Single ion magnets as magnetic probes of internal field in microparticle array
Introduction
Single Ion Magnets (SIMs) [[1], [2], [3]] and Single Molecular Magnets (SMMs) [[4], [5], [6]] are promising smallest elements of magnetic memory. Due to slow relaxation of magnetization they are able to keep magnetization induced by external magnetic field during some time after such field is switched off. Additionally to promising application for the creation of high-density magnetic data storage, chemically designed SMMs are attractive for molecular spintronics [7,8] and quantum computing [9,10].
Analysis of temperature and frequency dependences of AC susceptibility is a most often used experimental technique to check whether the system is SMM or not. An out-of-phase signal χ′′ indicates that the relaxation frequency of magnetization of the sample is lower than the frequency of AC magnetic field. Among complexes exhibiting slow relaxation one should mention a numerous systems, in which an out-of-phase signal is observed only in the presence of DC magnetic field. The reason for the absence of SMM behavior at zero field is fast quantum tunneling of magnetization (QTM) including both ground state tunneling and phonon-assistant one, which can appear when the non-axial contributions to magnetic anisotropy are important. Applied DC field acts as a factor suppressing QTM since such field allows the levels to avoid resonances. To distinguish such systems from those showing SMM behavior at zero field, they are often called field-induced SMMs (or SIMs). Important examples of such systems can be found in Refs. [11,12].
In SMM, slow relaxation is usually caused by the presence of a strong magnetic anisotropy of the “easy axis” type, which leads to the appearance of an effective barrier separating states with different spin orientations. The magnitude of this barrier depends on the values of the parameters of the spin Hamiltonian, which determine the energy spectrum of the complex (crystal field and spin-orbit interaction). The spin-lattice relaxation rate, in turn, is determined by both the size of the barrier and the strength of the spin-phonon interaction, which induces transitions between the spin levels that form the barrier. One of the factors suppressing the properties of SMM is Quantum Tunneling of Magnetization (QTM), which occurs when the symmetry of the system deviates from the axial one. This leads to the appearance of low-symmetry components of the crystal field. In this case, the rate of tunneling can significantly exceed the rates of phonon assisted thermally activated processes. The QTM significantly reduces the role of the anisotropy barrier, delaying the spin reorientation. In some cases, QTM can be completely suppressed by molecular design, but more often a constant external magnetic field directed along the anisotropy axis of a single-crystal sample is used as a factor suppressing QTM. Since in a powder sample different orientations of the anisotropy axes are presented, QTM is suppressed by the field component directed along the anisotropy axis in each complex [11,12]. This circumstance increases the external field required for the complete suppression of QTM in comparison with the case of a single crystal. A large number of systems are known that behave like SMM only in the presence of a constant external magnetic field. They are often referred to as field induced SMMs. In these compounds, in the absence of a field, QTM assisted relaxation is so fast, that it completely eliminates the slower phonon assisted relaxation. The applied field brings the spin levels of the system out of resonance, blocking tunneling. At temperatures lower than the barrier height (usually 2–5 K) QTM blocking causes a decrease in the spin relaxation frequencies down to 1–1000 Hz, available for low-frequency measurements in SQUID magnetometer. In contrast to SMM, in which the Orbach process makes the decisive contribution to the spin-lattice relaxation, in SIM the direct single phonon and Raman processes are dominating. In this context one can mention Kramers-type complexes for which QTM in a pure electronic subsystem is strictly forbidden but it becomes allowed due to hyperfine coupling of electronic and nuclear spins. Some of field-induced SIMs are based on Co(II) complexes (see review [13] and refs. Therein). Complexes of other 3 d ions are also known [13] as well as the field-induced SIMs based on lanthanide ions (e.g. Dy(III) [14], see more examples in Ref. [15]).
Note that the application of DC field can play a constructive role for both field induced SMMs and SIMs, and for systems showing SMM behavior at zero field. For the latter class of systems the application of field can often dramatically suppress relaxation as it was demonstrated for Mn12Ac SMM (see Ref. [16] and refs. Therein) and other systems including zero field SIMs [17].
