Jan 1, 1991 - 156X, 38042 Grenoble, France. C. Stassis. Physics Department and Ames Laboratory, Iowa State Uniuersity, Ames, Iowa 50011. P. Gopalan ...
PHYSICAL REVIEW B
VOLUME 43, NUMBER
1
1
JANUARY 1991
Magnetic and structural study of La& sSro 2NiO4 G. H. Lander Commission
of European
Joint Research Centre, Postfach 2340, D 750-0Karlsruhe, Federal Republic of Germany
Communities,
P. J. Brown Institut Laue-Langeuin,
156 X, 38042 Grenoble, France
C. Stassis and Ames Laboratory, Iowa State Uniuersity, Ames, Iowa 50011
Physics Department
Department
P. Gopalan, J. Spalek, and G. Honig of Physics and Chemistry, Purdue Universeity, Lafayette, Indiana 47907 (Received 16 July 1990)
Neutron-diffraction experiments with both polarized and unpolarized neutrons have been performed on single crystals of (Lal, Srp2)Ni04. The material is tetragonal at room temperature (I4/mmm) but distorts to the orthorhombic (Bmab) modification at 120+5 K with a second-order phase transition. The structural parameters are similar to those in the pure La2Ni04. The susceptibility is highly anisotropic at low temperature, with g, b (field applied perpendicular to the long axis) showing a peak at —17 K. However, we have found no evidence for long-range magnetic order. We speculate that the low-temperature state is an anisotropic spin glass, with 17 K being the freezing temperature. Polarized-neutron diffraction has been used to measure the induced magnetization density in a field of 4.6 T and at 20 K. The results can be understood by using a slightly expanded Ni + form factor and invoking a small positive susceptibility at the La site. There is also evidence for covalency between the Ni and O(2) atoms along the c axis. Surprisingly no unusual effects are found in the ab plane where we might expect strong covalency between the Ni d x 2 — 2 and p~ y
orbitals. The total moment as determined by these neutron experiments that determined by magnetization experiments.
I.
INTRODUCTION
superOne of the key aspects of the high-temperature conductors that is not yet properly established is the true nature of the electronic ground state. In the case of both 2:1:4, e.g. , LazCu04- based, and 1:2:3, e.g. , YBazCu307based compounds, the main interest focuses on the Cu-0 and the one unplanes. The configurations of Cu is paired electron is assumed to be in a d x —y 2 orbital that is strongly hybridized with oxygen p orbitals, p and p in experimental evidence estabthe plane. Unambiguous lishing this ground state is still lacking, nor is there any quantitative estimate of the extent of covalent mixing between the Cu d and oxygen p orbitals. The most direct the nature of this electronic method of establishing ground state would be to determine the complete charge density in the solid, but this is a complex task and there are as yet no experiments of sufficient accuracy reported. Alternatively, we may determine the spin density of these materials. This is not as simple to interpret (or to calculate) as the charge density, because the spin density is a difference between the density of majority and minority band states. Furthermore, it is possible to measure two different spin densities in those materials that are antiferromagnet (AF). The AF spin density may be determined by accurately measuring the AF structure factors.
d, &
0 p,
is in good agreement
with
This spin density must reAect the symmetry of the AF state and addresses the question of the ground-state AF wave functions. There is also the spin density induced by applying a magnetic field to the system and measured with polarized neutrons, which gives the spatial dependence of the susceptibility. The symmetries of these two spin densities are different. Neither of these spin densities is easy to measure. The AF magnetic moments in the 5 pit /Cu atom) and since Cu compounds are small the intensities are proportional to [pf(Q)], where p is the moment and f(Q) the form factor, it has proved difficult' to obtain accurate values of f(Q). For the inin LazCu04, the susceptibility duced spin density is small (2. 5 X 10 emu/mol at 330 K) and the experimental uncertainties are large. A more favorable situation exists in the nickel-based materials. Both the ordered moment and susceptibility are larger. In this paper we follow up the earlier work concerning structure and magnetization density studies of single crystals LazNi04 by reporting on similar experiments for single crystals of La& 8Sro zNi04. This should provide insight on the manner in which structure, magnetization, and bonding are affected by substitution of strontium for lanthanum at the 10% level. Whereas a large number of articles have been published on the physical properties of undoped lanthanum nickelates, much
(-0.
1991
The American Physical Society
MAGNETIC AND STRUCTURAL STUDY OF less is known about the characteristics of La& „Sr„Ni04. Aside from some measurements of magnetic, optical, and transport properties, very little work seems to have been done on structural investigations. The present study is an initial effort to study structural and bonding characteristics in the La& Sr„NiO4 system.
