- Open Access
Random transverse field effects on magnetic noise in spin systems
Phys. Rev. B 112, 014416 – Published 10 July, 2025
DOI: https://doi.org/10.1103/rf23-dnk7
Abstract
Motivated by experimental developments in non-Kramers spin-ice materials and the unclear role of disorder therein, we study the impact of random transverse fields on the dynamics of correlated magnetic systems. We model the effect of dilute, randomly placed transverse fields on quantities such as magnetic noise/susceptibility and the diffusivity of topological excitations. We consider a random ferromagnetic Ising chain (RTFIC) as well as three-dimensional spin ice. At low temperatures, both exhibit (sub-)diffusive defect dynamics, i.e., of domain walls and magnetic monopoles, respectively. Introducing sparse transverse fields leads to the emergence of an additional timescale on the order of the single-spin-flip time. We develop a Lindbladian framework that combines Monte Carlo simulations and exact diagonalization which allows us to characterize the dynamics and develop an analytical understanding of the phenomenon. This framework can be benchmarked in detail for the RTFIC. Our findings provide insights into the magnetization dynamics of disordered non-Kramers oxides, such as oxygen-diluted , and offer a framework for interpreting experimental observations in these systems.
Physics Subject Headings (PhySH)
Article Text
References (75)
- L. Savary and L. Balents, Quantum spin liquids: A review, Rep. Prog. Phys. 80, 016502 (2017).
- J. Knolle and R. Moessner, A field guide to spin liquids, Annu. Rev. Condens. Matter Phys. 10, 451 (2019).
- C. Broholm, R. Cava, S. Kivelson, D. Nocera, M. Norman, and T. Senthil, Quantum spin liquids, Science 367, eaay0668 (2020).
- J. Knolle, D. L. Kovrizhin, J. T. Chalker, and R. Moessner, Dynamics of a two-dimensional quantum spin liquid: Signatures of emergent Majorana fermions and fluxes, Phys. Rev. Lett. 112, 207203 (2014).
- J. Knolle, Dynamics of a Quantum Spin Liquid (Springer, Cham, 2016).
- M. Udagawa, L. D. C. Jaubert, C. Castelnovo, and R. Moessner, Out-of-equilibrium dynamics and extended textures of topological defects in spin ice, Phys. Rev. B 94, 104416 (2016).
- M. Gohlke, R. Moessner, and F. Pollmann, Dynamical and topological properties of the Kitaev model in a [111] magnetic field, Phys. Rev. B 98, 014418 (2018).
- H. Revell, L. Yaraskavitch, J. Mason, K. Ross, H. Noad, H. Dabkowska, B. Gaulin, P. Henelius, and J. Kycia, Evidence of impurity and boundary effects on magnetic monopole dynamics in spin ice, Nat. Phys. 9, 34 (2013).
- A. M. Samarakoon, S. Grigera, D. A. Tennant, A. Kirste, B. Klemke, P. Strehlow, M. Meissner, J. N. Hallén, L. Jaubert, C. Castelnovo et al., Anomalous magnetic noise in an imperfectly flat landscape in the topological magnet , Proc. Natl. Acad. Sci. USA 119, e2117453119 (2022).
- J. N. Hallén, S. A. Grigera, D. A. Tennant, C. Castelnovo, and R. Moessner, Dynamical fractal and anomalous noise in a clean magnetic crystal, Science 378, 1218 (2022).
- C.-C. Hsu, H. Takahashi, F. Jerzembeck, J. Dasini, C. Carroll, R. Dusad, J. Ward, C. Dawson, S. Sharma, G. M. Luke et al., Dichotomous dynamics of magnetic monopole fluids, Proc. Natl. Acad. Sci. USA 121, e2320384121 (2024).
- G. Misguich and F. Mila, Quantum dimer model on the triangular lattice: Semiclassical and variational approaches to vison dispersion and condensation, Phys. Rev. B 77, 134421 (2008).
- Z. Yan, Y.-C. Wang, N. Ma, Y. Qi, and Z. Y. Meng, Topological phase transition and single/multi anyon dynamics of spin liquid, npj Quantum Mater. 6, 39 (2021).
- F. Ritort and P. Sollich, Glassy dynamics of kinetically constrained models, Adv. Phys. 52, 219 (2003).
- A. J. Willans, J. T. Chalker, and R. Moessner, Site dilution in the Kitaev honeycomb model, Phys. Rev. B 84, 115146 (2011).
- O. Petrova, R. Moessner, and S. L. Sondhi, Hydrogenic states of monopoles in diluted quantum spin ice, Phys. Rev. B 92, 100401(R) (2015).
- A. Andreanov and P. A. McClarty, Order induced by dilution in pyrochlore XY antiferromagnets, Phys. Rev. B 91, 064401 (2015).
- T. Furukawa, K. Miyagawa, T. Itou, M. Ito, H. Taniguchi, M. Saito, S. Iguchi, T. Sasaki, and K. Kanoda, Quantum spin liquid emerging from antiferromagnetic order by introducing disorder, Phys. Rev. Lett. 115, 077001 (2015).
