Observation of a Half Step Magnetization in the $\{{\mathrm{Cu}}_3\}$-Type Triangular Spin Ring

We report pulsed field magnetization and ESR experiments on a $\{{\mathrm{Cu}}_3\}$ nanomagnet, where antiferromagnetically coupled ${\mathrm{Cu}}^{2+}$ ($S=1/2$) ions form a slightly distorted triangle. The remarkable feature is the observation of a half step magnetization, hysteresis loops, and an asymmetric magnetization between a positive and a negative field in a fast sweeping external field. This is attributed to an adiabatic change of magnetization. The energy levels determined by ESR unveil that the different mixing nature of a spin chirality of a total $S=1/2$ Kramers doublet by virtue of Dzyaloshinskii-Moriya interactions is decisive for inducing half step magnetization.

Figure 1

(a) The crystal structure of the ${\mathrm{Cu}}_3$-triangle spin ring. For clarity, only the copper (medium blue balls), the sodium (large purple balls), and the oxygen (small red balls) ions are shown. (b) A zoom of three ${\mathrm{Cu}}^{2+}$ ions with local coordinations. The solid lines are a connection between the nearest ${\mathrm{Cu}}^{2+}$ ions. The numbers represent $\mathrm{Cu}\cdots \mathrm{Cu}$ distances; ${\mathrm{Cu}}_1\cdots {\mathrm{Cu}}_2={\mathrm{Cu}}_1\cdots {\mathrm{Cu}}_3=4.696\AA$ and ${\mathrm{Cu}}_2\cdots {\mathrm{Cu}}_3=4.689\AA$.

Figure 2

Magnetization curve vs pulsed magnetic field at 0.4 K. The saturated magnetization is scaled to $g{\mu }_{B}S$. The thin line is the calculated isothermal magnetization curve. Arrows denote sweep directions ($A\to B\to C\to D$). The inset shows the pulsed magnetic field versus time.

Figure 3

(a) Representative ESR spectrum at 8.8 K. The numbers denote the ESR transitions between the energy levels marked in Fig. 4. (b),(c) Angle dependence of the ESR spectrum at 8.8 K. The solid lines are the calculated curves.

Figure 4

Energy level diagrams for the Hamiltonian of Eq. (1) for a magnetic field parallel and perpendicular to the plane, respectively. For the fitting parameters, see the text.