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Optical and magnetic circular dichroism study of the quadratic double layer antiferromagnet Rb3Mn2Cl7
B. Briat, J.C. Canit, A. Vervoitte, H. Güdel
To cite this version:
B. Briat, J.C. Canit, A. Vervoitte, H. Güdel. Optical and magnetic circular dichroism study of the quadratic double layer antiferromagnet Rb3Mn2Cl7. Journal de Physique, 1985, 46 (3), pp.479-487.
�10.1051/jphys:01985004603047900�. �jpa-00209988�
Optical and magnetic circular dichroism study of the quadratic
double layer antiferromagnet Rb3Mn2Cl7
B. Briat, J. C. Canit, A. Vervoitte
Laboratoire d’Optique Physique de l’ESPCI (*), 10, rue Vauquelin, 75231 Paris Cedex 05, France and H. Güdel
Institut für Anorganische und Physikalische Chemie, Freiestrasse 3, CH-3000 Bern 9, Switzerland
(Reçu le 16 août 1984, révisé le 12 novembre 1984, accepté le 20 novembre 1984 )
Résumé. 2014 Les raies excitoniques dipolaires électriques sont observées pour tous les multiplets à l’exception de
4T2(G) dans le domaine spectral 17 000-31000 cm-1. La fonction d’onde des états excités correspondants est
caractérisée à l’aide de mesures d’absorption en lumière polarisée et de dichroisme circulaire magnétique (DCM).
On détermine expérimentalement l’influence du champ tétragonal et du couplage spin-orbite sur les triplets orbi-
taux; les résultats sont en bon accord avec nos prévisions théoriques. Chaque raie excitonique est accompagnée
d’une bande exciton-magnon qui présente la polarisation attendue. L’énergie des magnons en bord de zone est
établie à 90 cm-1, l’interaction exciton-magnon étant négligeable.
Abstract. 2014 Electric dipole origins were observed for all multiplets except 4T2(G) in the 17 000-31000 cm-1 spectral range. The dominant orbital character of each corresponding excited state was unambiguously established via polarized absorption and magnetic circular dichroism (MCD) measurements. The influence of the tetragonal
distortion and spin-orbit coupling on all orbital triplets was determined experimentally, the results being in fair agreement with our theoretical predictions. Magnon sidebands were always observed with the predicted polariza-
tion. The zone-edge magnon frequency was found to be 90 cm-1, exciton-magnon interaction being negligible.
Classification Physics Abstracts
78.20L - 78.50 -75.50E - 71.35
1. Introduction.
Manganese fluoride [I] and many other related anti-
ferromagnets [2-7] have long been the object of spec-
troscopic investigations with the authors attention
being often focused on the temperature dependence
of the shape and intensity of magnon sidebands. The
magnetic properties of these materials have also been well studied, particularly in the case of the two-dimen- sional (2-D) Heisenberg antiferromagnets K2MnF4 [8]
and K3Mn2F7 [9-12].
We present here the first optical and magneto- optical study of Rb3Mn2CI7 which has the same tetra-
gonal, double layer structure as K3Mn2F 7. This
structure can be constructed [9] from Rb2MnCl4 by substituting unit cells of RbMnCl3 in place of the MnCl2 squares. It was confirmed by elastic neutron scattering work [13] which also indicated a Neel tem-
perature of 64.5 K and an interaction between next-
nearest-neighbour double layers which is ferromagne-
tic or antiferromagnetic depending on the sample preparation.
The site symmetry for Mn2+ in Rb3Mn2CI7 is C4v
and C4 above and below TN respectively. With the spins aligned up and down the four-fold axis, the ma- gnetic space group is either Fc m’ m’ m’ or P, 42/nn’ m’
[13]. An important feature of the Rb3Mn2C’7 struc-
ture is that there is no inversion centre at the Mn2 + site.
As a result one expects the appearance of electric dipole (ED) zero-phonon, zero-magnon excitonic origins
for the material.
In this paper, we shall focus on the characterization of these origins via polarized absorption and magnetic
circular dichroism (MCD) experiments. The latter is defined as the difference in absorbance (AA) for left
and right circularly polarized light. We shall also discuss the respective role of the tetragonal distortion, spin-orbit coupling and the exchange field on the
various excited multiplets in the visible and near
ultra-violet regions.
