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The spin structure of Nd2CuO4
PhysicaC 165 (1990) 131-132 North-Holland
COMMENT on “Afagnetic phase transitions and structural distortion in Nd2Cu04” by S. Skanthakumar et al., Physica C 160 ( 1989) 124 THE SPIN STRUCTURE K. YAMADA,
K. KAKURAI
OF NdZCuOd and Y. ENDOH
Department of Physics, Tokoku University, Aoba. Aramaki, 980 Sendai, Japan
Received 16 October 1989
In the paper entitled “Magnetic phase transitions and structural distortion in NdzCu04” by S. Skanthakumar et al., published in Physica C 160 ( 1989) 124-28, there is an incorrect argument on the spin structure. The observed magnetic peaks can all be indexed as (h/2, k/2, 1), with h, k odd integers. “However, peaks with I even are observed to have quite different intensities compared to those with 1 odd, which would require the unlikely situation that domain populations (to) be correspondingly unbalances (p. 126, column 1, line 8). The above cursive argument is not correct. Even in the case of balanced domain populations, the intensities from (h/2, k/2, 1) reflections are very different between 1 even and I odd ones. The spin structure in the high temperature phase (75 K< T< 245 K) in Nd*CuO, can be constructed from the two domains of so-called La,NiO, type structure: spin direction [ l/2, l/2, 0] is parallel to the antiferromagnetic propagation vector. In this spin structure, the structure factor for ( 1/ 2, l/2, 0) reflection is always zero and the structure factors for (h/2, k/2, I) reflections with h, k odd are non-zero and identical. However, their angle factors which depend on the relative orientation of the spin direction and the reciprocal lattice vector z are quite different between 1 odd and 1 even reflections. For the former reflections, the domain with the spin direction perpendicular to the z contributes to the reflections. Therefore their intensities change with the square of their form factors. On the other hand, for the latter reflections the relative spin orientation to the 7 depends on each reflection. Therefore it is obvious that we should observe the different intensities between two types of reflections with 1odd and even. In a tetragonal symmetry, it is possible to con0921-4534/90/$03.50 0 Elsevier Science Publishers ( North-Holland )
B.V.
struct the same non-collinear spin structure as proposed by Shanthakumer et al. by a superposition of two domains of La,NiO, type structure. However, in the case of balanced domain populations we cannot observe the difference in the intensities between the collinear and the non-collinear structures at least by using unpolarized neutrons. Furthermore we cannot understand why the polarized neutron measurement performed by Skanthakumer et al. could determine the non-collinear structure rather than the collinear one with balanced domain populations. In particular the sentence “ratio of the spin flip scattering intensities ...” (p. 126, column 1, line 16) is not very clear, since the scattering condition of the polarized neutron experiment, i.e. the orientation of the neutron spin polarization p and the scattering vector r is not given. If we assume the footnote of ref. [ 15 ] refers to the experimentally measured ratio, i.e. the ratio of the spin flip cross sections measured for pII r and p i ?, then the same results as observed by Skanthakumer et al. are expected in the case of the two-domain, collinear structure, if the scattering plane is spanned by z= (l/2, l/2,1) and (- l/2, l/2,0) andp perpendicular to this scattering plane for p_L ‘c. Namely, (da+-/dQ),,,, (da+-/W,,, for ( l/2,
= 1
l/2, I) with l=odd
integer, and
(da+-/dQ),,,, (do+-/dQ),l,=m for (l/2, l/2, 1) with l=even integer. This can be seen as follows: We denote the two domains in the high temperature phase as in fig. 1. They are depicted as pro-
132
K. Yamada et al. / Comment on the spin structure of Nd,CuO,
/’
!I
0 \
\
\
it is
l
L--; /
-c=(l/Z,l/Z,P)
~
perpendicular to both p and z. From fig. la), clear that for ( l/2, l/2, /=odd)
\
/
/
0
I
\
\
From fig. lb), for (l/2, all i, and
/
l/2, /=even)
s,~~,,=o
for
+
a) Domain
I
b)
Fig.
