- Email: [email protected]
One-magnon light scattering in exchange-noncollinear Nd2CuO4
PhysicaC 178 (1991) North-Holland
PHYSICA B
189-192
One-magnon light scattering in exchange-noncollinear
Nd*CuO,
I.M. Vitebskii a, A.V. Yeremenko a, Yu.G. Pashkevich b, V.L. Sobolev a and S.A. Fedorov a Institutefor Single Crystals. Academy ofSciences of Ukrainian SSR. Kharkov. 310141, USSR
b
b Physicotechnical Institute, Academy of Sciences of Ukrainian SSR, Donetsk, 340114, USSR Received
15 April 199
I
It is shown that in an exchange-noncollinear four-sublattice antiferromagnet Nd2Cu04 scattering from the exchange magnon should be observed. It makes it possible to determine exchange interaction.
Neodymium cuprate is the basic compound for a new class of high-temperature superconductors with the electron-type conductivity. Similar to other highT, objects, the crystal has unique magnetic properties. In a stoichiometric compound it is a four-sublattice exchange-noncollinear antiferromagnet with the magnetic ordering temperature TN z 240 K [ 1,2 ] ; its magnetic structure is of the “cross-like” type. As is well known, an exchange-noncollinear magnet has three acoustic modes of uniform oscillations of the spin subsystem. The rest modes are referred to as exchange ones and their activation energies are determined to be bilinear or biquadratic in spin parts of exchange interactions depending on the type of magnetic ordering. Exchange modes with the activation determined by bilinear exchange interactions were observed both in magnets collinear in the exchange approximation using, for example, the method of antiferromagnetic resonance [ 3 1, and in exchange-noncollinear ones using neutron scattering [4]. The feature of NdzCuOd as an exchange-noncollinear magnet is that its magnetic structure can be stabilized only by the biquadratic exchange interaction. And just in such magnets the activation energy of the exchange magnon is determined by that exchange interaction. The observation of exchange modes in similar crystals permits direct measuring of the biquadratic exchange interaction constant. Raman scattering makes it possible to study magnon modes inaccessible by methods of direct absorption spectroscopy. Studies of light scattering in magnets 0921-4534/91/$03.50
0 1991 Elsevier Science Publishers
an anomalously high intensity of light directly the constant of the biquadratic
are often difficult since the intensity involves the constants of the linear and quadratic magneto-optical effects reduced by small factors. The latter is determined by the ratio of relativistic to exchange interactions. In antiferromagnets collinear in the exchange approximation such a factor is the small parameter, describing the degree of noncollinearity of the magnetic structure [ 5 1. So a contribution to the scattering tensor from isotropic terms of spin orientations is not predominant. In an applied magnetic field noncollinearity increases, the contribution of that mechanism grows and, hence, the scattering intensity rises [ 6,7]. Therefore, it should be expected that in an exchange-noncollinear magnet (e.g., NdzCu04) the role of the exchange mechanism of scattering is more plausible. The peculiarities of magnetic ordering in NdzCu04 are associated with structural distortions appearing in the paraphase and resulting in the lowering of crystal symmetry from D&7,to D:z [ 8 1. A unit cell of the dissymmetrical phase involves four formula units of NdzCu04, magnetic copper ions are in 4f-positions. Their numbering is in accordance with ref. [ 81, i.e., 1: (x, x- 1, 4); 2: (x+ 1, -X, ;); 3: (1 -x, x, ;,; 4: ( -x, 1 -x, t ). The basic functions of irreducible representations of DA: can be expressed in terms of the following linear combinations of sublattice spins: F=s,
+sz +sJ +s,,
B=s, -s2 +sx
B.V. All rights reserved
-s4,
A=s,
+sz-Q-Q,
c=s,
-s2
-s3
+s4.
