Unidirectional terahertz light absorption in the pyroelectric ferrimagnet CaBaCo4O7

0.3 MB·

by  S. Bordács

Unidirectional terahertz light absorption in the pyroelectric ferrimagnet CaBaCo O
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S. Bord´acs,1,2 V. Kocsis,1 Y. Tokunaga,3,4 U. Nagel,5 T. Ro˜o˜m,5 Y. Takahashi,2,3 Y. Taguchi,3 and Y. Tokura2,3
1Department of Physics, Budapest University of Technology and Economics and MTA-BME
Lendu¨let Magneto-optical Spectroscopy Research Group, 1111 Budapest, Hungary
2Department ofAppliedPhysics andQuantum Phase Electronics Center(QPEC), University ofTokyo, Tokyo 113-8656, Japan
3RIKEN Center for Emergent Matter Science (CEMS), Wako 351-0198, Japan
4Department of Advanced Materials Science, University of Tokyo, Kashiwa 277-8561, Japan
5National Institute of Chemical Physics and Biophysics, 12618 Tallinn, Estonia
(Dated: January 5, 2016)
6 SpinexcitationswerestudiedbyabsorptionspectroscopyinCaBaCo4O7whichisatype-Imultifer-
1 roiccompoundwith thelargest magnetic-orderinducedferroelectric polarization (∆P=17mC/m2)
0 reported,sofar. Weobservedtwoopticalmagnonbranches: asolelyelectricdipoleallowedoneand
2 amixedmagnetoelectric resonance. Theentangledmagnetization andpolarization dynamicsofthe
n magnetoelectric resonance gives rise to unidirectional light absorption, i.e. that magnon mode ab-
a sorbstheelectromagneticradiationforonepropagationdirectionbutnotfortheoppositedirection.
J Oursystematicstudyofthemagneticfieldandtemperaturedependenceofmagnonmodesprovides
4 information about the energies and symmetries of spin excitations, which is required to develop a
microscopic spin model of CaBaCo4O7.

]
l PACSnumbers:
e
-
r
t Multiferroic materials have gained tremendous inter- In the long wavelength limit the directional dichroism
s
. estbecauseoftheir versatilepossibilities forapplications emerges from the dynamic magnetoelectric (ME) cou-
t
a in sensing, data storage and computing [1–3]. These pling, δPω=χˆem(ω)Hω and δMω=χˆmeEω [7, 8]. The
m functionalities rely on the magneto-electric (ME) effect induced polarization, δPω and magnetization, δMω in-
d- which is enhanced in multiferroics by the coexistence terfere constructively/destructively with Hω and Eω
n of ferroelectric and magnetic order. Recent studies of fields of the light as the relative orientation of Hω and
o multiferroic materials from gigahertz frequencies to X- Eω is opposite for foreward/backwardpropagating light
c raywavelengthshavedemonstratedthatfinite frequency beams [18]. Due to the strong hybridization between
[
ME effect gives rise to another useful phenomenon, the the electric and magnetic dipole excitations large direc-

1 directional dichroism [4–14]. The non-reciprocal direc- tional dichroism has been found recently for the collec-
v tional dichroism and its Kramers-Kronig counterpart, tive spin excitations of multiferroics. Non-reciprocal di-
4
non-reciprocal directional birefringence, are the absorp- rectional dichroism has been observed in two distinct
4
tion coefficient and refractive index differences, respec- cases, so far. The first one, the so-called magnetochi-
4
0 tively, for counter-propagating light beams detectable ral dichroism (MChD), requires a chiral material with
0 irrespective of the light polarization state. These ef- finite magnetization, and the directional dichroism is
. fects enable new applications for multiferroics in pho- present for light beams propagating parallel and an-
1
0 tonics, e.g. one-way light guides and polarization rota- tiparallel to the direction of the magnetization. MChD
6 tors. The largestdirectionaldichroisminmultiferroics is has been detected in several akermanite compounds,
1 at terahertz (THz) frequencies [11] what can boost ter- (Ba CoGe O , Sr CoSi O , Ca CoSi O ) [8, 11] and in
2 2 7 2 2 7 2 2 7
:
v ahertz photonics in the future, similar to the prospect Cu(Fe,Ga)O2 [12]. The second one is realized when a
i of graphene non-reciprocal terahertz devices [15]. The materialsimultaneouslypossessesmagnetization,Mand
X
dc and the finite frequency ME effect, which deter- electric polarization (or a polar axis), P [19]. In this
r
a mine the efficiency of any multiferroic device, are inti- case, the absorption is different for beams propagating
mately connected by a sum rule [16] allowing a large along and opposite to the toroidal moment, which is
static ME effect only if a large non-reciprocal direc- the cross product of the electric polarization and the
tionaldichroismis presentinthe absorptionspectrumof magnetization, T=P M. We term the latter effect as
×
electromagnetic radiation. The pyroelectric ferrimagnet toroidal dichroism (TD), which has been observed in
CaBaCo O is a type-I multiferroic compound with the Ba CoGe O [7], (Eu,Y)MnO [9], (Gd,Tb)MnO [10].