2. ExperimentaL
Single crystals were prepared from the melt, as indicat- ed in [14]. Polarized absorption and MCD spectra
were taken on our own laboratory made instruments
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:01985004603047900
480
with the appropriate resolution. The monochromator
was calibrated with a mercury lamp. Axial (a) measu-
rements were done on freshly cleaved samples of
thickness t varying from 0.15 mm to 3 mm, depending
upon the spectral range. Since it proved extremely
difficult to produce a very thin, optically good crystal
with the axis in plane, the Q (E 1 C4) and n (E/ C4)
spectra could not be obtained (with t = 3.35 mm) for
the stronger bands. All ordinate scales for absorption
were normalized to t = 1 mm on our figures.
The photoelastic modulator used for MCD expe- riments is described in [15]. These were performed
under a magnetic field B of up to 2.5 T (superconduct- ing magnet) at 4.2 K and below 0.7 T (electromagnet)
at higher temperatures. Ordinate scales for MCD
were standardized to t = 1 mm and B = 1 T. Our dichrometer was calibrated with solutions of epi-
androsterone in dioxane (Ae = 3.310 at 304 mm,
differential molar extinction coefficient) and cam- phoquinone in methanol (1BA/A = 1.050 x 10-’ at
480 nm). The latter was also used to check that our
crystals did not depolarize the light beam. The noise level of the apparatus (in presence of a weakly absorb- ing sample) was found to correspond to ~A ~ 3 x
10-6 in absorbance units.
Some of our data were analysed by the method of moments. We define the nth order moments of a band with bandshape F(E) as :
where E is the barycentre of the band, defined so that
n
j 1 1
stands for A/E and ðAIE for absorption and MCD respectively. The parameters of interest to us here are
Hereafter, all energies will be expressed in wavenum-
bers.
3. Theoretical background.
In Rb3Mn2C17, each spin is surrounded by five nearest neighbours, one of which is located in the adjoining layer. As for K3Mn2F 7 [9], we expect the spin-wave dispersion of this four sublattice antiferromagnet
to have two two-fold degenerate branches (Fig. 1), the
lower one associated with in-phase precession of the paired layers, the upper one having energies larger
than 4 1 J S, with anti-phase precession. The upper branch has a flat maximum slightly above (- 2 %) the
zone boundary energy value. We therefore expect
exciton-magnon bands to peak essentially at the edge
of the Brillouin zone (B.Z.) (around 90 cm-’) on the
basis of TN since the two maxima will be undistin-
guishible. Note that, although there is also a maximum in the magnon density of states for k = 0, this point
Fig. 1. - Dispersion of the 2 x 2 degenerate spin waves
in K,Mn,F, along the [10] and [11] directions in the 2 D Brillouin zone schematic (taken from Ref. [9]).
does not contribute since the effective dipole moment M(k) for the exciton-magnon absorption transition is
zero for k = 0 [3].
The site symmetry of all Mn 21 ions in the
Rb3Mn2CI7 crystal is C4v in the paramagnetic phase.
With the spins aligned up and down the four-fold axis below TN, the site symmetry is C4 and the magnetic
space group is isomorphous to D4h for k = 0 and at the edge of the B.Z.
In order to derive the selection rules for excitonic transitions, we must study those combinations of
single-ion transitions from two ionic sites a (spin down) and b (spin up) in the same layer, that produce
excitons at the centre (k = 0) of the B.Z. This has been done in detail for Rb2MnCl4 [16J and the same forma-
lism applies here except for one important difference, i.e., the site symmetry for Mn 21 is C4h below TN for Rb2MnC’4’ We refer to gy and mY (y, polarization) as
the magnetic and electric dipole moment operators
respectively, with p * = + (i/,12-) (/lx ± iJly) and simi- larly for mt. Then, in C4h symmetry, p + and p- trans- form as r3 and F4 +-+ Fl ) whereas in C4 sym-
metry, one has m, *-+ F’, m_ - T/ and m_, +-+ F’
Therefore, the selection rules obtained previously for Rb2MnCl4 are also valid for excitons in Rb3Mn2CI7, apart from the replacement of gy by my. The results can
be summarized by using Griffith’s [18] tetragonal
basis functions 14r, Mr, Ms >. Then for one ion in
sublattice a, the spin forbiddingness is relaxed via the
spin-orbit coupling between the ground state 1 6Ai, 0, 5/2 ) and I 4T l’ 1, 3/2 >. This 4T1 character provides the electric dipole (ED) intensity for excitonic origins and transitions are allowed from m+ to T2 0 ) and I Ee ) (we omit the MS symbol), m- to T 0 ), I E() ) and I Al ), and mz to IT,I> and T2 - 1 ).
