Magnetic order in the quasi-one-dimensional spin-$1∕2$ molecular chain compound copper pyrazine dinitrate

We present evidence of magnetic order in the quasi-one-dimensional spin-1/2 molecular chain compound, copper pyrazine dinitrate $\mathrm{Cu}\left({\mathrm{C}}_4{\mathrm{H}}_4{\mathrm{N}}_2\right){\left(\mathrm{N}{\mathrm{O}}_3\right)}_2$. Zero field muon-spin relaxation measurements made at dilution refrigerator temperatures show oscillations in the measured asymmetry characteristic of a quasistatic magnetic field at the muon sites. Our measurements provide convincing evidence for long-range magnetic order below a temperature $T_{\mathrm{N}}=107\left(1\right)\mathrm{mK}$. This leads to an estimate of the interchain coupling constant of $\mid J^{\prime }\mid ∕k_{\mathrm{B}}=0.046\mathrm{K}$ and to a ratio of $\mid J^{\prime }∕J\mid =4.4\times {10}^{-3}$.

Figure 1

ZF ${\mu }^{+}\mathrm{SR}$ spectra for CuPzN at three temperatures. (a) $T=36\mathrm{mK}$: Oscillations are observed in the asymmetry, characteristic of long-range magnetic order. A fit is shown in Eq. (2). (b) $T=120\mathrm{mK}$: the spectra are described by two components. A fast relaxing signal, probably due to the existence of a radical state, and a larger component, seen to be exponential in form. A fit is shown to Eq. (3). (c) $T=405\mathrm{mK}$: The fast relaxing component is still evident although the larger component now shows a Gaussian form. A fit is shown to Eq. (3).

Figure 2

Temperature evolution of the variable parameters in Eq. (2) for $T⩽140\mathrm{mK}$. (a) Muon precession frequencies ${\nu }_i$ with fits shown to the expression ${\nu }_i\left(T\right)={\nu }_i\left(0\right){[1-{(T∕T_{\mathrm{N}})}^{\alpha }]}^{\beta }$. (b) Transverse relaxation rates ${\lambda }_i$ are seen to increase as the magnetic transition is approached from below. (c) The longitudinal relaxation rate $\Lambda$, which decreases as the transition is approached from below.

Figure 3

(a) Results of fitting data for $T>110\mathrm{mK}$ to Eq. (3). (Dashed lines show $T=T_{\mathrm{N}}$.) Inset: The parameter $\delta$ changing from $\delta =1$ (exponential relaxation) to $\delta =2$ (Gaussian relaxation) as the dynamics move out of the muon time window with increasing temperature. Main panel: The relaxation rate ${\lambda }_5$ increases as the transition is approached from above. (b) LF ${\mu }^{+}\mathrm{SR}$ spectra made at $T=2\mathrm{K}$ in several applied magnetic fields $B_{\mathrm{L}}$. Fits are shown to the LFKT function with $\Delta$ fixed at $0.271\mathrm{MHz}$ for all fields.