Dornnin
II
I And since S,,
jections in the ab plane. Note that the scattering vector does not lie in this plane but is tilted out of the plane dependent on I# 0. Because the collinear structure has an orthorhombic symmetry, one has to differentiate between ( l/2, l/2, /)- and ( - l/2, l/2, /)-type reflections. We restrict ourselves on the ( 1 / 2. l/2, /)-type reflections, because all the following arguments apply to the ( - l/2, l/2, /)-type by just interchanging domain I and domain II. First of all we should note that because of the phase factor only domain I contributes to the (l/2, l/2, I=odd) reflections and only domain II to the ( l/2, 1/2,l=even) reflections. The spin flip cross sections are: P* 1
e’T(‘l-‘J)(S,,-S,,)
for pllr with S, denoting the spin component perpendicular to r, because (SlrxSI,) =O for the collinear structure and =P*Ce
Jr(r,-r,) s (
1lP.T
4.p.r)
PlT
for plr
with S,Ip,r denoting
the spin component
is finite for all I#0
In the same manner one can show the similar result, only odd and even interchanged, on the ratios of the spin flip scattering intensities, if the scattering plane is spanned by ( l/2, l/2,0) and (0, 0, I ) and p perpendicular to the scattering plane forp i ‘5.These examples show that the ratios of the spin flip scattering intensities may differ at ( l/2, l/2, I) peaks for I=even and I=odd even in the case of the multidomain collinear structure. In our previous paper titled “Two-dimensional spin correlations and successive magnetic phase transitions in Nd2Cu04” by Y. Endoh et al., to appear as a Rapid Communication in Phys. Rev., we proposed the La,NiO, type structure for the high temperature phase but did not exclude the possibility of the non-collinear structure because we knew a distinction between the equally populated two-domain, collinear case and the single-domain, non-collinear case was impossible here. We have already presented a similar discussion in our paper on the successive magnetic phase transitions of La&Zoo, (K. Yamada et al., Phys. Rev. B 39 (1989) 2336).
COMMENT on “Afagnetic phase transitions and structural distortion in Nd2Cu04” by S. Skanthakumar et al., Physica C 160 ( 1989) 124 THE SPIN STRUCTURE K. YAMADA,
K. KAKURAI
OF NdZCuOd and Y. ENDOH
Department of Physics, Tokoku University, Aoba. Aramaki, 980 Sendai, Japan
Received 16 October 1989
In the paper entitled “Magnetic phase transitions and structural distortion in NdzCu04” by S. Skanthakumar et al., published in Physica C 160 ( 1989) 124-28, there is an incorrect argument on the spin structure. The observed magnetic peaks can all be indexed as (h/2, k/2, 1), with h, k odd integers. “However, peaks with I even are observed to have quite different intensities compared to those with 1 odd, which would require the unlikely situation that domain populations (to) be correspondingly unbalances (p. 126, column 1, line 8). The above cursive argument is not correct. Even in the case of balanced domain populations, the intensities from (h/2, k/2, 1) reflections are very different between 1 even and I odd ones. The spin structure in the high temperature phase (75 K< T< 245 K) in Nd*CuO, can be constructed from the two domains of so-called La,NiO, type structure: spin direction [ l/2, l/2, 0] is parallel to the antiferromagnetic propagation vector. In this spin structure, the structure factor for ( 1/ 2, l/2, 0) reflection is always zero and the structure factors for (h/2, k/2, I) reflections with h, k odd are non-zero and identical. However, their angle factors which depend on the relative orientation of the spin direction and the reciprocal lattice vector z are quite different between 1 odd and 1 even reflections. For the former reflections, the domain with the spin direction perpendicular to the z contributes to the reflections. Therefore their intensities change with the square of their form factors. On the other hand, for the latter reflections the relative spin orientation to the 7 depends on each reflection. Therefore it is obvious that we should observe the different intensities between two types of reflections with 1odd and even. In a tetragonal symmetry, it is possible to con0921-4534/90/$03.50 0 Elsevier Science Publishers ( North-Holland )
B.V.