A magnetic field B applied along the tetragonal axis
shifts the single-ion transitions for ionic sites a and b in opposite directions. A derivative-like MCD a1 term
thus occurs, withLBM1jMo = a1 JlB B(JlBBohrmagne-
ton). It is a simple matter to establish that a, is pre-
dicted to be positive for I rMr) = T, 0 >, E0 >
and I Al ) while it is negative for T2 0 ) and EE >.
A positive al value implies a positive MCD lobe on the high energy edge of the optical transitions. For all transitions seen in the axial spectrum, the above model
predicts I a, 1 = 5 g - 3 g’ I where g and g’ stand
for the Lande factors in the ground and excited states
respectively (g - 2).
No a, term is expected for exciton-magnon (E.M.)
combination bands since the splitting of the r 5- crystal excitons is compensated by the change in the
r 5+ magnon energy. Following Loudon [17], we further
conclude that E.M. bands should have the same pola-
rization as the associated ED origins, i.e., a = J or n for « unlike » (rg ) or « like » (T 2 ) excitons respecti- vely. Our overall predictions regarding optical selec-
tion rules and the sign of the MCD are summarized in table I.
The model presented so far should be refined by considering the effect of the tetragonal field X4, the spin-orbit coupling JCs and the exchange field HE on the
various cubic terms. This has been done for orbital
triplets Ti (i = 1, 2) by diagonalizing the Hamilto-
nian [16] :
u(a) = ’.l( C() where C is the spin-orbit coupling cons-
tant of Mn2+ ; s(a) and u(a) are the spin and orbital
angular momentum operators for electron a ; D is the
tetragonal field parameter and H = g’ /lB Hi is the exchange energy ; the minus and plus signs are asso-
Table I. - Selection rules for exciton and exciton-
magnon transitions in Rb3Mn2C’I’ a and n stand for the
electric vector of the light beam perpendicular and parallel to the C4 axis respectively. The notations Mr (orbital component) and T (polarization) are appropriate for a down (a) sublattice. In parentheses are indicated
the relative dipole strengths for transitions to the various Mr substates of a r octahedral term.
ciated with the down (a) and up (b) sublattices respec-
tively if H is taken as positive. The matrix elements of
Hs are evaluated by means of equation (9.28) of
reference [18]. They are the same for T1 and T2 if
we express them in terms of the parameter rl =
-(1/3 /10) 4Ti II L s.u 11 4Ti > (i = 1, 2). In the
absence of H and A, D positive means that the tetra- gonal doublet of Ti lies highest. In the absence of H and D, A positive implies that the pseudo « MJ » =
:t 1 j2 doublet is lowest.
In the absence of an exchange field and spin-orbit coupling, D positive means that the tetragonal doublet
of Ti lies highest. For H = D = 0, C positive implies
that the pseudo « Mj » = 1/2 doublet is lowest.
At the moment, we leave H, D and as adjustable
parameters to fit our data. Two important conclusions arise from the above treatment : (i) only one T2 but
two F excitons are expected for T = T, since 11, 3/2 ) does not mix while 0, 3/2 ) combines with
1, 1/2 >; (ii) three T 2 (and also two r 5-) excitons might occur for r = T2 since - 1, 3/2>) combines with 0, 1/2 ) and l, - 1/2 ) under S.O. coupling.
Of course, the associated dipole strengths will depend
upon the relative value of D, A and H.
We stress the fact that an error was inadvertently
commited in Appendix 1 of reference [16]. One should read 1, - 1/2 I Je 11, - 1/2 ) = D/3 +(H-A)12 (instead of D/3 - (H - A)/2).
