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Dmitry A. Garanin - Research

General direction of my research is Theory of Magnetic Phenomena and Statistical Physics, including 

  • Current topics:
    • random-field and random-anisotropy magnets
    • relaxation and decoherence, including spin-lattice interaction, superradiance and phonon bottleneck
    • magnetomechanical effects in nanomagnets
    • quantum transitions including Landau-Zener effect
    • spin tunneling in molecular magnets, including fronts of tunneling
    • magnetic deflagration
    • structure and dynamics of small magnetic particles, including internal spin waves
    • collapse of skyrmions in ferro- and antiferromagnets
  • Older topics:
    • magnetic phase transitions
    • low-dimensional magnetism and surface magnetis
    • relaxation of spin waves
    • domain-wall motion
My publication list allows viewing papers that belong to any of these groups separately. At the time being, my hot topics are random-field and random-anisotropy magnets, fronts of tunneling in molecular magnets, and collective spin-phonon relaxation.

Theoretical arguments of 70th by Imry & Ma, Larkin, and Chudnovsky predict that whatever small random field or random anisotropy would destroy a long-range order in magnetic and other system (vortex lattice in superconductors, charge-density waves, etc.). Using modern computer power and advanced numerical algorithms, we are carrying out an extensive investigation of ordering in different models described by n-component classical spins in d dimensions. Contrary to theoretical expectations, we have found that initially ordered systems only partially disorder if the system supports singularities (vortices and vortex lines, hedgehogs) or smooth topological structures (kinks, skyrmions). The former exist for n d, and necessarily arize in the completely disordered Imry-Ma state, as follows from our new topological argument. As creating singularities cost energy, the Imry-Ma state is not the ground state of the system and the system remains partially ordered. The case n = d + 1 is a marginal case. Although the IM state is the grounds state, the system cannot reach it by relaxation because of conservation of the topological charge (e.g., of skyrmions). We have published a big paper on the 3d random-field xy model (n = 2) [Phys. Rev. B 88, 224418 (2013)] and posted a Letter containing the above general arguments illustrated by numerical results [arXiv]. Here is the info page of the project containing animations.

Pinned vortex lines in the 3d random-field xy model

I am especially interested in the so-called "PhononBottleneck" problem in the spin-lattice relaxation that has not recieved a proper analytical treatment since 1941. While first steps have been done in Spring 2006 and two papers have been published [Phys. Rev. B 75, 094409 (2007) and Phys. Rev. B 77, 024429 (2008)], a lot of new efforts are due, both on the way of analytics and numerical calculations for quantum and classical models. A possible competition between the phonon bottleneck (that tends to suppress spin relaxation) and the photon [Phys. Rev. Lett. 89, 157201 (2002)] and phonon [Phys. Rev. Lett. 93, 257205 (2004)] superradiance (that tends to increase spin relaxation) is an exciting question to be investigated.

The phonon bottleneck: Emitted phonons are being reabsorbed by spins and thus spin-lattice relaxation slows down dramatically

Right now the so-called Landau-Lifshitz-Bloch (LLB) equation of motion for the magnetization at finite temperatures, derived in 90th [see, e.g., Phys. Rev. B 55, 3050–3057 (1997)], becomes the best candidate to be applied to the processes of thermal magnetic recording. The LLB equation describes both transverse and longitudinal relaxation of the magnetization vector. My colleagues and I are further developing the aspects of the LLB equation that are important for industrial applications in magnetic information storage.

LLB equation captures dynamics of the magnetization length and can be used to describe the effect of heating in fast magnetization reversal

We are continuing working on the beautiful parameter-free spin-phonon interaction that in the rotating lattice frame has the form as simple as -S [Phys. Rev. B 72, 094426 (2005)]. This very basic interaction that allows to obtain some new model-independent results in spin relaxation and rederive some old results in a simple way, has confused a number of theorists.  

Another hot topic is the magnetic burning or deflagration that recently was experimentally observed by Myriam Sarachik's group at the City College of the CUNY and by Javier Tejada's group at the University of Barcelona. Although the first and simplest theory of the magnetic burning has been recently published (Suzuki et al, PRL 2005) that were a lot of questions to be clarified such as the role of spin tunneling and the ignition of the magnetic avalanch. Here is the support page with animations and link to our first paper on magnetic deflagration, Phys. Rev. B 76, 054410-(13) (2007).

Magnetic deflagration (burning): Decay of a metastable state triggered by the temperature

Continuing the research on magnetic deflagration, we discovered fronts of spin tunneling in molecular magnets [Phys. Rev. Lett. 102, 097206-(4) (2009), Phys. Rev. B 80, 014406-(11) (2009)]. This is the so-called "cold" or quantum deflagration. In contrast to the standard deflagration, here the parameter controlling the escape rate of magnetic molecules out of the metastable state is not temperature but the dipolar field produced by the magnetic molecules themselves. This self-consistent dipolar field can bring the system on or off tunneling resonance. We have shown that the system of magnetic molecules self-organizes in such a way that the molecules are on resonance in a broad region along the propagation direction, thus facilitating tunneling and motion of the front.

"Cold" or quantum magnetic deflagration: Decay of the metastable state via resonance quantum transition controlled by the dipolar field

With PhD student Reem Jaafar and further with undergraduate student Saaber Shoyeb we incorporated both thermal and quantum effects in our generalized theory of magnetic deflagration in 1d, [Phys. Rev. B 81, 180401(R) (2010) and Phys. Rev. B 85, 094403 (2012)]. Current work is being done on the full 3d theory.

The latest of my areas of interest is magnetomechanical effects in nanomagnets related to conservation of the angular momentum. Recently E. M. Chudnovsky and I have shown that the problem of spin tunneling in a rigid nanoparticle has a beautiful analytical solution. If the particle's moment of inertia is below some critical value, the spin cannot tunnel and localizes in one of the up/down states. The EPL article of our PHD student Reem Jaafar considering a single magnetic molecule rotating between conducting leads has been chosen for a feature in Europhysics News and has been featured in Lehman Today. A new type of spin decoherence arises from interaction of an embedded spin with a torsional cantilever, Phys. Rev. X 1, 011005 (2011).

Spin tunneling transitions excite torsional cantilever

Our very new topic is skyrmion collapse in 2d magnets that occurs because the discreteness of the lattice. With our PhD student Liufei Cai we have calculated analytically and numerically the lifetime of skyrmions in both ferro- and antiferromagnets in Phys. Rev. B 86, 024429 (2012). The results can be relevant in high-temperature superconductivity since all these materials have planes of magnetic atoms.

1) Skyrmion and a gas of emitted spin waves; 2) Spin waves carry away the remaining energy of a collapsed skyrmion. Vertical axis: Mz.

These are my main current external collaborations:

  • Prof. Eugene Chudnovsky, Lehman College, CUNY - collective spin-phonon relaxation, spin tunneling
  • Prof. Rolf Schilling, University of Mainz, Germany - Landau-Zener effect
  • Prof. Hamid Kachkachi, University of Perpignan, France - small magnetic particles
  • Dr. Oksana Chubykalo, Institute of Material Science, Madrid, Spain - small magnetic particles

Look at the Stoner-Wohlfarth's astropyramid

Faculty Recognition Award for Research - 2010 - My prepared speech