(1)
Table 1 presents their classification. Using the table. the spin system Hamiltonian can be represented in the form:
ht,,=a?E“+rr,(.,~‘+B’)
At,._ =i.,F, At,_=-;,F, +&(A,
+B,,)‘+u,(A,.+B,)’
+u,(.,l,
-B,)2+uX(.A,.-BB,)2.
(2)
where .I. D and u are the bilinear exchange. biquadratic exchange and anisotropy constants, respectively. The stability of all the possible exchange-noncollinear structures which can appear from the paramagnetic phase without unit cell multiplication has been analyzed in ref. [ 8 1. A comparison with experiments [ 1.21 shows that those phases are realized in which the equilibrium spin distributions are transformed by one or two irreducible representations: A,, (Pl phase with magnetic point symmetry D4,,(D4). and ground state ~q.,=B, =S”‘s) or BZu (P2 phase with magnetic point symmetry D4,, ( Dz) and ground state ,q,.=B, = 8 “*s. Both phases are of decreases, exa “cross-like” type. As temperature change-noncollinear phases replace each other as Pll+P2+Pl [ 1,2]. To describe one-magnon light scattering let us represent depending on spins crystal permittivity AC,, as a series of in powers of basic functions [ 5.7 1. In terms quadratic in operators ( 1 ) we shall retain only those of the exchange origin. viz. AC,, =cr,,F*+.,
A’+a2B’
A~,.,.=~,F*+cT~A*+cJ, Table I Classification of Cartesian resentatlons of D$ group.
;
B’ ;
components
( I ) by irreducible
rep-
+j.:(‘,
:
;
--,12C,.
(3)
Orthogonality relations for vectors ( 1 ) were taken into account here. Values of g can be easily expressed via spin-dependent polarizabilities of the ion pail from (Y and p sublattices x$,~. E.g. (5, =~sp(Jtli,,-Jc::,,);
0~=~sp(7tc:~,,-7r~~,,)
(SJ= ; sp ( JI ‘Z,, - Jt Y,/) :
f7( = 4 sp 7LI:,,
:
If in eqs. (3) basic functions ( 1 ) are substituted by their equilibrium values, then we obtain a change of crystal permittivity due to magnetic ordering. It can be easily seen that At,, =At,.,, in both phases P 1 and P2. Linear in deviations from equilibrium values terms, taken into account in eqs. (3 ), give a part of the At(‘) tensor describing one-magnon light scattering. Tie scattering tensor form a; depends on the components of sublattices magnetization which take part in vibrations of the magnon mode v. Uniform vibrations of the spin subsystem have been classified by symmetry types and their energies have been calculated in ref. [ 81. Further the relative vibration amplitudes of vector components ( 1) in each magnon mode will be required. The simplest way to obtain those amplitudes is by means of coefficients of the u-v transformation in the scheme of secondary quantization [ 5 1. To do it, one should go from s,, to the operators s; in eq. (2), each of them being written down in its own local frame of reference with the O?-axis directed along the equilibrium spin value. Matrices of the transition $ for different ions which permutations are due to symmetry operations are interrelated. Therefore, the relation of L to L’ of the type of eq. (1 ) (L=A, B, C, F, L’=A’. B’, C’. F’) can be also found. In phase Pl we have
191
I.M. Vitebskii et al. /Light scattering in Nd2Cu0,
and in phase P2
Matrix fi is of the form