4. Results.
4.1 SURVEY SPECTRA. - Figure 2 shows a survey of the room and low temperature axial spectra with the nomenclature appropriate for the various excited states (octahedral notations). Two bands occurring
in the UV region [14] have not been investigated in
detail. The broad band MCD was run around 20 K. It is essentially similar to that published recently [7]
for RbMnF3. Negative MCD terms (absorption-like)
are observed for all orbital triplets while they are posi-
tive for orbital doublets (and 4 AI), The a (axial) and Q
broad band spectra are identical, indicating the ED
character expected.
4.2 4T,(G) AND 4T2(G). - Figure 3 shows our data
for the two lower bands 4T1 (G) and 4T2(G). Dipole strengths associated with the broad bands (Fig. 3a) are
Fig. 2. - Survey of the room and low temperature axial spectra ofRb3Mn2C17.
482
Fig. 3. - Broad band spectra (a) and red edge data for 4T l(G) (b) and 4T2(G) (c). The MCD associated with the E2
exciton is also shown on an enlarged scale.
found to be 10 % (4T1) and 20 % (4T2) lower in n than
in 6 polarization. Considering the sharp features on
the red edge of 4T l’ E1, which is solely n polarized, is symmetrical and shows no MCD. It is readily assigned
to the 1, 3/2 ) ED origin (see Table I). E2 (E2 - E 1 = 55 cm -1 ) is seen in the a = a spectrum and there is an associated positive at term. No other al
term was found up to 300 cm -1 above E1. From the polarization of E2 and the sign of the MCD, we assign
it to an origin with a 0, 3 /2 ) character. Note that E2
which was not observed in the excitation spectrum [19J
has only a maximum absorbance of roughly 10-2 for
t = 1 mm, and a width of a few cm-1. The sensitivity
of the MCD technique is well illustrated here since the
signal to noise ratio is 50 for t = 1 mm and B = 2.5 T.
Other features S 1 and M 1 in the n spectrum are exci- ton-phonon and exciton-magnon side-bands. M 1 has
the polarization expected (n) and is located about 90 cm -1 above E1. From the determined positions
of E1 and E2, we conclude that the tetragonal field parameter is negative. This correlates well with the fact that the barycentre of the broad band J spectrum lies 120 cm - 1 higher than that of the n spectrum.
As far as 4T2(G) is concerned (Fig. 3a, c) no fine
structure or MCD was found on its red edge. Some
broad features are seen in the a = Q spectrum in the 21 200-21 400 em -1 region while A n is strictly zero.
They are certainly of a vibrational origin. The bary-
centre of the n spectrum occurs 340 cm -1 above that of A,,, thus indicating a large, positive D value.
4.3 4T 1 (P). - Two excitons are observed on the red edge (Fig. 4) of the 4T 1 (P) band. E1, which is seen solely in the n spectrum, is assigned to Ti, 1, 3/2 ).
E2 (E2 - El = 12 em -1) occurs in the a and J spec- tra and has an associated positive a1 term. It is readily assigned to a state of dominant 0, 3/2 > character.
This result indicates that the tetragonal splitting is
small, as indeed confirmed by the fact thai Ea for the
broad band is only about 50 cm-1 above E1[’ Both E1
and E2 excitons have magnon sidebands E.Ml and E.M2 at roughly 90 cm-’. From its symmetrical line-shape and energy, E.P 1 (El + 73 em -1) is a phonon sideband of E1. E.P2, which has an associated MCD, is a phonon sideband of E2. The MCD is strictly zero (as expected) for E.M2. Weak features a
and b, seen solely in the MCD spectrum are due to
impurities since (i) at most two excitons are predicted
in the a = Q spectrum (10, 3/2 > and l, 1/2 >);
(ii) if, e.g., a was correlated with 11, 1/2 ), its weakness would imply a large, negative D parameter, and place E2 much higher than E1 in what is actually observed.
4.4 4T2(D). - Our results are shown in figure 5. The assignment of E1 at 26 580 cm-1 to an excited state
Fig. 4. - Polarized absorption and MCD on the red edge
of the 4T1(P) band.
