Equal-interval splitting of quantum tunneling in single-molecule magnets with identical exchange coupling

Yan-Rong Li, Rui-Yuan Liu, Hai-Qing Liu, and Yun-Ping Wang

Phys. Rev. B 89, 184401 – Published 1 May 2014

Abstract

The equal-interval splitting of quantum tunneling observed in simple-Ising-model systems of Ni $_{4}$ (3D) and Mn $_{3}$ (2D) single-molecule magnets (SMMs) is reported. The splitting is due to the identical exchange coupling in the SMMs, and is simply determined by the difference between the two numbers of the spin-down $n_{↓}$ and spin-up $n_{↑}$ molecules neighboring to the tunneling molecule. The splitting may be presented as $(n_{↓} - n_{↑}) J S / g μ_{0} μ_{B}$ , and the number of the splittings follows $n + 1$ where $n = n_{↓} + n_{↑}$ is the coordination number. Besides, since the quantum tunneling is heavily dependent on local spin environment, the manipulation of quantum tunneling may become feasible for this kind of system, which may shed light on applications of SMMs.

Received 22 January 2014

DOI:https://doi.org/10.1103/PhysRevB.89.184401

Authors & Affiliations

Yan-Rong Li, Rui-Yuan Liu, Hai-Qing Liu, and Yun-Ping Wang

Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, People's Republic of China

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Issue

Vol. 89, Iss. 18 — 1 May 2014

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Images

Figure 1
Field dependence of susceptibility $χ^{'}$ from $-$ 0.3 to 0.3 T at different temperatures measured on the Ni $_{4}$ single crystal, with the sweeping rate of 0.001 T/s and frequency of 11.3 kHz. The quantum tunneling peaks marked by black dotted lines originate from tunnelings between $| - 4 〉$ and $| 4 〉$ spin state, and the labeled number set in parentheses besides each dotted line indicates the local spin environment $(n_{↓}, n_{↑})$ of the tunneling molecules.
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Figure 2
(a) Field dependence of susceptibility $χ^{'}$ from $-$ 0.45 to 0.45 T at different given orientations measured on the Ni $_{4}$ single crystal, with the sweeping rate of 0.001 T/s and frequency of 11.3 kHz. (b) The field component parallel to the easy axis vs the angle between the field direction and the easy axis. Each group of data with the same orientation is obtained from the corresponding resonant field on the $χ^{'}$ - $H$ curves with the same color in (a).
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Figure 3
Magnetization ( $M / M_{s}$ ) of Mn $_{3}$ single crystal versus applied magnetic field with the sweeping rate of 0.003 T/s at different temperatures. The inset shows ZFC and FC curves.
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Figure 4
Sweep-rate-dependent magnetization ( $M / M_{s}$ ) versus applied magnetic field $μ_{0}$ H $_{z}$ (from $-$ 1.5 to 2.2 T) at 1.6 K measured on Mn $_{3}$ single crystal. The $d M / d H$ curve with a sweeping rate of 0.0005 T/s is given. The quantum tunneling peaks marked by the dotted lines of the same color belong to the same tunneling of $| m_{i} 〉 \to | m_{f} 〉$ , the labeled number set in parentheses besides each dotted line indicates the local spin environment $(n_{↓}, n_{↑})$ of the tunneling molecules.
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Figure 5
Sketch maps of three pairs of spin configurations with different LSE $(n_{↓}, n_{↑})$ in Ni $_{4}$ SMM, in correspondence to the tunnelings occurring at $-$ 0.21, $-$ 0.11, and 0 T in Fig. 1, respectively. Other equivalent spin configurations are not listed here for simplicity. The tunneling molecule is marked in black with a black arrow indicating its spin state, its four neighbors are marked in gray, with green and red arrows indicating spin-up and spin-down states, respectively, the blue lines between molecules represents the exchange couplings.
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Figure 6
Sketch maps of four spin configurations with different LSE $(n_{↓}, n_{↑})$ in Mn $_{3}$ SMM, other equivalent spin configurations are not listed here for simplicity. The tunneling molecule is marked in black, which could occupy either a spin-up or spin-down state. Its neighboring molecules occupying spin-up and spin-down states are marked in green and red, respectively. The black lines between molecules represent the exchange couplings.
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