The column index on the left-hand side of eqs. (4) and (5 ) indicates the number of modes, vector components of the column taking part in the mode vibrations. In a four-sublattice exchange-noncollinear magnet the three modes of uniform vibrations Al, A2 and A3 are acoustic and the E-mode is an exchange mode. Operators L’ are expressed through the HolsteinPrimakoff spin deviation ones. The operators are given in ref. [ 71 where the substitution A’, B’, C’ t* L; , L;, L; should be made. Substituting eqs. (4) and (5) into the Hamiltonian (2), we determine in a standard way energies and transformation u-v coefficients from spin-deviation operators to those of magnon creation <+ and annihilation c of the branch v. As a result, operators L’ which are linear in <’ and r take the form: L,:=(2s)“2t,,(<++<)
; (6)
In phase Pl l/4
>
;
d&A2 +2a2 a,-a,
‘14,
Jo-J,
F.AI
=
>
a;=(n.+1(Atl’)In,)(n,+1)-“2,
d,,, = t ,h2 ;
d
F,A I =tF,;,
’
-Jo-2a2 ( 8s)2D+ 2a6 - 2a2 >
=
;
(8)
where n, are magnon occupation numbers. Using eqs. ( 3 )- ( 8 ) we obtain the tensor forms similar both for Pl and P2: aA’=(-i
aE= ;
L;=(~s)“~&((+--)
t
from eq. (7), in both phases three types of acoustic magnons are in correspondence with such precession of sublattice spins at which the “cross-like” structure rotates mainly as a whole. So, in phase P 1 for modes with gies A2 and A3 degenerated oAz = mA3= 8s [ a2 (2J, -Jo + 4a2 ) ] ‘I’, a turn is along the y- and x-axes, respectively. In Al with the energy oA,=8s[2(az-a4) (JI-Jo+2a2)]‘/2atumisinthe xy-plane. In the exchange mode E with the energy o,=8s{ [ (8s)‘D+2a,-a21 [ -Jo-2a2]}“’ antiferromagnetism vectors of adjacent layers precess out of phase. All the three acoustic modes in NdzCu04 were observed in antiferromagnetic resonance. Modes A2 and A3 are also electrically-dipole-active in the exchange approximation [ 81. According to the experimental conditions, just those modes were observed in ref. [ 9 1. The exchange mode E does not manifest itself in magnetic resonance. In one-magnon light scattering all the four magnon modes manifest themselves in both phases. Let us define the one-magnon scattering tensor a; as a matrix element of the form
i
d 0
0 -d
(0
0
g); 0 0
aAiA3=(_B
-8
.
(9)
0)
Values of b and c involve constants of linear magneto-optical effects which are exchange-attenuated by u-v coefficients. For example, c= ( -II I +A2).s’12 x tA.A2.It is similar to the case of scattering by acoustic magnons in collinear antiferromagnets. As for scattering by exchange magnons, d involves constants of quadratic magneto-optical effects of the exchange origin, viz.
l/4
’
dc,E =G
.
(7)
For phase P2 the substitutions should be made in eqs. (7), i.e., A - B, a, - a,; a4 - a+ Thus, as follows
i);
d=(uz-a,)(8S)“*S
-Jo-2a2 (8s)‘D+2a6-2a2
l/4
>
(10)
192
I.M.
I’frehskli
ei al. / Llghr scaltering
Thus if the condition Jx=- D B a is satisfied the scattering intensity with the exchange mode should exceed that with acoustic ones by some orders of magnitude. In collinear magnets the situation is quite opposite, i.e., the scattering intensity by acoustic magnons is much higher than that by exchange ones, if one takes into account only contributions of linear magneto-optical effects [ 5,7]. It should be noted that the difference a, - r~, is nonzero even in the absence of structural distortions. This is due to the peculiarities of the cross-like structure in magneto-optical effects. Since the tensor of scattering by the exchange mode E is the same as for phonons with the symmetry B,, and the scattering intensity is high, the number of phonons with