Nonlinear Optical
Spectroscopy in Multiferroics
Speaker: Zuanming Jin
Outline
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Multiferroics
RMnO3
Linear Optical Property X(1)
Nonlinear Optical Property X(2) --SHG
Time-resolved nonlinear Optical Spectroscopy (TRNLOS) X(3)
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BiFeO3
Linear Optical Property X(1)
Nonlinear Optical Property X(2) --SHG
Third Nonlinear response
Our results
• Materials with strongly coupled magnetic and electronic
degrees of freedom provide challenges for both fundamental
many-body physics and advanced functional materials.
• Recently, multiferroics, where both electric and magnetic
orders coexist in the same phase, have attracted great
interest. However, such systems are rare in nature.
• Multiferroic materials with both polar and magnetic order
parameters usually show a relatively low-symmetry crystal
structure due to the absence of both time and space inversion
symmetries; hence, a strong interaction between the low-lying
magnetic and lattice excitations can occur, leading to rich new
physics phenomena.
RMnO3
• These material systems have two kinds of crystal structure.
Depending on the rare-earth ionic radius, they form either an
orthorhombic phase R =La–Dy or a hexagonal phase R=Ho–
Lu (or Sc, Y).
RMnO3
• These material systems have two kinds of crystal structure.
Depending on the rare-earth ionic radius, they form either an
orthorhombic phase R =La–Dy or a hexagonal phase R=Ho–
Lu (or Sc, Y).
RMnO3
• Rare-earth manganites (R
=Sc, Y, Ho, Er, Tm, Yb, Lu,
In) which crystallize in a
hexagonal structure.
• Along with the crystal
structure, the local
environment of the Mn3+ ions
in the orthorhombic and
hexagonal manganites is
also different.
• Therefore the electronic and
magnetic properties in these
two classes of materials are
vastly different.
Crystallographic unit cell of hexagonal
RMnO3, space group P63cm
PHYSICAL REVIEW B 74, 014422 (2006)
• Schematic drawing of the crystal structure and the 3d orbitals
in the MnO5 polyhedron for hexagonal RMnO3.
Electronic energy-level scheme
Linear Optical Property
• Optical spectroscopy has been a powerful tool for
investigating systematic electronic band structure of the
strongly correlated electron systems.
Phys. Rev. B 78, 054440 (2008)
•The inter-site transition peak shifted more rapidly when the
temperature crossed the Neel temperature, suggesting that a change
in the non-collinear spin correlation can influence the electronic
properties of multiferroic hexagonal manganites.
SHG
• One of which is caused by the noncentrosymmetric
ferroelectric ordering of charges, whereas the other is due to
the centrosymmetric antiferromagnetic ordering of spins.
Time-resolved nonlinear optical spectroscopy
• All-optical studies in a two-beam configuration, in which an
intense (pump) light beam excites the medium and a less
intense (probe) beam monitors the pump-induced nonlinear
changes of its properties.
• In such a configuration, the nonlinearity can be expressed
through the third-order nonlinear polarization vector P3(w)
arising from the interaction of the pump E(w) and probe e(w)
electric fields:
Time-resolved nonlinear optical spectroscopy
• Equation can be rewritten as a relation between the pumpinduced perturbation of the dielectric permittivity tensor Ɛ (w)
and the nonlinear susceptibility tensor X(3) :
• The product Ek(w)El*(w) can be conveniently decomposed
into a symmetric and an antisymmetric part with respect to
permutations of the indices k and l.
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The symmetric part is real and nonzero when the pump is
linearly polarized, while the antisymmetric part is imaginary
and nonzero when the pump beam is circularly polarized.
Time-resolved nonlinear optical spectroscopy
• The tensor
itself comprises a symmetric
and an
antisymmetric part
with respect to permutations of the
indices i and j.
• The nonlinearities resulting in
and
can be shown to
be determined by the real and imaginary parts of Ek(w)El*(w),
respectively.
• Within the studied spectral range, the observed nonlinear
optical properties are determined by the d –d transition in
Mn3+ ions.
Time-resolved nonlinear optical spectroscopy
• Spectral dependences of the photo-induced magneto-optical
Kerr rotation (full circles) and ellipticity (open circles) in (a)
ErMnO3, (b) ScMnO3, and (c) YMnO3.
Photo-induced
“MOKE”
• The dependence of the Kerr ellipticity upon Δtd is shown for
ErMnO3.
Photo-induced
“birefringence”
•From the maximum value reached by the amplitude B of the fast
component within the experimental spectral range, we could
estimate the maximum of the relevant third-order susceptibility x(3)
of ErMnO3 to be of the order of 2*10-9 esu.
Time-resolved nonlinear optical spectroscopy
• Spectral dependences of B and C, amplitudes of the relaxing
contributions to the photo-induced differential refractive index
of ErMnO3.
The amplitude B of the fast
relaxing contribution shows a
maximum at the energy of the
transition in Mn 3+ ions,
whereas the amplitude C of the
slowly relaxing part changes
sign at approximately the same
energy.
Time-resolved nonlinear optical spectroscopy
• The complex refraction index should be sensitive to this
nonequilibrium state. Thus the temporal behavior of the
photo-induced ‘‘birefringence’’ is driven by the dynamical
phenomena involving phonons.
• The spectral dependence of the refraction index within a given
energy range comprising only one electronic transition can be
presented as the sum of an energy-independent contribution
resulting from all electronic transitions outside the considered
spectral range and of a contribution resulting from the
transition within this range.