4 7 2 2 7 3 3
largest magnetic-order induced ferroelectric polarization All the above listed compounds are type-II multifer-
(∆P=17mC/m2) reported, so far [17]. In this paper we roics,wheretheusuallyweakferroelectricityappearsbe-
report a magnon mode in CaBaCo O which shows uni- low the magnetic phase transition. On the other hand,
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directional light absorption. Namely, the non-reciprocal type-I multiferroics usually have large ferroelectric po-
directional dichroism is so strong for the magnon res- larizationwhichis alreadypresentintheir paramagnetic
onance that it absorbs terahertz radiation only in one phase [3]. Moreover, they often have higher magnetic
direction, but not in the opposite direction. ordering temperature which enables room temperature
Typeset by REVTEX
2
applications. However, in this class of compounds, the (a) (b)
dynamic magnetoelectric effect of spin-wave excitations 300
E ||c, B c E c, B ||c
has been studied only very recently in BiFeO3 [14], and 4 K 4 K
information about the non-reciprocal directional dichro- -1 m)200 4600 KK 5655 KK
ism is still scarce. Here, we focus on the non-reciprocal (c 65 K
directional dichroism spectrum of a type-I multiferroic
material, CaBaCo O , which belongs to the Swedenbor- 100
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gitefamilyhavingmemberswithmultiferroicphasesclose
to room-temperature [20]. 0
1.0 1.2 1.4 1.6 1.0 1.2 1.4 1.6
Frequency (THz) Frequency (THz)
(a) (b)
z) (c) (d)
H
TM P P T ce frequency (T001...680 001...680 (/f.u.)McB -1 (cm)230000 EEET=|4|ccc K,,, BBB ||ccc
M n0.4 0.4
a 100
n
o
s0.2 0.2
b e
R
a 0.00 20 40 60 800.0 0 1.0 1.2 1.4 1.6
Temperature (K) Frequency (THz)
FIG. 1: (Color online) The magnetic order in CaBaCo4O7 FIG.2: (Coloronline)(a)-(b)Thetemperaturedependenceof
whichdevelopsonthekagomeandtriangularlatticelayersof the low-frequency absorption spectrum in CaBaCo4O7. The
Coions[22]. Thedifferentcolors indicatefourdifferentmag- magnon modesat 1.07THzand1.41THz,indicated byblack
neticmomentsofinequivalentCoions. The(a)and(b)panels arrows, disappear above the magnetic ordering temperature,
showtwomagneticdomainswithoppositemagnetization, M Tc=60K. (c) The temperature dependence of the resonance
(up/down) and opposite toroidal moment, T (left/right). frequencyofthemagnetoelectricresonance(filledcircles)and
the in-plane magnetization in B=0.1T magnetic field (solid
line). (d) The polarization selection rules for the THz exci-
At room temperature CaBaCo O has an orthorhom-
4 7 tations of CaBaCo4O7. The 1.07THz excitation is sensitive
bic, non-centrosymmetric crystal structure (space group
to the orientation of both the electric and magnetic compo-
Pbn21) [21], which allows electric polarization along the nents of the light, while the magnetic mode at 1.41THz can
c axis. The tetrahedrally coordinated cobalt ions, re- be excited only by the electric field of the radiation when
sponsible for magnetism of this compound, form alter- Eωkc. The absorption spectra were cut when theabsorption
nating kagome and triangular lattice layers as shown coefficient exceeded the detection limit.
in Fig. 1. These sublattices with the strong antifer-
romagnetic exchange coupling between the cobalt ions
aretextbookexamplesofgeometricalfrustratedsystems. ray diffraction pattern was consistent with the space
In CaBaCo4O7 an orthorhombic distortion releases the group Pbn21. X-ray diffraction and polarized optical
frustration, and a ferrimagnetic order develops below microscopy imaging revealed that orthorhombic twin-
Tc=60K (see Fig. 1) [21, 22]. The c axis is the hard ning occurs on microscopic scale in the studied samples.