- Z. Zhu, P. A. Maksimov, S. R. White, and A. L. Chernyshev, Disorder-induced mimicry of a spin liquid in , Phys. Rev. Lett. 119, 157201 (2017).
- Spin Ice, edited by M. Udagawa and L. Jaubert (Springer, Cham, 2021).
- C. Castelnovo, R. Moessner, and S. L. Sondhi, Magnetic monopoles in spin ice, Nature (London) 451, 42 (2008).
- C. Castelnovo, R. Moessner, and S. L. Sondhi, Spin ice, fractionalization, and topological order, Annu. Rev. Condens. Matter Phys. 3, 35 (2012).
- G. Kolland, O. Breunig, M. Valldor, M. Hiertz, J. Frielingsdorf, and T. Lorenz, Thermal conductivity and specific heat of the spin-ice compound : Experimental evidence for monopole heat transport, Phys. Rev. B 86, 060402(R) (2012).
- S. T. Bramwell, S. Giblin, S. Calder, R. Aldus, D. Prabhakaran, and T. Fennell, Measurement of the charge and current of magnetic monopoles in spin ice, Nature (London) 461, 956 (2009).
- C. Castelnovo, R. Moessner, and S. L. Sondhi, Thermal quenches in spin ice, Phys. Rev. Lett. 104, 107201 (2010).
- S. Mostame, C. Castelnovo, R. Moessner, and S. L. Sondhi, Tunable nonequilibrium dynamics of field quenches in spin ice, Proc. Natl. Acad. Sci. USA 111, 640 (2014).
- L. Savary and L. Balents, Disorder-induced quantum spin liquid in spin ice pyrochlores, Phys. Rev. Lett. 118, 087203 (2017).
- O. Benton, Instabilities of a U(1) quantum spin liquid in disordered non-Kramers pyrochlores, Phys. Rev. Lett. 121, 037203 (2018).
- G. Lindblad, On the generators of quantum dynamical semigroups, Commun. Math. Phys. 48, 119 (1976).
- V. Gorini, A. Kossakowski, and E. C. G. Sudarshan, Completely positive dynamical semigroups of -level systems, J. Math. Phys. 17, 821 (1976).
- R. Dusad, F. K. Kirschner, J. C. Hoke, B. R. Roberts, A. Eyal, F. Flicker, G. M. Luke, S. J. Blundell, and J. S. Davis, Magnetic monopole noise, Nature (London) 571, 234 (2019).
- F. Morineau, V. Cathelin, P. C. W. Holdsworth, S. R. Giblin, G. Balakhrishnan, K. Matsuhira, C. Paulsen, and E. Lhotel, Satisfaction and violation of the fluctuation-dissipation relation in spin ice materials, Phys. Rev. Lett. 134, 096702 (2025).
- W. K. Hastings, Monte Carlo sampling methods using Markov chains and their applications, Biometrika 57, 97 (1970).
- R. Augusiak, F. Cucchietti, F. Haake, and M. Lewenstein, Quantum kinetic Ising models, New J. Phys. 12, 025021 (2010).
- P. L. Krapivsky, S. Redner, and E. Ben-Naim, A Kinetic View of Statistical Physics (Cambridge University Press, Cambridge, 2010).
- S. Suzuki, J.-i. Inoue, and B. K. Chakrabarti, Dilute and random transverse Ising systems, in Quantum Ising Phases and Transitions in Transverse Ising Models (Springer, Berlin, 2013), pp. 105–122.
- H.-P. Breuer and F. Petruccione, The Theory of Open Quantum Systems (Oxford University Press, Oxford, 2002).
- G. T. Landi, D. Poletti, and G. Schaller, Nonequilibrium boundary-driven quantum systems: Models, methods, and properties, Rev. Mod. Phys. 94, 045006 (2022).
- H. Weisbrich, C. Saussol, W. Belzig, and G. Rastelli, Decoherence in the quantum Ising model with transverse dissipative interaction in the strong-coupling regime, Phys. Rev. A 98, 052109 (2018).
- A. Rajagopal, The principle of detailed balance and the Lindblad dissipative quantum dynamics, Phys. Lett. A 246, 237 (1998).
- This is not to be confused with the angular frequency used in the PSD study later on in the manuscript.
- N. Wiener, Generalized harmonic analysis, Acta Math. 55, 117 (1930).
- C. Cardiner, Handbook of Stochastic Methods (Springer, Berlin, 1985).
- P. Welch, The use of fast fourier transform for the estimation of power spectra: A method based on time averaging over short, modified periodograms, IEEE Trans. Audio Electroacoust. 15, 70 (1967).
- D. Chandler, Introduction to Modern Statistical Mechanics (Oxford University Press, Oxford, 1987).
- K. Nishi, M. L. Kilfoil, C. F. Schmidt, and F. C. MacKintosh, A symmetrical method to obtain shear moduli from microrheology, Soft Matter 14, 3716 (2018).
