Quantum magnetism in anisotropic dipolar systems

Final Report Summary - QMADS (Quantum magnetism in anisotropic dipolar systems)

The interplay of disorder, quantum fluctuations, and many body correlations in anisotropic dipolar systems, such as LiHo(Y)F4 and single molecule magnets is of much interest, fundamentally, in relation to understanding recent intriguing experimental results, and in designing future experiments. Specifically, anisotropic dipolar systems realize a ferromagnetic phase with competing interactions and an underlying spin glass phase. Furthermore, the application of a transverse field induces quantum fluctuations, which in turn induce an effective random longitudinal field. These random fields affect both thermodynamic and dynamic properties of anisotropic dipolar magnets. With respect to thermodynamic properties, in a recent experiment a peculiar linear dependence of the critical ferromagnetic temperature on the applied transverse field was found. Dynamically, single and pair of interacting magnetic dipoles have been experimentally investigated in the context of quantum bits. Studying the effect of the random field on pair dynamics is of much interest in this respect.

With respect to ferromagnetic systems with competing interactions and an underlying spin-glass phase, we have shown that the effective random field induced by the applied transverse field disorders the ferromagnetic phase via a novel disordering mechanism, which goes beyond the Imry-Ma result. An anlytic formula was derived for the transition line between a ferromagnet and a "quasi spin-glass". This expression was verified numerically, establishing the fact that a 3-dimensional ferroamgnet with competing interactions is disordered in a field much smaller than the interaction. We then showed that it is this mechanism, of disordering the ferromagnet by the underlying spin-glass phase, which results in the peculiar linear dependence of the critical temperature on the field, as mentioned above. These results were published as a Physical Review Letter, see Ref. [1] below.

We have then extended this study to include generic systems of near neighbor competing interactions, with a ferromagnetic mean. The interactions are taken from a random distribution which however is ferromagnetically biased, and the transition temperature is calculated as function of the random longitudinal field. Our results for the dipolar systems mentioned above are qualitatively reproduced, showing that this novel disordering mechanism is general to ferromagnetic systems with competing itneractions. These results are currently written up in a paper intended to be submitted to the Physical Review B, see Ref. [5] below.

In a second part of this project, we have exactly diagonalized the full 2-Ho problem, including the hyperfine interactions, and have calculated explicitly the random field in this system beyond perturbation theory. An unexpected consequence of this work is the ability to use our results to conceive an experiment that will measure explicitly the random field in the LiHo system as function of the applied external field. We have calculated the spin susceptibility as function of longitudinal and transverse field at various sweep rates, and made the connection between its value and the effective random field. Our results are published in the Physical Review B, see Ref. [2] below. We have made contact with the groups of Prof. Bernard Barbara in Grenoble and Prof. Romain Giraud in Dresden, who are interested to perform the relevant experiment.

With my student, Yair Vardi, we have studied pair dynamics in the LiHo system. We have found that in this system one can realize the intruiging physics of quantum dynamical arrest and quantum dynamical release, reported previously for amorphous solids. This first demonstration of quantum dynamical arrest in magnetic systems gives insight to the root of the mechanism. We further show that depding on the pair interaction, the release could be obtained through single spin (independent) dynamics, or through cooperative pair dynamics. These results will be written up next month, with the intention to submit the paper to Nature Physics, see Ref. [4] below.

The collaboration with Prof. Katzgraber and his group has lead to an intruiging work not conceived in the original IRG proposal, but certainly a result of the activities within it. We have investigated the question of the nature of anisotropic dipolar systems in the extreme dilute regime. The nature of the phase of this system was a subject of high controversy in the community, with contradicting theoretical, numerical, and experimental results. Using a well tailored algorithm that deals efficiently with the strong fluctuations in the extreme dilute systems, we have shown that the system maintains a low temperature spin-glass phase with a critical temperature linear in the concentration for dipole concentrations down to 2 orders of magnitude smaller than ever studied before. We further showed that at all small dilutions the system has the same critical exponent, suggesting that systems at all small concentrations are geometrically similar and belong to the same universality class. Our paper reporting these results (see Ref. [3] below) is to be submitted this month to Nature Physics.

The results achived in this project have significantly improved the understanding of disordered magnets in general, and of the LiHo system in particular. Our results in Refs. [1,5] below introduce a novel mechanism for the disordering of ordered systems, and provides a solution for very peculiar experimental results. Our results in Refs. [2,4] below shed light on the mechanism of quantum dynamical arrest, and provide insight to pair dynamics that could prove useful for quantum computing. Our results in [3] below solve a fundamental problem in condensed matter physics, with consequences to experiments, and to future numerical analysis of highly disordered systems.

Broader impact of the research includes
- Two M.Sc theses which were based on it.
- Strengthening collaboration with colleagues in Europe and in North America, which have led also to works on subjects beyond those included in this report.
- Significant contribution towards the PI receiving tenure and promotion to Associate Proffessor, both expected next year.

[1] J. C. Andresen, K. C. Thomas, H. G. Katzgraber, and M. Schechter. Novel disordering mechanism in ferromagnetic systems with competing interactions. Phys. Rev. Lett. 111, 177202 (2013).
[2] Y. Pollack and M. Schechter. Proposal for direct measurement of random fields in the LyHoF4 crystal. Phys. Rev. B 89, 064414 (2014).
[3] J. C. Andresen,H. G. Katzgraber, V. Oganesyan, and M. Schechter. Existence of a thermodynamic spin-glass phase in the zero-concentration limit of anisotropic dipolar systems. In preparation.
[4] Y. Vardi and M. Schechter. Quantum dynamical arrest and release in anisotropic dipolar magnets. In preparation.
[5] J. C. Andresen, H. G. Katzgraber, and M. Schechter. Disordering of anisotropic ferromagnetic systems with competing interactions by a small random field. In preparation.

Final Report Summary - QMADS (Quantum magnetism in anisotropic dipolar systems)

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