that symmetry is required. In a number of experiments [ 10-I 21 for studying Raman scattering in NdzCuO, phonons were classified in symmetry groups on the basis of Dir:. In this case there exists a single phonon with the B,,-symmetry. However, the scattering spectrum recorded in the (x, x)-geometry at 30 K [lo] exhibits a great number of A,, and B,, lines. This indirectly confirms the presence of structural distortions. Recently it was suggested [ 131 that structural distortions in NdzCuO, resulting in lowering the space symmetry D:L - D:z are not spontaneous, but are induced by the adjustment of crystal lattice to magnetic ordering of the “cross-like” type (similar to the magnetostriction effect). It can be shown that this suggestion is inconsistent with the system magnetic symmetry. Thus, the above spontaneous structural distortions exist independently of long-range magnetic order. Let us consider the classification of atomic vibrations NdCuO_, by symmetry types for D:;1: Nd atoms occupy the 8j-site and participate in vibrations of normal modes 2A,, +AZg+BIg+2BXg +3E,+A,,+2Az, + 2B, u + Bzu + 3E,; Cu atoms in 4f-sites are distributed in vibrations A,,fAz,+B,,+B>g + E, + Azu + B, u+ 2E,; oxygen atoms in CuO planes of 2a- and 2b-sites participate in vibrations .4?,+B,.+2E,, and those of 4c-sites in vibrations
In n;d,C‘uO,
A,, + A>” + B, u+ Bzu + 4E,; other oxygen atoms of 4d distributed in and 4e-sites arc and B,,+Bz,+2E,+A,“+Az,+2E, A,,+Blg+2Eg+Az,+B,.+2E,, respectively. Thus, with due regard for structural distortions there appear three types of B,, and four types of A,,. In ref. light scattering. [ 10.11 I, studying two-magnon J,,zz lo7 cm-’ was estimated. Setting Dz 10 cm-‘. one can obtain the exchange mode energy equal to wEz 10’ cm-‘. It stands to reason, the real value of that energy can be higher or lower than lo2 cm-‘. Unfortunately, the scattering spectrum at about 10’ cm-’ in the geometry corresponding to A,, and B,, [lo] is not sufficiently informative due to a strong side-band of the basic line and noise.
References [ I ] S. Skanthacumar, H. Zhang, T.W. Clinton, W.-H. Lt. J.W. Lynn, Z. Fisk and S.-W. Cheong, Physica C 160 ( 1989) 124. [2] M.J. Rosseinsky and K. Prassides. Physica c‘ 162-164 (1989) 522. [3] V.G. Bar’yakhtar, V.V. Eremenko. V.M. Naumenko, Yu.G. Pashkevich, V.V. Pishko and V.L. Sobolev. Sov. Phys. JETP 61 (1985) 823. [4] R.M. Moral, W.J.L. Buyers, R.L. Armstrong and K. Hirakawa, Phys. Rev. B 38 ( 1988) 543. [ 51V.G. Bar’yakhtar, Yu.G. Pashkevich and V.L. Sobolev. Sov. Phys. JETP 58 ( 1983) 945. [6] S.O. Demokritov, N.M. Kreines and V.I. Kudynov. JETP 92 ( 1987) 689, in Russian. [ 71 Yu.G. Pashkevich, V.L. Sobolev and S.A. Fedorov. J. Phys. C 21 (1988) 1265. [ 81 V.A. Blinkin, I.M. Vitebskii. O.D. Kolotii, N.M. Lavrinenko. V.P. Seminozhenko and V.L. Sobolev. JETP 98 (1990) 2098. in Russian. [9] V.V. Eremenko, S.A. Zvyagin, V.V. Pishko, V.V. Tsapenko, S.N. Barilo and D.I. Zhigunov, Pis’ma JETP 52 ( 1990) 955, in Russian. [IO] S. Sugar, T. Kobayasht and J. Akimitsu, Phys. Rev. B 40 (1989) 2686. [ 1 I ] P.E. Sulewski. P.A. Fleury, K.B. Lyons, SW. Cheong and Z. Fisk, Phys. Rev. B 41 ( 1990) 225. [ 121 V.M. Orera, M.L. Sanjuan, R. Alcala, J. Fontcuberta and S. Pinol, Physica C 168 ( 1990) I61 [ 13 JD.A. Yablonskii, Sverkhprovodimost’: Fizika, Khimiya. Tekhnika. vol. 3 ( 1990) p. 2706, in Russian.