magnetization axis, while the magnetization anisotropy THz transmission spectra were measured on 300-500µm
within the ab plane is small if any [23]. The magnetic thickplatelet-likesampleswithdifferentcrystallographic
unit cell, which is equivalent to the structural unit cell, orientations using time-domain THz [25] and Fourier-
contains 16 cobalt spins, and the symmetry of the fer- transform infrared spectroscopy [26].
rimagnetic state reduces to Pb′n2′. Upon the magnetic The THz spectra of CaBaCo O measured with lin-
1 4 7
phase transition a peak-like anomaly shows up in the earlightpolarizationalongtheprincipalcrystallographic
temperature dependence of the dielectric function, indi- axes using Fourier-transform spectroscopy are shown in
cating a coupling between fluctuating spin and charge Fig. 2. Since the a and b axis are indistinguishable due
degrees of freedom [17, 23]. Pyrocurrent measurements totheorthorhombictwinning,thein-planedirectionsare
revealed a magnetic-order induced electric polarization, labeled as c. The temperature dependence of the THz
∆P 17mC/m2 being the largest observed among mul- spectra(see⊥Fig.2(a)-(b))showsthatbesidethe temper-
≈
tiferroics known, so far [17]. First principles calculations atureindependentphononmodesobservedintheparam-
suggest that magnetostriction is the dominant driving agneticphasetwonewresonancesappearbelowTc=60K
mechanism of the large change in the ferroelectric polar- whoseresonancefrequenciesareshiftedtolowerfrequen-
ization [24]. cies as the temperature increased (Fig. 2(c)). In the low
Single crystals of CaBaCo O were grown by the temperature phase no additional infrared active phonon
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floating-zone technique [17]. The room temperature X- mode is expected since (i) the magnetic and the struc-
3

tural unit cells are the same and (ii) the space group
(a)
changes from Pbn2 to Pb′n2′ upon the magnetic phase 1600 E c, B ||c k||Bdc c
1 1
transition, while keeping all spatial symmetries intact. 1400 14T
Therefore, the two resonances, located at 1.07THz and
1200 12T
1.41THz at T=4K can be identified as magnetic excita- -1 m)1000 10T
tions. Thesepeaksshifttolowerfrequenciesandbecome c
(
broaderasthetemperatureincreasesasexpectedforcol- 800 8T
lective excitations of a magnetic order. 600 6T
The selection rules for the low-frequency excitations 400 4T
were obtained from the light polarization dependent
200 2T
measurements, see Fig. 2(d). The modes at 1.23THz
and 1.67THz are ab-plane lattice vibrations, while the 0 0T
(b)
1.63THzresonanceisac-axisopticalphononmodesince 1600 E ||c, B c k ||Bdc c
all of these excitations are sensitive only for the orien- 1400 14T
tation of Eω and they are also present in the paramag- 1200 12T
neticphaseaboveTc asshowninFig.2(a)-(b). However, -1 m)1000 10T
the intensity of the 1.07THz resonancechangeswhen ei- (c
ther Bω or Eω is rotated out from the ab plane, there- 800 8T
fore, this mode is assigned to a both electric and mag- 600 6T
netic dipole active resonance excitation. The magnetic
400 4T
modeat1.41THzcanbeexcitedonlywithEωkc,thus,it 200 2T
is an electric-dipole allowed but magnetic-dipole forbid-
0 0T
den magnetic resonance. Such strong electric dipole ac- 1.0 1.2 1.4 1.6
tiveelectromagnonshavebeenfoundalsoinorthorhomic Frequen cy (THz)
manganites [9, 27]. (c) 200
meTahsuermedagfonretdicifffieerledntdefipeeldndoerniecnetoaftitohnesTaHt z4Kspeacstrsahowwans -1 (cm) 110500 106TT kE||Bdcc, |B|c c
in Fig. 3. The experiments were performed in Fara-
50
day geometry, where the external magnetic field is par-
allel to the light propagation direction, k Bdc, thus no 0 1.0 1.2 1.4 1.6
directional dichroism is expected by symmk etry. When Frequency (THz)
the magnetic field lies within the ab plane, Bdc c (see FIG. 3: (Color online) (a)-(c) Solid lines, the magnetic field
⊥
Fig. 3(a)-(b)), the magnetoelectric mode at 1.07THz is dependence of the absorption spectra of CaBaCo4O7 at 4K.
asymmetrically split into two branches, which get sep- The spectra are shifted vertically proportional to the mag-
nitude of the field in panels (a) and (b). Dashed lines, the
arated linearly by 25GHz/T, while the 1.41THz reso-
evolution of theresonance frequencies in field.
nanceisshiftedtohigherfrequenciesbyabout13GHz/T.