As to field-induced SMMs and SIMs, it is worth saying that the requirement to use external field of few kOe intensity (typical magnitude of DC field able to switch on slow relaxation of magnetization) is not compatible with the strategy of the design of the low-energy local memory elements, which can give the impression that such systems are of minor technological importance as compared with zero-field SMMs and SIMs.
Our goal here is to demonstrate that field-induced SMMs and SIMs are no less attractive systems for the design of elements of quantum computers or magnetic memory units than zero-field SMMs and SIMs, if instead of field generated by external electromagnet one uses controllable “internal” magnetic field. In this work, we propose experimental technique which can be used to generate internal magnetic field in a composite material containing ferromagnetic rare-earth micromagnets and powder of field-induced SIM complexes, which atomic structure and SIM behavior was reliably analyzed in previous paper [18]. Remnant demagnetizing field of micromagnets is proportional to their residual magnetization Mr. In zero external field, ferromagnetic particles can be used as local sources of field. The local field affecting SIM rapidly decreases with distance, r, between the SIM and the center of individual ferromagnetic MPs ~1/r3, correspondently to known field distribution around magnetic dipole. In case of the chaotically distributed multiple MPs, the local field at the local SIM complex position depends a on space distribution of the MPs, gaps in between MPs and the local positions of SIM molecules around the particles. Multiples series of experiments allowed us to tune optimal volume concentration of SIM powder, corresponding to more or less homogeneous SIM distribution around MPs. Relatively homogeneous residual magnetic field in between ferromagnetic MPs allows us to detect a non additive AC susceptibility signal at zero external DC field for a composite material of SIM molecules with rare-earth micromagnets and to prove the possibility of observing SIM properties of the complex at zero external field due to the existence of residual field of microparticles in composite material.
Section snippets
Sample preparation
In our study the rare-earth PrDyFeCoB balls [17] are used as magnetically hard sources of demagnetizing field (Fig. 1a), acting on the SIMs molecules (Fig. 1b). Fig. 1S shows the comparison of optical images of MPs before and after coating with SIM complexes. Recently reported hexacoordinated Co(II) complex [CoLCl2]·H2O (L = bis-condensation product of diacetyl and 2-hydrazinyl-4,6-dimethylpyrimidine) is used as field-induced SIM exhibiting slow magnetic relaxation in applied fields HDC = 1 kOe
Separate analysis of AC susceptibility in microparticles and SIM complexes
The micromagnet free powder of Co(II) complex exhibits no slow magnetic relaxation at zero applied field as it evidences from the absence of χ′′ signal (straight line 1 in Fig. 3).
When external DC field of 3200 Oe has been applied to this powder sample, two maxima in the χ′′(f) dependence have appeared (curve 2 in Fig. 3) indicating that such DC field induces SIM properties typical of the case when both intra- and intermolecular relaxation mechanisms are involved in the game. The observed AC
Conclusions
- 1.
In composite material, containing PrDyFeCoB microparticles and Co(II) single ion magnet, two known in advance spin relaxation processes are observed in SIM molecules in the absence of external magnetic field. Residual demagnetizing fields of the rare-earth microparticles ~3 kOe are well enough to reproduce double peaks on the frequency dependence of magnetic susceptibility of composite material consisting of tuned amounts of the SIM powder and ferromagnetic MPs.
- 2.
Susceptibility of SIM, measured
CRediT authorship contribution statement
E. Dvoretskaya: Methodology, Validation, Investigation, Data curation, Writing – original draft, Visualization. A. Palii: Supervision, Conceptualization, Writing – review & editing. O. Koplak: Methodology, Validation, Investigation, Data curation, Writing – original draft, Visualization. R. Morgunov: Supervision, Conceptualization, Writing – review & editing.
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
The work was supported by the Ministry of Science and Higher Education of the Russian Federation (Grant No. 075-15-2020-779). The authors thank S. M. Aldoshin, D. V. Korchagin, for fruitful discussions and I N. Shcherbakov, Yu. P. Tupolova for providing the powder sample of the Co complex.
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