PHYSICA B
189-192
One-magnon light scattering in exchange-noncollinear
Nd*CuO,
I.M. Vitebskii a, A.V. Yeremenko a, Yu.G. Pashkevich b, V.L. Sobolev a and S.A. Fedorov a Institutefor Single Crystals. Academy ofSciences of Ukrainian SSR. Kharkov. 310141, USSR
b
b Physicotechnical Institute, Academy of Sciences of Ukrainian SSR, Donetsk, 340114, USSR Received
15 April 199
I
It is shown that in an exchange-noncollinear four-sublattice antiferromagnet Nd2Cu04 scattering from the exchange magnon should be observed. It makes it possible to determine exchange interaction.
Neodymium cuprate is the basic compound for a new class of high-temperature superconductors with the electron-type conductivity. Similar to other highT, objects, the crystal has unique magnetic properties. In a stoichiometric compound it is a four-sublattice exchange-noncollinear antiferromagnet with the magnetic ordering temperature TN z 240 K [ 1,2 ] ; its magnetic structure is of the “cross-like” type. As is well known, an exchange-noncollinear magnet has three acoustic modes of uniform oscillations of the spin subsystem. The rest modes are referred to as exchange ones and their activation energies are determined to be bilinear or biquadratic in spin parts of exchange interactions depending on the type of magnetic ordering. Exchange modes with the activation determined by bilinear exchange interactions were observed both in magnets collinear in the exchange approximation using, for example, the method of antiferromagnetic resonance [ 3 1, and in exchange-noncollinear ones using neutron scattering [4]. The feature of NdzCuOd as an exchange-noncollinear magnet is that its magnetic structure can be stabilized only by the biquadratic exchange interaction. And just in such magnets the activation energy of the exchange magnon is determined by that exchange interaction. The observation of exchange modes in similar crystals permits direct measuring of the biquadratic exchange interaction constant. Raman scattering makes it possible to study magnon modes inaccessible by methods of direct absorption spectroscopy. Studies of light scattering in magnets 0921-4534/91/$03.50
0 1991 Elsevier Science Publishers
an anomalously high intensity of light directly the constant of the biquadratic
are often difficult since the intensity involves the constants of the linear and quadratic magneto-optical effects reduced by small factors. The latter is determined by the ratio of relativistic to exchange interactions. In antiferromagnets collinear in the exchange approximation such a factor is the small parameter, describing the degree of noncollinearity of the magnetic structure [ 5 1. So a contribution to the scattering tensor from isotropic terms of spin orientations is not predominant. In an applied magnetic field noncollinearity increases, the contribution of that mechanism grows and, hence, the scattering intensity rises [ 6,7]. Therefore, it should be expected that in an exchange-noncollinear magnet (e.g., NdzCu04) the role of the exchange mechanism of scattering is more plausible. The peculiarities of magnetic ordering in NdzCu04 are associated with structural distortions appearing in the paraphase and resulting in the lowering of crystal symmetry from D&7,to D:z [ 8 1. A unit cell of the dissymmetrical phase involves four formula units of NdzCu04, magnetic copper ions are in 4f-positions. Their numbering is in accordance with ref. [ 81, i.e., 1: (x, x- 1, 4); 2: (x+ 1, -X, ;); 3: (1 -x, x, ;,; 4: ( -x, 1 -x, t ). The basic functions of irreducible representations of DA: can be expressed in terms of the following linear combinations of sublattice spins: F=s,
+sz +sJ +s,,
B=s, -s2 +sx
B.V. All rights reserved
-s4,
A=s,
+sz-Q-Q,
c=s,
-s2
-s3
+s4.
(1)
Table 1 presents their classification. Using the table. the spin system Hamiltonian can be represented in the form:
ht,,=a?E“+rr,(.,~‘+B’)
At,._ =i.,F, At,_=-;,F, +&(A,
+B,,)‘+u,(A,.+B,)’
+u,(.,l,
-B,)2+uX(.A,.-BB,)2.