II.
measured on a vibrating sample magnometer in fields of 0.9 T is shown in Fig. 1; the subscript ab refers to measurements with the field in the ab plane perpendicular to the long c axis of the structure. One should note the large anisotropy that develops below 100 K, which is greatly reduced at the lowest temperatures. These results may be contrasted with earlier susceptibility measurements on LazNi04+&, in the latter case y, rather than y, & exhibits a cusp near 200 K and the two susceptibilities are similar above 250 K and below 90 K. The presence of the cusp g, b of La& 8Sro zNiO4 is conordering at sistent with the onset of antiferromagnetic the temperature =17 K. This conjecture gains additional support from the observation of remanent magnetization in the low-temperature regime as shown in the inset of Fig. 1. However, in an unpublished experiment, a time-dependent magnetization with a nonzero remanent value has been observed. The effect is most pronounced in La», Sr0»Ni04, as shown explicitly in Fig. 2. A clear logarithmic time dependence is detected for the in-plane component of magnetization; this dependence can be ascribed to an anisotropic spin-glass behavior, with a glass transition temperature T =17 K for x =0.2. These observations of macroscopic properties provide background information for microscopic studies described below. A further signature of this spin-glass state is the deviation
CO
l-
CL
Ld
V)
100
e080— 70— 60—
CRYSTAL PREPARATION AND SUSCEPTIBILITY
The method of crystal preparation is identical to that described for the growth of stoichiometric LazNi04, except that appropriate amounts of SrO were added to the initial reaction mixture. The magnetic susceptibility as
0
I
0
50
I
100
I
150
200
250
500
TEMPERATURE (K)
FIG. 1.
Susceptibility measured in the two directions parallel and perpendicular to the long c axis of the unit cell (field applied =0.9 T). The inset shows the remanent magnetization as a function of temperature.
La& 8Sro zNiO&
E
5040—
5020— 10— I
I
1.
3.0
2.0
0
lOg, o
t(S)
FIG. 2. Variation of magnetization La&
vs log t
(t
in s) for
85Sr0»Ni04 under various conditions.
of the susceptibility from linearity at higher fields, which has been found in this system (Johnston, private communication).
III.
STRUCTURAL STUDIES
Neutron experiments were performed with two crystals, crystal 3 with dimensions 0.75X4X1 mm and crystal D with dimensions —3 X 10 X 3 mm, where these dimensions are approximately in the directions a, b, and c of the tetragonal system. For all experiments the crystals were oriented with their long axes (b) parallel to the rotation axis ~ of the diffractometer, i.e. , perpendicular to the scattering plane and parallel to the applied field on D3. Diffraction experiments were performed with the D 15 and D3 diffractometers at the high-Aux reactor, Institut Both have normal-beam Grenoble. Laue-Langevin, geometry, so that reAections of the form hOl, h11, and h21 could be examined. For D15, a wavelength of 1.176 The A, /2 A was used from a Cu(331) monochromator. contamination was -6X 10 Crystal 2 was thoroughly examined at 6 K on D15 with a final data set of 114 nonzero independent rejections (mostly measured 2 —4 times). The results of refining the structural parameters using these integrated intensities are given in Table I, in which we also give the results for various other compositions. All these parameters are similar. One of the more important parameters in this structure is the ratio R between the Ni-O(2) distance and the Ni-O(1) distance. For a perfect octahedron this ratio would, of course, be unity. In LazCu04 this ratio is 1.27 and represents a very extended octahedron, which is ascribed to a 3ahn-Teller distortion around the Cu + ion. In the nickelates the octahedron is far less distorted. In both pure and the 10% Sr-doped LazNi04 we find a ratio of 1.14, although the individual distances are some 2 —3% shorter in the doped material. duo and
LANDER, BROWN, STASSIS, GOPALAN, SPALEK, AND HONIG
450
43
TABLE I. Structural parameters of pure and doped 2:1:4 materials at —10 K in the orthorhombic (Bmab notation) phase. Note that pure La2Ni04 does not have the orthorhombic Bmab structure at low temperature, see Ref. 3. The angles a& and a2 are the tilt angles of the octahedra as explained in the text. e is the strain =2(b — a)/(b+a). We have not measured this in our sample. Scattering lengths in our refinement were 0.824 for La, 0.729 for Sr, 1.03 for Ni, and 0.581 for 0 (all in units of 10 ' cm).