This strong magnetic field dependence also supports the
above assignment of 1.07THz and 1.41THz resonances
to magnetic excitations. The other lines are infrared electric polarization, while their magnetization and thus
active phonon modes showing no magnetic field depen- their toroidal moments have opposite signs. The finite
dence. When an external magnetic field of 16T is ap- magnetization of the domains allows to switch between
pliedparalleltothecaxis,thespectrumdoesnotchange thembyanexternalmagneticfieldlargerthanabout2T
significantly (Fig. 3(c)); only the 1.07THz resonance is at T=5K. Due to the strong exchange coupling between
shifted slightly to higher frequencies and the 1.41THz the spins and the small in-plane anisotropy, we expect
mode becomes weakly active. This result suggests that thatthetoroidalmomentformedbythepolarcaxisanda
themagneticstructurecanbehardlymodifiedbyBdc c, magnetizationpointing to anyin-plane directionscanbe
thus, the strong anisotropy forces the spins to lie withkin reversedbyreversingthe externalmagneticfield. There-
the ab plane. fore, instead of reversing the position of the source and
the detector, which would be the time reversed experi-
In CaBaCo O , symmetry allows TD when the light
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propagatesalongthe toroidalmoment, T=P M, where ment, we measured the absorption difference in positive
the electric polarization P points along the×c axis and and negative in-plane magnetic fields while keeping the
the magnetization M is within the easy-plane. Since opticalsystemintactinordertosensitivelydetectthedi-
the symmetry reduces from Pbn2 to Pb′n2′ upon the rectionaldichroism. Inthisway,wereversedthetoroidal
1 1
moment of the sample instead of the light propagation
paramagnetictoferrimagneticphasetransition,twomag-
vector,as TD depends only on their relativeorientation.
netic domains interchanged by the time reversal opera-
tion can exist, Fig. 1. The domains possess the same The magnetic field dependence of the absorption
4
SB−)/(SB++SB−), where SB+ and SB− are the
(a) E ||Bdc c, B ||c (b) E ||c, B ||Bdc c strength of the resonance in positive and negative fields,
T)
450 B+ T=4K B ( B+ T=4K 450 respectively [18]. First, SB+ was determined by fitting
400 B - 8 B - 400 the absorption spectrum with a sum of Lorentzian func-
350 7 350 tions,thenthenegativefieldspectrawerefittedbyallow-
-1 (cm)223050000 456 223050000 -1 (cm) itdnhigffeeotrnwenloytltmihgeahgtsntpereotinlcagrtfiihzealpdtiaodrnaesmpetenhtdeere,dniScsisBeys−matmsoesbthreoywvfanarciietndor.FiFhgao.4sr
150 3 150 (c). When Eω c the TD is saturated close to the theo-
⊥
100 2 100 retical maximum η=1 above 5T for the lower branch of
50 1 50 the 1.07THz magnetoelectric mode. However, for the
0 0 0 orthogonal polarization Eω c, the dissymmetry factor
0.9 1.0 1.1 1.2 1.3 0.9 1.0 1.1 1.2 1.3 k
monotonously increases in the studied field range. The
Frequency (THz) Frequency (THz)
(c) )B- differenceinthefielddependenciesislikelycausedbythe
S 1.0
+ different hybridizations between the magnon mode and
+0.8
SB higherenergypolarmodesgovernedbydifferentselection
)/(B-00..46 rules for the two light polarizations.
-S+0.2 As it was shown previously [11], such a strong direc-
SB0.0 tionaldichroism,η 1,canbeachievedforamagnetoelec-
( ≈
tricresonancewhentheratioofthemagneticandelectric
0 1 2 3 4 5 6 7
B (T) dipolematrixelements, nm0 and np0 ,respectively,
h | | i h | | i
is equal to the speed of light within the material for the
FIG. 4: (Color online) (a)-(b) The magnetic field depen-
denceoftheTHzabsorptionspectrainCaBaCo4O7measured transparent direction:
for light propagation along the toroidal moment, T=P×M
formedbythecrossproductofthemagnetization,Mandthe hn|m|0i = c0 . (1)
electric polarization, P. Upon the reversal of the magnetic np0 √ε
h | | i
field the toroidal moment is reversed which results in strong
Herec isthe speedoflightinvacuumandεistheback-
non-reciprocal directional dichroism. (c) The magnetic field 0
grounddielectricconstant. Wegetε=14.7fromourtime-
dependence of the dissymmetry factor (defined in the text).