- J. W. Haus and K. W. Kehr, Diffusion in regular and disordered lattices, Phys. Rep. 150, 263 (1987).
- U. Choudhury, A. V. Straube, P. Fischer, J. G. Gibbs, and F. Höfling, Active colloidal propulsion over a crystalline surface, New J. Phys. 19, 125010 (2017).
- Y. Su, P.-Y. Lai, B. J. Ackerson, X. Cao, Y. Han, and P. Tong, Colloidal diffusion over a quasicrystalline-patterned surface, J. Chem. Phys. 146, 214903 (2017).
- R. D. Hanes and S. U. Egelhaaf, Dynamics of individual colloidal particles in one-dimensional random potentials: A simulation study, J. Phys.: Condens. Matter 24, 464116 (2012).
- F. Evers, C. Zunke, R. D. L. Hanes, J. Bewerunge, I. Ladadwa, A. Heuer, and S. U. Egelhaaf, Particle dynamics in two-dimensional random-energy landscapes: Experiments and simulations, Phys. Rev. E 88, 022125 (2013).
- P. Fulde, L. Pietronero, W. Schneider, and S. Strässler, Problem of Brownian motion in a periodic potential, Phys. Rev. Lett. 35, 1776 (1975).
- R. Festa and E. G. d'Agliano, Diffusion coefficient for a Brownian particle in a periodic field of force I. Large friction limit, Physica A 90, 229 (1978).
- E. J. Nilsson Hallén, Dynamics of frustrated magnetic systems—emergent fractals and anomalous magnetic noise in spin ice, Ph.D. Thesis, University of Cambridge (2023).
- B. K. Chakrabarti and M. Acharyya, Dynamic transitions and hysteresis, Rev. Mod. Phys. 71, 847 (1999).
- G. Sala, M. Gutmann, D. Prabhakaran, D. Pomaranski, C. Mitchelitis, J. Kycia, D. Porter, C. Castelnovo, and J. Goff, Vacancy defects and monopole dynamics in oxygen-deficient pyrochlores, Nat. Mater. 13, 488 (2014).
- J. Goff (private communication, 2023).
- L. D. Jaubert and P. C. Holdsworth, Signature of magnetic monopole and Dirac string dynamics in spin ice, Nat. Phys. 5, 258 (2009).
- A. Sen and R. Moessner, Topological spin glass in diluted spin ice, Phys. Rev. Lett. 114, 247207 (2015).
- Z. Lu, R. Schäfer, J. N. Hallén, and C. R. Laumann, [111]-strained spin ice: Localization of thermodynamically deconfined monopoles, Phys. Rev. B 110, 184421 (2024).
- T. Yu, Non-Markovian quantum trajectories versus master equations: Finite-temperature heat bath, Phys. Rev. A 69, 062107 (2004).
- B. Tomasello, C. Castelnovo, R. Moessner, and J. Quintanilla, Correlated quantum tunneling of monopoles in spin ice, Phys. Rev. Lett. 123, 067204 (2019).
- Y. Wang, T. Reeder, Y. Karaki, J. Kindervater, T. Halloran, N. Maliszewskyj, Y. Qiu, J. Rodriguez, S. Gladchenko, S. Koohpayeh et al., Monopolar and dipolar relaxation in spin ice , Sci. Adv. 7, eabg0908 (2021).
- D. Radicevic, Spin structures and exact dualities in low dimensions, arXiv:1809.07757.
- A. W. Sandvik, Computational studies of quantum spin systems, AIP Conf. Proc. 1297, 135 (2010).
- A. W. Sandvik, Stochastic series expansion methods, arXiv:1909.10591.
- K. B. Lauritsen and H. C. Fogedby, Critical exponents from power spectra, J. Stat. Phys. 72, 189 (1993).
- K. B. Lauritsen and N. Ito, Spectral method determination of dynamic exponents for Ising models, Physica A 202, 224 (1994).
- K. MacIsaac and N. Jan, On the dynamic exponent of the two-dimensional Ising model, J. Phys. A: Math. Gen. 25, 2139 (1992).
- L. Landau and E. Lifshitz, Chapter XII—Fluctuations, in Statistical Physics, 3rd ed. edited by L. Landau and E. Lifshitz (Butterworth-Heinemann, Oxford, 1980), pp. 333–400.
- A. A. Clerk, M. H. Devoret, S. M. Girvin, F. Marquardt, and R. J. Schoelkopf, Introduction to quantum noise, measurement, and amplification, Rev. Mod. Phys. 82, 1155 (2010).
- A. J. Daley, Quantum trajectories and open many-body quantum systems, Adv. Phys. 63, 77 (2014).
- H. van Beijeren, Transport properties of stochastic Lorentz models, Rev. Mod. Phys. 54, 195 (1982).
- B. Derrida, Velocity and diffusion constant of a periodic one-dimensional hopping model, J. Stat. Phys. 31, 433 (1983).
- welch—scipy v1.14.1 manual (2024).