General direction of my research is Theory
of Magnetic Phenomena and Statistical Physics, including
 Current topics:
 microwave absorption in magnetic material with static
randomness
 randomfield and randomanisotropy
magnets
 relaxation and decoherence, including
spinlattice interaction, superradiance and phonon bottleneck
 magnetomechanical effects in nanomagnets
 quantum transitions including LandauZener
effect
 spin tunneling in molecular magnets,
including fronts of tunneling
 magnetic deflagration
 structure and dynamics of small magnetic particles,
including internal spin waves
 skyrmions in ferro and
antiferromagnets
 melting of 2D lattices
 Older topics:
 magnetic phase transitions
 lowdimensional magnetism and surface magnetis
 relaxation of spin waves
 domainwall motion
At the time being, my hot topics are randomanisotropy magnets,
skyrmions, and 2D melting.
Theoretical arguments of 70th by Imry & Ma, Larkin, and Chudnovsky predict that
whatever small random field or random anisotropy would destroy a longrange
order in magnetic and other system (vortex lattice in superconductors,
chargedensity waves, etc.). Using modern computer power and advanced numerical
algorithms, we are carrying out an extensive investigation of ordering in
different models described by ncomponent 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 ImryMa state, as follows
from our new topological argument. As creating singularities cost energy, the
ImryMa 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 randomfield xy model (n = 2) [Phys.
Rev. B 88, 224418 (2013)] and a Letter [Phys.
Rev. Lett. 112, 097201 (2014)] containing the above general arguments
illustrated by numerical results. In the large followup paper [Eur.
Phys. J. B 88, 81 (2015) ] we numerically investigated the randomfield
model for any d and n in depth and found that the only model
whose ground state is not fully disordered is 3D xy model.
Pinned vortex lines in the 3d randomfield xy
model
I am especially interested in the socalled "PhononBottleneck"
problem in the spinlattice 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 spinlattice relaxation slows down dramatically Right now the socalled LandauLifshitzBloch (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 parameterfree spinphonon
interaction that in the rotating lattice
frame has the form as simple as W·S [Phys.
Rev. B 72, 094426 (2005)]. This very basic interaction that allows to obtain
some new modelindependent 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 socalled "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 selfconsistent dipolar field can bring the
system on or off tunneling resonance. We have shown that the system of magnetic
molecules selforganizes 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)]. The full 3d
theory of this process is presented in my paper Turbulent fronts of quantum
detonation in molecular magnets [Phys.
Rev. B 88, 064413 (2013) ]. This spectacular effect is still waiting for an
experimental realization.
Quantum detonation fronts in Mn12 One more 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 During
the last years we worked a lot on skyrmions that are topological formations in
2D Heisenberg magnets
Neel skyrmion Although within the continuous
approxomation (field theory) skyrmions are stable and their energy does not
depend of their size, we have found that skyrmions collapse in the
pureexchange 2d magnets because of 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). Other interactions, such as dipoledipole
interaction and DzialoshinskiiMoriya interaction (DMI) can stabilize skyrmions.
1) Skyrmion and a gas of emitted spin waves; 2) Spin waves carry away the
remaining energy of a collapsed skyrmion. Vertical axis: M_{z}.
In systems with DMI, skyrmions repel each other via the interaction energy
exponential in the distance, as found numerically in our work with our PhD
student Daniel Capic [J.
Phys.: Condens. Matter 32, 415803
(2020)]. This allows considering skyrmions in some cases as point
particles with repulsion.
Pair of skyrmions has a positive repulsion energy because of the deformation of
the spin field in the region between the skyrmions.
Recently we investigated the melting of the skyrmion lattice by
considering skyrmions as point particles with repulsion [Phys.
Rev. B 107, 014419 (2023)]. In the ordered phase, skyrmions
arrange themselves in a hexagonal lattice. The equilibrium number of skyrmions
in the system can be found by minimizing the total energy being the negative
selfenergy of each skyrmion plus the positive energy of their repulsion that we
have found in 2020. With increasing the temperature, skyrmion lattice melts and
becomes a skyrmion liquid. Skyrmion lattice can also be a polycrystal, in
particular, under the influence of rigid walls that favor the orientation of
hexagons parallel to the boundary (see picture below).
Polycrystalline skyrmion lattice bound by a circular rigid wall. Orientation of
hexagons is color coded.
These are my main current external collaborations:

Prof. Eugene
Chudnovsky, Lehman College, CUNY  collective
spinphonon relaxation, spin tunneling

Prof. Rolf
Schilling, University of Mainz, Germany  LandauZener
effect

Prof. Hamid
Kachkachi, University of Perpignan, France  small
magnetic particles

Dr. Oksana Chubykalo, Institute of Material Science, Madrid, Spain 
small
magnetic particles
Faculty
Recognition Award for Research  2010  My prepared speech
