Field-induced magnetic ordering in the Haldane system ${\mathrm{PbNi}}_2{\mathrm{V}}_2{\mathrm{O}}_8$

The Haldane system ${\mathrm{PbNi}}_2{\mathrm{V}}_2{\mathrm{O}}_8$ was investigated by temperature-dependent magnetization $M\left(T\right)$ measurements at fields higher than $H_{\mathrm{c}}$; $H_{\mathrm{c}}$ is the critical field required to close the Haldane gap. It has been revealed that for $H>H_{\mathrm{c}}$, $M\left(T\right)$ exhibits a cusplike minimum at $T_{\min }$, below which it increases with a decrease in $T$ following a convex curve. These results were observed for both $H\Vert c$ and $H\perp c$, with the $c$ axis parallel to the chain. These data indicate the occurrence of field-induced magnetic ordering around $T_{\min }$. The phase boundaries for $H\Vert c$ and $H\perp c$ do not cross each other. This result is consistent with the theoretical calculation for a negative single-ion anisotropy $D$.

Figure 1

Field dependence of the magnetization of the ${\mathrm{PbNi}}_2{\mathrm{V}}_2{\mathrm{O}}_8$ powder samples.

Figure 2

Temperature dependence of the magnetization of ${\mathrm{PbNi}}_2{\mathrm{V}}_2{\mathrm{O}}_8$ for (a) $H\Vert c$ and (b) $H\perp c$. Arrows indicate $T_{\min }$ described in the text.

Figure 3

Magnetic phase diagram of ${\mathrm{PbNi}}_2{\mathrm{V}}_2{\mathrm{O}}_8$ derived from the present experiments (symbols). “AFO” and “Haldane state” represent the antiferromagnetically ordered state and the nonmagnetic spin-singlet state with a Haldane gap, respectively. Open symbols represent the data for $H\Vert c$, while filled ones are for $H\perp c$. Circles indicate $T_{\min }$ determined from the $M\left(T\right)$ curves, while diamonds indicate $H_{\mathrm{c}}$ estimated from the $M\left(H\right)$ curves.