_2{\mathrm{O}}_4$

${}^{51}\mathrm{V}$ NMR studies on $\mathrm{Ca}{\mathrm{V}}_2{\mathrm{O}}_4$ single crystals and ${}^{17}\mathrm{O}$ NMR studies on ${}^{17}\mathrm{O}$-enriched powder samples are reported. The temperature dependences of the ${}^{17}\mathrm{O}$ NMR linewidth and nuclear spin-lattice relaxation rate give strong evidence for a long-range antiferromagnetic transition at $T_N=78\mathrm{K}$ in the powder. Magnetic susceptibility measurements show that $T_N=69\mathrm{K}$ in the crystals. A zero-field ${}^{51}\mathrm{V}$ NMR signal was observed at low temperatures ($f\approx 237\mathrm{MHz}$ at $4.2\mathrm{K}$) in the crystals. The field-swept spectra with the field in different directions suggest the presence of two antiferromagnetic substructures. Each substructure is collinear, with the easy axes of the two substructures separated by an angle of 19(1)°, and with their average direction pointing approximately along the $b$ axis of the crystal structure. The two spin substructures contain equal numbers of spins. The temperature dependence of the ordered moment, measured up to $45\mathrm{K}$, shows the presence of an energy gap $E_G$ in the antiferromagnetic spin wave excitation spectrum. Antiferromagnetic spin wave theory suggests that $E_G∕k_B$ lies between 64 and $98\mathrm{K}$.

Figure 1

The orthorhombic crystal structure of $\mathrm{Ca}{\mathrm{V}}_2{\mathrm{O}}_4$ at room temperature. Large spheres, two inequivalent V sites; small dark spheres, Ca; and small light spheres, O. The crystallographic $a$ and $b$ axes are along the vertical and horizontal directions in the plane of the page, respectively. The $c$ axis is perpendicular to the page. The cuboid denotes the size of a unit cell.

Figure 2

Magnetic susceptibility $\chi$ versus temperature $T$ of the ${}^{17}\mathrm{O}$-enriched $\mathrm{Ca}{\mathrm{V}}_2{\mathrm{O}}_4$ powder sample measured in a field of $H=1\mathrm{T}$. The vertical arrow indicates the position of the antiferromagnetic transition temperature $T_N=78\mathrm{K}$.

Figure 3

Magnetic susceptibility $\chi$ versus temperature $T$ of $\mathrm{Ca}{\mathrm{V}}_2{\mathrm{O}}_4$ crystal 2 measured with the applied field $H=1\mathrm{T}$ along the $a$ and $b$ directions. The vertical arrow indicates the antiferromagnetic transition temperature $T_N=69\mathrm{K}$. The measurements were carried out under either field-cooled or zero-field-cooled conditions, as indicated.

Figure 4

Absorption spectrum of the ${}^{17}\mathrm{O}$ NMR signal for an ${}^{17}\mathrm{O}$-enriched powder sample of $\mathrm{Ca}{\mathrm{V}}_2{\mathrm{O}}_4$ at three different temperatures in an applied magnetic field $H=3.0\mathrm{T}$. A strong inhomogeneous broadening is observed close to the magnetic transition temperature $T_N=78\mathrm{K}$. The solid line at $77\mathrm{K}$ is a guide for the eye.

Figure 5

Temperature $T$ dependence of the ${}^{17}\mathrm{O}$ nuclear spin-lattice relaxation rate $1∕T_1^{*}$ [see Eq. (1)] of ${}^{17}\mathrm{O}$-enriched powder $\mathrm{Ca}{\mathrm{V}}_2{\mathrm{O}}_4$ in applied magnetic fields $H=3.0$ and $4.7\mathrm{T}$. A strong peak is observed close to the antiferromagnetic transition temperature $T_N=78\mathrm{K}$, as labeled by the arrow. Inset: The stretching exponent $\beta$ versus $T$.

Figure 6

Field-swept spectra with the applied magnetic field parallel to the $a-b$ plane at rf of $231\mathrm{MHz}$ (left panels) and $243\mathrm{MHz}$ (right panels). The angles between the field and the average of the two projections of the two spin directions onto the $a-b$ plane (${\mathit{S}}_m^{\prime }$ in Fig. 10) are labeled in each panel. The arrows indicate the positions of the peaks. ${\mathit{S}}_m^{\prime }$ is approximately parallel to the crystallographic $b$ axis. The spectra were measured at $4.2\mathrm{K}$ on crystal 1.

Figure 7

Semilogarithmic plot of nuclear spin-spin relaxation curves at rf $f=222$ MHz and external magnetic fields of 1.346 and $1.86\mathrm{T}$. The errors on the data points are smaller than the sizes of the symbols. The fields are parallel to the $a-b$ plane and form an angle of 31° from the ${\mathit{S}}_m^{\prime }$ direction. Inset: The field-swept spectrum measured at a fixed pulse separation of $18\mu \mathrm{s}$ and $f=222$ MHz in the same field direction. The vertical arrows show the field positions of 1.346 and $1.86\mathrm{T}$. The measurements were performed at $4.2\mathrm{K}$ on crystal 2.