Time-resolved nonlinear optical spectroscopy
• The latter depends on photon energy and is characterized by
an s-like spectrum.
• In the frame of this model, the fast relaxing component arises
from photo-induced changes of the energy-independent part
of the signal, i.e., it is mostly due to spectral changes outside
the considered energy range.
• A spectral maximum of the fast relaxing contribution within
this range shows that the initial optical excitation of the
system consists of
transitions in Mn3+ ions.
• The fast relaxation can therefore be attributed to phonon
thermalization through the anharmonic decay of optical
phonons.
• On the other hand, the slowly relaxing component shows a
distinctive dispersion mostly conditioned by effective changes
of the spectral weight of the
resonant transition.
summary
• The decay of the nonlinearity resulting in an antisymmetric
perturbation of the dielectric permittivity tensor was shown to
be conditioned by the relaxation of the excited electrons. The
nonlinear symmetric perturbation of the tensor extends over a
longer time span, and experiences a drastic change of its
spectral dependence within the first 1.5 ps, the analysis of
which led us to attribute its decay to both phonon
thermalization and lattice cooling.
BiFeO3
• Bismuth ferrite, BiFeO3, the focus of
this study, has a robust ferroelectric
polarization (~100 uC/cm-2) at room
temperature, that is the largest
among known ferroelectrics.
• At RT, BiFeO3 is a rhombohedrally
distorted ferroelectric perovskite with
space group R3c and a Curie
temperature, TC~1100 K.
• It also shows a G-type canted
antiferromagnetic order below Néel
temperature, TN~640 K, and, in the
bulk, an incommensurately spacemodulated spin structure along (110)h.
Linear optical spectroscopy
• electronic energy-level scheme for the Fe3+ ion
PHYSICAL REVIEW B 79, 224106 (2009)
Vol. 17, No. 13 / OPTICS EXPRESS 10971
Linear optical spectroscopy
PHYSICAL REVIEW B 79, 224106 (2009)
Appl. Phys. Lett. 97, 121102 (2010)
Linear optical spectroscopy
Linear optical spectroscopy
• The 1965 discovery and identification of magnon side bands
in the linear optical-absorption spectrum of simple
antiferromagnetic insulators contributed to a comprehensive
understanding of the static and dynamical optical properties of
ordered magnetic systems.
R. L. Greene, D. D. Sell, W. M. Yen, A. L. Schawlow, and R. M. White,
Phys. Rev. Lett. 15, 656 (1965)
• These studies were based on the resonant enhancement of
the susceptibility,
, that appears in the linear
interaction
.
• One can generally express as
Linear optical spectroscopy
• When electric-dipole-active magnetic excitations couple to
electronic excitations, magnon sidebands are located at
• where
is a single-magnon energy, n is the number of
magnons assisting the transition, and Ee corresponds to the
electronic crystal-field transitions.
Linear optical spectroscopy
• Magnon sidebands have been extensively studied by linear
spectroscopy at low temperatures.
• magnon sidebands were recently observed in the linear
magneto-optical absorption spectrum of BiFeO3 under high
magnetic fields and low temperatures.
•Phys. Rev. B 79, 134425 (2009)
• With the rapid development
of modern lasers, secondharmonic generation (SHG),
as the lowest-order nonlinear optical process, has
emerged as a powerful tool
to study light-matter
interactions.
• In a magnetically ordered
system, spin waves can also
effectively couple to the
nonlinear susceptibility
tensor.
• With the rapid development
of modern lasers, secondharmonic generation (SHG),
as the lowest-order nonlinear optical process, has
emerged as a powerful tool
to study light-matter
interactions.
• In a magnetically ordered
system, spin waves can also
effectively couple to the
nonlinear susceptibility
tensor.
Appl. Phys. Lett. 92, 121915 (2008)
Raman scattering
• Recent works on low-energy
Raman-scattering
experiments in BiFeO3 have
shown a strong interaction
between optical phonons and
magnons manifested as
several sharp resonances (up
to 12 peaks in the 5–60 cm−1
energy range) corresponding
to two species of
electromagnon excitations
with distinctive dispersive
energy curves depending on
their coupling to the electrical
polarization.
Vol. 17, No. 13 / OPTICS EXPRESS 10971
Third-order nonlinear response
Filled and open circles are the OA
and CA Z-scans, respectively.
Intensity independence of (a)
2PA coefficient α2 and (b)
nonlinear refraction index n2 for
the BFO film.
J Supercond Nov Magn (2011) 24: 731–734
Dual-Color
Femtosecond Spectroscopy
Ultrafast dynamics in multiferroic BiFeO3
Yu-Miin Sheu, Rohit Prasankumar, Antoinette Taylor
(Los Alamos National Laboratory)
• We report the ultrafast time-resolved optical measurements of
multiferroic BiFeO3, which exhibits both magnetic and
ferroelectric ordering at room temperature. The coupling
between these two orders makes it an attractive material for
potential data-storage devices. However, a detailed
understanding of this coupling is still under debate. Ultrafast
optical spectroscopy can potentially shed light on
magnetoelectric coupling in BiFeO3 by unraveling the different
contributions in the time domain. Here, we use degenerate 400
nm pump-probe spectroscopy to excite and probe a BiFeO3 thin
film above its bandgap. The measured relaxation consists of a
fast decay (˜1 ps) followed by a slow recovery (˜150 ps). We
attribute the fast component to the recovery of photoexcited
carriers. The slow recovery may be due to spin-lattice relaxation.