(2)
where .I. D and u are the bilinear exchange. biquadratic exchange and anisotropy constants, respectively. The stability of all the possible exchange-noncollinear structures which can appear from the paramagnetic phase without unit cell multiplication has been analyzed in ref. [ 8 1. A comparison with experiments [ 1.21 shows that those phases are realized in which the equilibrium spin distributions are transformed by one or two irreducible representations: A,, (Pl phase with magnetic point symmetry D4,,(D4). and ground state ~q.,=B, =S”‘s) or BZu (P2 phase with magnetic point symmetry D4,, ( Dz) and ground state ,q,.=B, = 8 “*s. Both phases are of decreases, exa “cross-like” type. As temperature change-noncollinear phases replace each other as Pll+P2+Pl [ 1,2]. To describe one-magnon light scattering let us represent depending on spins crystal permittivity AC,, as a series of in powers of basic functions [ 5.7 1. In terms quadratic in operators ( 1 ) we shall retain only those of the exchange origin. viz. AC,, =cr,,F*+.,
A’+a2B’
A~,.,.=~,F*+cT~A*+cJ, Table I Classification of Cartesian resentatlons of D$ group.
;
B’ ;
components
( I ) by irreducible
rep-
+j.:(‘,
:
;
--,12C,.
(3)
Orthogonality relations for vectors ( 1 ) were taken into account here. Values of g can be easily expressed via spin-dependent polarizabilities of the ion pail from (Y and p sublattices x$,~. E.g. (5, =~sp(Jtli,,-Jc::,,);
0~=~sp(7tc:~,,-7r~~,,)
(SJ= ; sp ( JI ‘Z,, - Jt Y,/) :
f7( = 4 sp 7LI:,,
:
If in eqs. (3) basic functions ( 1 ) are substituted by their equilibrium values, then we obtain a change of crystal permittivity due to magnetic ordering. It can be easily seen that At,, =At,.,, in both phases P 1 and P2. Linear in deviations from equilibrium values terms, taken into account in eqs. (3 ), give a part of the At(‘) tensor describing one-magnon light scattering. Tie scattering tensor form a; depends on the components of sublattices magnetization which take part in vibrations of the magnon mode v. Uniform vibrations of the spin subsystem have been classified by symmetry types and their energies have been calculated in ref. [ 81. Further the relative vibration amplitudes of vector components ( 1) in each magnon mode will be required. The simplest way to obtain those amplitudes is by means of coefficients of the u-v transformation in the scheme of secondary quantization [ 5 1. To do it, one should go from s,, to the operators s; in eq. (2), each of them being written down in its own local frame of reference with the O?-axis directed along the equilibrium spin value. Matrices of the transition $ for different ions which permutations are due to symmetry operations are interrelated. Therefore, the relation of L to L’ of the type of eq. (1 ) (L=A, B, C, F, L’=A’. B’, C’. F’) can be also found. In phase Pl we have
191
I.M. Vitebskii et al. /Light scattering in Nd2Cu0,
and in phase P2
Matrix fi is of the form