Figure 8

Field-swept spectra with the applied magnetic field parallel to the $b\text{−}c$ plane at rf of $231\mathrm{MHz}$ (left panels) and $243\mathrm{MHz}$ (right panels). The angles between the field and the average of the two projections of the two spin directions onto the $b\text{−}c$ plane (${\mathit{S}}_m^{″}$ in Fig. 10) are labeled in each panel. The arrows indicate the positions of the peaks. The spectra were measured at $4.2\mathrm{K}$ on crystal 1.

Figure 9

Comparison of two spectra measured at rf $f=222\mathrm{MHz}$ with and without the field direction reversed. The fields are parallel to the $a\text{−}b$ plane and form angles of $-31°$ and 149° from the ${\mathit{S}}_m^{\prime }$ direction, respectively. The spectra were measured at $4.2\mathrm{K}$ on crystal 1.

Figure 10

The proposed ordered spin structure in $\mathrm{Ca}{\mathrm{V}}_2{\mathrm{O}}_4$. There are two different antiferromagnetic ordering substructures with equal numbers of spins, each of which has a collinear antiferromagnetic spin arrangement. $\Delta \theta$, $\Delta {\theta }^{\prime }$, and $\Delta {\theta }^{″}$ are the angles between these two directions, and their projections on $a\text{−}b$ and $b\text{−}c$ planes, respectively. ${\mathit{S}}_m$, ${\mathit{S}}_m^{\prime }$, and ${\mathit{S}}_m^{″}$ are the average of the two directions and their projections on $a\text{−}b$ and $b\text{−}c$ planes, respectively. ${\theta }_H^{\prime }$ $\left({\theta }_H^{″}\right)$ and ${\theta }_m^{\prime }$ $\left({\theta }_m^{″}\right)$ are the angles formed between a fixed arbitrary experimental reference direction in the $a\text{−}b$ $\left(b\text{−}c\right)$ plane and the applied field $\mathit{H}$ and ${\mathit{S}}_m^{\prime }$ $\left({\mathit{S}}_m^{″}\right)$, respectively.

Figure 11

Dependence of the peaks in the spectra at $4.2\mathrm{K}$ on the direction of the applied magnetic field, with the field in the $b\text{−}c$ (top two panels) and $a\text{−}b$ (bottom two panels) planes of crystal 1, where the rf are equal to 231 and $243\mathrm{MHz}$, respectively. For definitions of the angles ${\theta }_H^{\prime }$, ${\theta }_m^{\prime }$, ${\theta }_H^{″}$, and ${\theta }_m^{″}$, see Fig. 10. Circles and filled squares correspond to the two different spin ordering directions of the two magnetic substructures, respectively. The symbol ⋆ is used when the two peaks from the two spin directions overlap and only a single peak can be observed. The error in $H_{\text{peak}}$ is comparable to the size of the symbols unless shown explicitly. The solid and dotted lines represent the fits by the theoretical prediction in Eq. (3).

Figure 12

[(a) and (b)] Field-swept ${}^{51}\mathrm{V}$ NMR spectra at four different frequencies at $4.2\mathrm{K}$. The frequencies are given under each spectrum in units of MHz. The field is applied parallel to the ${\mathit{S}}_m^{″}$ direction. (c) The frequency versus the peak field of the spectra. The solid lines are linear fits by Eq. (7). The measurements were done on crystal 1 at $4.2\mathrm{K}$.

Figure 13

rf $f$ versus peak $H_{\text{peak}}$ in field-swept spectrum in crystal 2 at $4.2\mathrm{K}$. The field is applied along the ${\mathit{S}}_m^{\prime }$ direction. The solid lines are fits with Eq. (7).

Figure 14

Field-swept spectra at different temperatures on crystal 2. The temperature and the rf for each measurement are labeled in each panel. The solid lines are fits by Eq. (8) to extract the peak positions.

Figure 15

Temperature dependence of the ${}^{51}\mathrm{V}$ NMR spectra peak position in zero applied field in $\mathrm{Ca}{\mathrm{V}}_2{\mathrm{O}}_4$ crystal 2. The dotted and solid curves are fits by Eq. (19) with one-dimensional spin wave dispersion and Eq. (20) with three-dimensional dispersion, respectively.

Figure 16

Zigzag spin structure in $\mathrm{Ca}{\mathrm{V}}_2{\mathrm{O}}_4$. Due to the alternation of the spin directions along the $c$ axis, the interaction between the spins in the two legs of the zigzag chain is essentially decoupled. The possible misalignment of 19° between spins in the two legs of the zigzag chain is ignored. $J_1$ and $J_2$ are the nearest-neighbor interleg and intraleg exchange interactions, respectively.