Fig. 5. - Polarized absorption and MCD on the red edge
of the 4T2(D) band.
having a dominant I 4T 2 0, 3/2 ) character (a sublat- tice) is straightforward from its appearance in the
a = 6 spectrum and the associated intense negative
a, term. E2 which is seen solely in the 7t spectrum
(E2 - El = 113 cm-l) and shows no MCD is corre-
lated with 14T 2’ - 1, 3/2 ). We thus conclude that D is positive. From the comparison of our J and 7t
spectra, we observe that the crystal was fairly accu- rately oriented for these experiments. Weak features
(A, B, C) seen in the MCD spectrum (Fig. 5) indicate the location of weak phonon sidebands of E1.
As predicted in table I, E has an associated magnon sideband in 6 polarization. It peaks at 90 cm-1 at the
lowest temperature and moves slightly towards low
energies upon heating (shift of 7 cm-1 at TN) while
its overall intensity decreases slightly between 4.2 K
and 56 K. This behaviour (shift and intensity variation)
is a reflection of changing spin correlations since the
intensity mechanism for magnon sidebands is an
exchange mechanism [24].
Finally, we note that the exciton-magnon band of Rb2MnCl4 [14] does not show up as a residual (100 cm-’ below E.M.) in figure 5. We therefore conclude that our Rb3Mn2CI7 crystal is almost free
( 1 %) of the parent compound.
4.5 4E, 4A1(G). - The dominant feature in this
region (Fig. 6) consists of three sharp lines E1 - E3
with accompanying ai terms. As is well known,
the tetragonal field and spin-orbit interaction have
only second-order effects on the 4E state. For sublat- tice a, one therefore expects two strong (intensities le
and IE) and almost degenerate lines to I 8, 3/2 > and I E, 3/2 >. Spin-orbit coupling can however produce
some very weak intensity /g and le to the I e, - 1/2 >
and 10, - 1/2 > states predicted roughly 2 H above 10, 3/2 ) and E, 3/2 ). One should have 1,’,110 - 10’11,: - (Aj2 H)2 where H is typically 100 cm-’ and IAI- 10 cm-1.
From the sign of the MCD (and ð-M1jMo), Ei and E2 (separated by 8.6 cm-’) are readily assigned to the
0 and e orbital components (sublattice a). The ratio of dipole strengths for E2 and E1 is found to be roughly
I instead of 3 as predicted (Table I). This discrepancy
has already been noted for K2MnF4 [6] and for the almost tetrahedral compound CS3MnC’5 [20]. It is presently unexplained.
E 3 (E3 - El = 19.2 cm -1 ) has a dipole strength comparable to that of E 1 and E2, but the correspond- ing a1 term is roughly an order of magnitude smaller
than the two others. Although the sign of a1 is consis-
tent with 4A (Table I), we do not favour this assign-
ment since : (i) al is considerably smaller than expected
and the S-shaped MCD is zero at an energy slightly higher than E3 ( N 3 em - 1) ; (ii) 4A 1 is usually found at
much higher an energy in related compounds [6]. We
rather believe that vibronic components are present in that region. This is further supported by our low-
resolution data on an extended energy range in figure 7.
Fig. 6. - Polarized absorption and MCD on the red edge
of the 4E, 4 At (G) band. The MCD features associated with lines a, b and d have been magnified 50 times to be clearly
seen in this figure.
Fig. 7. - Axial absorption (----) and MCD (-) in the
23 500-23 850 cm-1 range at 1.8 K and 4.2 K. The scales are
for t = 1 mm and B = 1 T. Exciton lines are too weak to be observed at that scale.
The magnon and magnon-phonon components show
zero MCD while weak features are seen (comparable
to that near E3) for unobserved absorption compo- nents which must have an exciton-phonon character.
This argument stands also for E.P. (Fig. 6) which
occurs near E3 and is substantially broader than E1
and E3’
The weak features a-d seen in the absorption (e.g., c)
or solely in the MCD (e.g., a) spectrum (Fig. 6) were
found to be sample dependent and are due to impu-
rities (e.g., MnC’2, RbMnCl3). As discussed else-
where [14] this illustrates the difficulty in growing