The column index on the left-hand side of eqs. (4) and (5 ) indicates the number of modes, vector components of the column taking part in the mode vibrations. In a four-sublattice exchange-noncollinear magnet the three modes of uniform vibrations Al, A2 and A3 are acoustic and the E-mode is an exchange mode. Operators L’ are expressed through the HolsteinPrimakoff spin deviation ones. The operators are given in ref. [ 71 where the substitution A’, B’, C’ t* L; , L;, L; should be made. Substituting eqs. (4) and (5) into the Hamiltonian (2), we determine in a standard way energies and transformation u-v coefficients from spin-deviation operators to those of magnon creation <+ and annihilation c of the branch v. As a result, operators L’ which are linear in <’ and r take the form: L,:=(2s)“2t,,(<++<)
; (6)
In phase Pl l/4
>
;
d&A2 +2a2 a,-a,
‘14,
Jo-J,
F.AI
=
>
a;=(n.+1(Atl’)In,)(n,+1)-“2,
d,,, = t ,h2 ;
d
F,A I =tF,;,
’
-Jo-2a2 ( 8s)2D+ 2a6 - 2a2 >
=
;
(8)
where n, are magnon occupation numbers. Using eqs. ( 3 )- ( 8 ) we obtain the tensor forms similar both for Pl and P2: aA’=(-i
aE= ;
L;=(~s)“~&((+--)
t
from eq. (7), in both phases three types of acoustic magnons are in correspondence with such precession of sublattice spins at which the “cross-like” structure rotates mainly as a whole. So, in phase P 1 for modes with gies A2 and A3 degenerated oAz = mA3= 8s [ a2 (2J, -Jo + 4a2 ) ] ‘I’, a turn is along the y- and x-axes, respectively. In Al with the energy oA,=8s[2(az-a4) (JI-Jo+2a2)]‘/2atumisinthe xy-plane. In the exchange mode E with the energy o,=8s{ [ (8s)‘D+2a,-a21 [ -Jo-2a2]}“’ antiferromagnetism vectors of adjacent layers precess out of phase. All the three acoustic modes in NdzCu04 were observed in antiferromagnetic resonance. Modes A2 and A3 are also electrically-dipole-active in the exchange approximation [ 81. According to the experimental conditions, just those modes were observed in ref. [ 9 1. The exchange mode E does not manifest itself in magnetic resonance. In one-magnon light scattering all the four magnon modes manifest themselves in both phases. Let us define the one-magnon scattering tensor a; as a matrix element of the form
i
d 0
0 -d
(0
0
g); 0 0
aAiA3=(_B
-8
.
(9)
0)
Values of b and c involve constants of linear magneto-optical effects which are exchange-attenuated by u-v coefficients. For example, c= ( -II I +A2).s’12 x tA.A2.It is similar to the case of scattering by acoustic magnons in collinear antiferromagnets. As for scattering by exchange magnons, d involves constants of quadratic magneto-optical effects of the exchange origin, viz.
l/4
’
dc,E =G
.
(7)
For phase P2 the substitutions should be made in eqs. (7), i.e., A - B, a, - a,; a4 - a+ Thus, as follows
i);
d=(uz-a,)(8S)“*S
-Jo-2a2 (8s)‘D+2a6-2a2
l/4
>
(10)
192
I.M.
I’frehskli
ei al. / Llghr scaltering
Thus if the condition Jx=- D B a is satisfied the scattering intensity with the exchange mode should exceed that with acoustic ones by some orders of magnitude. In collinear magnets the situation is quite opposite, i.e., the scattering intensity by acoustic magnons is much higher than that by exchange ones, if one takes into account only contributions of linear magneto-optical effects [ 5,7]. It should be noted that the difference a, - r~, is nonzero even in the absence of structural distortions. This is due to the peculiarities of the cross-like structure in magneto-optical effects. Since the tensor of scattering by the exchange mode E is the same as for phonons with the symmetry B,, and the scattering intensity is high, the number of phonons with that symmetry is required. In a number of experiments [ 10-I 21 for studying