struct the same non-collinear spin structure as proposed by Shanthakumer et al. by a superposition of two domains of La,NiO, type structure. However, in the case of balanced domain populations we cannot observe the difference in the intensities between the collinear and the non-collinear structures at least by using unpolarized neutrons. Furthermore we cannot understand why the polarized neutron measurement performed by Skanthakumer et al. could determine the non-collinear structure rather than the collinear one with balanced domain populations. In particular the sentence “ratio of the spin flip scattering intensities ...” (p. 126, column 1, line 16) is not very clear, since the scattering condition of the polarized neutron experiment, i.e. the orientation of the neutron spin polarization p and the scattering vector r is not given. If we assume the footnote of ref. [ 15 ] refers to the experimentally measured ratio, i.e. the ratio of the spin flip cross sections measured for pII r and p i ?, then the same results as observed by Skanthakumer et al. are expected in the case of the two-domain, collinear structure, if the scattering plane is spanned by z= (l/2, l/2,1) and (- l/2, l/2,0) andp perpendicular to this scattering plane for p_L ‘c. Namely, (da+-/dQ),,,, (da+-/W,,, for ( l/2,
= 1
l/2, I) with l=odd
integer, and
(da+-/dQ),,,, (do+-/dQ),l,=m for (l/2, l/2, 1) with l=even integer. This can be seen as follows: We denote the two domains in the high temperature phase as in fig. 1. They are depicted as pro-
132
K. Yamada et al. / Comment on the spin structure of Nd,CuO,
/’
!I
0 \
\
\
it is
l
L--; /
-c=(l/Z,l/Z,P)
~
perpendicular to both p and z. From fig. la), clear that for ( l/2, l/2, /=odd)
\
/
/
0
I
\
\
From fig. lb), for (l/2, all i, and
/
l/2, /=even)
s,~~,,=o
for
+
a) Domain
I
b)
Fig.
Dornnin
II
I And since S,,
jections in the ab plane. Note that the scattering vector does not lie in this plane but is tilted out of the plane dependent on I# 0. Because the collinear structure has an orthorhombic symmetry, one has to differentiate between ( l/2, l/2, /)- and ( - l/2, l/2, /)-type reflections. We restrict ourselves on the ( 1 / 2. l/2, /)-type reflections, because all the following arguments apply to the ( - l/2, l/2, /)-type by just interchanging domain I and domain II. First of all we should note that because of the phase factor only domain I contributes to the (l/2, l/2, I=odd) reflections and only domain II to the ( l/2, 1/2,l=even) reflections. The spin flip cross sections are: P* 1
e’T(‘l-‘J)(S,,-S,,)
for pllr with S, denoting the spin component perpendicular to r, because (SlrxSI,) =O for the collinear structure and =P*Ce
Jr(r,-r,) s (
1lP.T
4.p.r)
PlT
for plr
with S,Ip,r denoting
the spin component
is finite for all I#0
In the same manner one can show the similar result, only odd and even interchanged, on the ratios of the spin flip scattering intensities, if the scattering plane is spanned by ( l/2, l/2,0) and (0, 0, I ) and p perpendicular to the scattering plane forp i ‘5.These examples show that the ratios of the spin flip scattering intensities may differ at ( l/2, l/2, I) peaks for I=even and I=odd even in the case of the multidomain collinear structure. In our previous paper titled “Two-dimensional spin correlations and successive magnetic phase transitions in Nd2Cu04” by Y. Endoh et al., to appear as a Rapid Communication in Phys. Rev., we proposed the La,NiO, type structure for the high temperature phase but did not exclude the possibility of the non-collinear structure because we knew a distinction between the equally populated two-domain, collinear case and the single-domain, non-collinear case was impossible here. We have already presented a similar discussion in our paper on the successive magnetic phase transitions of La&Zoo, (K. Yamada et al., Phys. Rev. B 39 (1989) 2336).