Thecolorsofthesymbolscorrespondstothoseof thedashed domain measurement, thus, the ratio, Eq.1, is c0/3.7 for
lines in panels (a) and (b) showing the field evolution of the the 1.07THz mode of the CaBaCo O above 5T and
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resonance frequencies. In panel (c) the solid lines are guides Eω c, Bω c.
to theeyes. F⊥rom a kclassical spin-wave theory one expects maxi-
mum 16 magnon modes in CaBaCo O as the unit cell
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contains16magneticallydifferentatoms. IntheFaraday
spectra both for positive and negative in-plane fields, geometry (see Fig.3) three modes are observed with res-
was measured using time-domain THz spectroscopy in onance frequencies monotonously increasing in field. In
Voigt geometry, k Bdc, for light propagation along the theVoigtgeometry(seeFig.4)the1.07THzmodeissplit
toroidalmomentT⊥(seeFig.4). Inthissetupthehighest intoamagneticfieldindependentmode andahigherfre-
field was limited to 7T, and the high frequency cut- quencybranch,whichisalsoobservedintheFaradaycon-
±
off was below 1.4THz. Fig. 4 (a) and (b) present two figuration. This raises the number of observed magnon
sets of spectra measured with the two orthogonal light modes to four. The missing spin excitations are outside
polarizations, Eω c and Eω c, respectively. In order to the frequency window of the current Faraday and Voigt
⊥ k
study a single magnetic domain, first the highest posi- experimentsortheydonotinteractwiththeelectromag-
tive (negative) magnetic field, +7T (-7T) was applied netic radiation.
to reachthe saturationmagnetization,and the magnetic Inconclusion,wehavestudiedthemagneticresonances
field dependence was measured with decreasing the field in the type-I multiferroic CaBaCo O . The lowest-
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downtozero. Remarkably,thelowerfrequencybranchof energy mode at 1.07THz is a mixed magnetic and elec-
the 1.07THz magnetoelectric mode can be excited only tric dipole resonance, while the 1.41THz resonance can
inpositivefieldsabove+5TforlightpolarizationEω c. be excited only by the electric field component of the
⊥
Sincethismodeabsorbslightonlyforoneofthepropaga- light. Such magnetoelectric and electric dipole modes
tiondirectionswithrespecttothetoroidalmomentandit are probably allowed by the strong inversion symmetry
istransparentfortheother,CaBaCo4O7 allowsunidirec- breakingfieldsofthepresentpyroelectriccompound. For
tional light propagation around the resonance frequency counter-propagatinglightbeams,the1.07THzresonance
of the magnetoelectric mode. absorbstheelectromagneticradiationonlyforonepropa-
The strength of the directional dichroism is quan- gationdirectionduetothedynamicmagnetoelectriccou-
tified by the dissymmetry factor defined as η=(SB+- pling. Nearly perfect unidirectional light absorption is
5
realized in CaBaCo4O7, and the transparent/absorbing [9] Y. Takahashi, R. Shimano, Y. Kaneko, H. Murakawa,
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This work was supported by the Funding Program for
[16] D. Szaller, S. Bord´acs, V. Kocsis, T. Ro˜˜om, U. Nagel,
World-LeadingInnovativeR&DonScience andTechnol- and I.K´ezsma´rki, Phys.Rev. B 89, 184419 (2014).
ogy (FIRST Program), Japan, by Hungarian Research [17] V.Caignaert,A.Maignan,K.Singh,Ch.Simon,V.Pra-
Funds OTKA K 108918, OTKA PD 111756, Bolyai long, B. Raveau, J. F. Mitchell, H. Zheng, A. Huq, and
00565/14/11 and by the Lendu¨let Program of the Hun- L. C. Chapon, Phys. Rev.B 88, 174403 (2013).
garian Academy of Sciences, and by the Estonian Min- [18] L. D. Barron, Molecular light scattering and optical ac-
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[19] Tobeprecise,whentheferroicorderofthelocaltoroidal
the Estonian Science Foundation Grant ETF8703.
momentsarepresent,theTDcanbeobservedevenifthe
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