Raman scattering in NdzCuO, phonons were classified in symmetry groups on the basis of Dir:. In this case there exists a single phonon with the B,,-symmetry. However, the scattering spectrum recorded in the (x, x)-geometry at 30 K [lo] exhibits a great number of A,, and B,, lines. This indirectly confirms the presence of structural distortions. Recently it was suggested [ 131 that structural distortions in NdzCuO, resulting in lowering the space symmetry D:L - D:z are not spontaneous, but are induced by the adjustment of crystal lattice to magnetic ordering of the “cross-like” type (similar to the magnetostriction effect). It can be shown that this suggestion is inconsistent with the system magnetic symmetry. Thus, the above spontaneous structural distortions exist independently of long-range magnetic order. Let us consider the classification of atomic vibrations NdCuO_, by symmetry types for D:;1: Nd atoms occupy the 8j-site and participate in vibrations of normal modes 2A,, +AZg+BIg+2BXg +3E,+A,,+2Az, + 2B, u + Bzu + 3E,; Cu atoms in 4f-sites are distributed in vibrations A,,fAz,+B,,+B>g + E, + Azu + B, u+ 2E,; oxygen atoms in CuO planes of 2a- and 2b-sites participate in vibrations .4?,+B,.+2E,, and those of 4c-sites in vibrations
In n;d,C‘uO,
A,, + A>” + B, u+ Bzu + 4E,; other oxygen atoms of 4d distributed in and 4e-sites arc and B,,+Bz,+2E,+A,“+Az,+2E, A,,+Blg+2Eg+Az,+B,.+2E,, respectively. Thus, with due regard for structural distortions there appear three types of B,, and four types of A,,. In ref. light scattering. [ 10.11 I, studying two-magnon J,,zz lo7 cm-’ was estimated. Setting Dz 10 cm-‘. one can obtain the exchange mode energy equal to wEz 10’ cm-‘. It stands to reason, the real value of that energy can be higher or lower than lo2 cm-‘. Unfortunately, the scattering spectrum at about 10’ cm-’ in the geometry corresponding to A,, and B,, [lo] is not sufficiently informative due to a strong side-band of the basic line and noise.
References [ I ] S. Skanthacumar, H. Zhang, T.W. Clinton, W.-H. Lt. J.W. Lynn, Z. Fisk and S.-W. Cheong, Physica C 160 ( 1989) 124. [2] M.J. Rosseinsky and K. Prassides. Physica c‘ 162-164 (1989) 522. [3] V.G. Bar’yakhtar, V.V. Eremenko. V.M. Naumenko, Yu.G. Pashkevich, V.V. Pishko and V.L. Sobolev. Sov. Phys. JETP 61 (1985) 823. [4] R.M. Moral, W.J.L. Buyers, R.L. Armstrong and K. Hirakawa, Phys. Rev. B 38 ( 1988) 543. [ 51V.G. Bar’yakhtar, Yu.G. Pashkevich and V.L. Sobolev. Sov. Phys. JETP 58 ( 1983) 945. [6] S.O. Demokritov, N.M. Kreines and V.I. Kudynov. JETP 92 ( 1987) 689, in Russian. [ 71 Yu.G. Pashkevich, V.L. Sobolev and S.A. Fedorov. J. Phys. C 21 (1988) 1265. [ 81 V.A. Blinkin, I.M. Vitebskii. O.D. Kolotii, N.M. Lavrinenko. V.P. Seminozhenko and V.L. Sobolev. JETP 98 (1990) 2098. in Russian. [9] V.V. Eremenko, S.A. Zvyagin, V.V. Pishko, V.V. Tsapenko, S.N. Barilo and D.I. Zhigunov, Pis’ma JETP 52 ( 1990) 955, in Russian. [IO] S. Sugar, T. Kobayasht and J. Akimitsu, Phys. Rev. B 40 (1989) 2686. [ 1 I ] P.E. Sulewski. P.A. Fleury, K.B. Lyons, SW. Cheong and Z. Fisk, Phys. Rev. B 41 ( 1990) 225. [ 121 V.M. Orera, M.L. Sanjuan, R. Alcala, J. Fontcuberta and S. Pinol, Physica C 168 ( 1990) I61 [ 13 JD.A. Yablonskii, Sverkhprovodimost’: Fizika, Khimiya. Tekhnika. vol. 3 ( 1990) p. 2706, in Russian.