The use of superposition states of electronic spin is an important concept in the field of quantum computing. These states have the potential to advance information processing by allowing quantum bits or qubits to exist in multiple states simultaneously, vastly increasing computational power. However, one major hurdle in realizing the full potential of quantum computing is the challenge of maintaining quantum coherence for extended periods. To address this limitation, a study recently published in the Journal of Dalton Transactions, Dr. Toshiharu Ishizaki and Professor Tomoji Ozeki from the Department of Chemistry at Nihon University in Japan investigated S = 1/2 mononuclear metal complexes, which have recently garnered attention for their prolonged quantum-coherence lifetimes, making them promising candidates for spin qubits. Spin-lattice relaxation is a crucial aspect of their research, as it directly impacts the observation of quantum coherence, especially at higher temperatures where the longitudinal relaxation time tends to decrease rapidly. To address this challenge, the authors investigated the spin-lattice magnetic relaxation properties of an S = 1/2 3d-transition-metal complex embedded in a molecular metal oxide or polyoxometalate framework, with the expectation that these materials would exhibit slow magnetic relaxation.
Creating molecules with slow magnetic relaxation is a formidable task due to the dominance of fast quantum-mechanical relaxation pathways, primarily driven by intermolecular dipolar interactions. These interactions are typically responsible for rapid relaxation of electronic spin states, hampering the observation of quantum coherence. However, polyoxometalates, characterized by their large molecular skeletons, have shown promise in reducing intermolecular dipolar interactions. Additionally, the introduction of large cations further suppresses these interactions. For instance, the new study highlights the reduced intermolecular magnetic interactions observed in tetrabutylammonium salts compared to their potassium counterparts, even in undiluted form.
To decelerate magnetic relaxation at higher temperatures, it is essential to minimize spin-lattice relaxation. In systems with S = 1/2, such as the ones explored by the authors, zero-field splitting (ZFS) is not observed, eliminating the possibility of Orbach relaxation through excited quantum states. Instead, Raman spin-lattice relaxation becomes significant at elevated temperatures. This process involves the simultaneous absorption and emission of phonons, triggering spin flips. The rate of Raman spin-lattice relaxation exhibits an exponential dependence on temperature (T^n).
The research team initiated their investigation by synthesizing the potassium salt of a mononuclear copper(II) complex of the monolacunary α-Keggin silicotungstate, followed by the addition of a tetrabutylammonium cation via cation metathesis. This procedure yielded the tetrabutylammonium salt of the copper(II) complex, which was subjected to various analyses to confirm its composition and structure.
The authors demonstrated that continuous-wave X-band electron-spin-resonance (CW-ESR) spectrum of the tetrabutylammonium salt of the copper(II) complex resulted in several notable features. First, the spectrum indicated reduced intermolecular dipolar interactions, likely owing to the large tetrabutylammonium cations. Secondly, the analysis of the spectra revealed significant changes in the g-factors and hyperfine constants compared to the corresponding potassium salt. These changes suggested alterations in the coordination geometry of the copper ion from six-coordinated octahedral to five-coordinated square-pyramidal. They also investigated the static magnetic properties of the copper(II) complex by measuring the χMT product at various temperatures and magnetic field strengths. The results showed that the χMT value remained virtually constant, with only a slight deviation from the spin-only value of S = 1/2 at 300 K. This indicated that the copper(II) complex indeed exhibited an S = 1/2 spin state. Furthermore, magnetization measurements confirmed the absence of ZFS.
To investigate in more details the magnetic relaxation behavior of the copper(II) complex, the researchers performed AC magnetic susceptibility measurements on a magnetically diluted solid solution of the complex, which included a diamagnetic zinc(II) congener. These measurements revealed slow magnetic relaxation, especially when an external static magnetic field was applied. The position and movement of the χ″ peak in response to changes in the static magnetic field strength indicated the presence of slow magnetic relaxation. This observation was indicative of the suppression of inter- and intramolecular quantum-mechanical relaxations, particularly at higher static magnetic field strengths. The researchers further investigated the temperature dependence of magnetic relaxation at a fixed static magnetic field strength of 3000 Oe. As the temperature increased, the χ″ peak shifted to higher frequencies, suggesting an decrease in relaxation time. Notably, this peak was observed even at temperatures as high as 20 K, indicating the presence of slow magnetic relaxation. The experimental data were successfully fitted with a generalized Debye model, and the obtained relaxation time was among the longest reported for polyoxometalate-based transition-metal systems. This finding underscores the potential utility of this copper(II) complex in applications such as room-temperature molecular spin qubits.
The authors conducted relaxation time’s dependence analysis on the static magnetic field and temperature to gain insights into the underlying relaxation mechanisms. The analysis revealed that quantum-mechanical relaxation dominated at lower static magnetic field strengths, while direct relaxation took precedence at higher magnetic field strengths. In the intermediate region, the Raman process became the dominant relaxation mechanism. Interestingly, the Raman exponent (n = 2.30) associated with this complex was smaller than those observed in other S = 1/2 systems with organic ligands, implying a smaller decrease in relaxation time at higher temperatures.
The study also sought to understand the origin of the small Raman exponent (n = 2.30) observed in the complex. To do this, the authors conducted AC measurements on an undiluted powder sample of the complex. These measurements revealed shorter relaxation times compared to the magnetically diluted sample, indicating that magnetic relaxation mainly occurred through molecular processes. The larger dispersion coefficients for the undiluted sample compared to the diluted one suggested a significant influence of intermolecular dipolar interactions on magnetic relaxation.
In conclusion, Dr. Toshiharu Ishizaki and Professor Tomoji Ozeki’s research on slow magnetic relaxation in an S = 1/2 copper(II) complex incorporated into an α-Keggin-type silicotungstate has yielded valuable insights into the field of quantum computing. Their findings have illuminated the potential of polyoxometalate-based complexes as promising candidates for room-temperature molecular spin qubits with extended quantum coherence lifetimes. This study’s significance lies in its ability to bridge the gap in knowledge regarding S = 1/2 systems of polyoxometalates with a single S = 1/2 magnetic center, a previously unexplored territory. The observation of slow magnetic relaxation, combined with the small Raman exponent, suggests that this copper(II) complex may have advantages in maintaining quantum coherence at higher temperatures, a crucial requirement for practical quantum computing applications.
Ishizaki T, Ozeki T. Slow magnetic relaxation of a S = 1/2 copper(II)-substituted Keggin-type silicotungstate. Dalton Transaction . 2023;52(15):4678-4683.