a (A) b (A)
c(A) T-0
5.350(1) 5.359(1) 13.077(3)
5.3240(1) 5.3547(1) 12. 1832(1)
K'
(This work)
5.346 (5.346) 12.40
—0.002 8(2)
—0.004 97(1)
—0.0056(5)
—0.0066(7)
0.361 90(3) 0.47(1)
0.360 77(2) 0.281(5)
0.3610(1) 0. 13(2)
0.3630(1) 0. 10(3)
(0,0,0) (A'2)
0.37(2)
0.214(6)
0. 18(5)
0.05(3)
z
—0.0032(1)
—0.005 73(6)
3)
z
B O(1)
B(A
)
120 W
—0.0055(5)
—0.0060(3)
0.66(2)
0.40(1)
0.47(4)
0. 13(3)
0.001 44(3) 0. 182 71(5)
0.025(1) 0. 1826(2)
1.33(3)
0.025 5(1) 0. 182 60(6) 0.66(1)
0.028(3) 0. 1747(1) 0.37(4)
3.22 lo 1.8 0.2
3.0 3.5
1.7
5.7
(O, y, z)
O(2)
z
B(A
)
R (F) (deg) a2 (deg) cz&
e strain
X10'
'This high-transition
temperature
+ b) =—16 X 10
It is diScult to perform a structural refinement with single crystals above 70 K because of the twinning problem of the peaks. Neutronand the large separation diffraction experiments have been used to determine the structural parameters at room temperature 6 and the The small strain for strain as a function of temperature. La2Cu04 shown in Table I is atypical; values of 8 X 10 are more usual and have been ascribed to the presence of a small amount of Li at the Cu site. La, 8Sr02Ni04 exhibits only a single phase transition from the high(I4/mmm ) to the lowtetragonal temperature structure (Bmab) orthorhombic temperature (HTT~LTO) at 120+5 K; this is accompanied by a pho' The non instability and rocking of the octahedra. rocking angle involving the motion of G(1) or G(2) is
"
1.06(7)
—7%
may be due to inhomogeneities
have discussed the magnetism of La2Ni04 Temmerman in terms of this parameter and we shall return to this. At La2Ni04 undergoes two structural transitions. high temperature a tetragonal to orthorhombic transition (HTT~LTO) at T =650 K, and a low-temperature transition from the orthorhornbic to a new tetragonal phase (LTO~LTT) at -70 K. The strain above 70 K is
b) /(a
5.356(2) 5.375(2) 13.183(6)
La i. 8 Sro. 2Nl04
380
B (A')
2(a
3Cu04 (Ref. 10)
La& 7Sro
200 K
(Oy
Cu, Ni
La l. 85Sro. 15Cu04 (Ref. 9)
533 K
transition
La, Sr
La2Cu04 (Ref. 8)
4. 3. 1 3.2 3.5
0%%ui
3.2% 3.2 4.0
in the samples.
a i = arctan(4zc /b) and respectively by where z and y are positional parameters for O(1) and O(2). All structural parameters are listed in Table I; they are clearly quite similar in the various Sr-doped compounds. %e have not determined the strain of La& 8Sr0 2Ni04 because this requires the examination of a crystal with the c axis vertical, or measurements on a high-resolution diffractometer of polycrystalline material. However, from the value of a& and az one can estimate that the strain is of the order of 5 X 10 at 6 K. Perhaps the only unusual feature of our refinement is that, in crystal A, the volumes occupied by each of the two twins in the orthorhombic phase were unequal, with approximately twice the volume of the (ab) twin as compared to the (ba) twin. We attribute this to the small volume ( — 3 mm ) of the crystal and to strains introduced by glueing the sample to the support. No differences in twin population were found in crystal D. The exctinction parameter g=0. 083(1) is larger than in pure LazNi04 (g =0.035) but corrections are still manageable, especially at shorter wavelengths. Crystal D was examined briefly at 15 K to determine the extinction parameter. It was found to be similar to that of crystal A. specified
a2=arctan(yb/zc)
43
MAGNETIC AND STRUCTURAL STUDY OF
+~ +
+~
+
+ I
40
I
I
I
80
Temperature
I
120 (K)
FIG. 3. Intensity of (0,5, 10) reAection as a function of temperature. [Note that, because of the twinning this is observed at a position corresponding to the (5,0, 10) refiection]. The units are arbitrary.
The HTT-LTO phase transition may be studied by monitoring the intensities of the superlattice rejections. For example, the intensity of the (0,5, 10) refiection is plotted versus temperature in Fig. 3 and the transition to the LTO phase occurs at 120+5 K. Notice that, unlike in pure LazNi04, there is no LTO-LTT phase transition in the 10%%uo Sr-doped material. As a further test that the material remains in the Bmab phase at low temperature, we have examined a series of refiections (11l) with I =even. These are not allowed in the LTO phase but appear in the LTT phase. ' We found negligible intensity for all these reAections.
confirm such a warming. In view of the above it is plausible to suggest that the 17 K peak in Fig. 1 is a consequence of short-range correlations leading to an anisotropic spin-glass state. Since y, in Fig. 1 exhibits no such peak, the spins presumably are confined to the basal ab plane. The presence of short-range magnetic correlation is well established in the Strong two-dimensional (2D) La2 Sr CuO& system. ' in stoichiometric fluctuations have also been reported' and oxygen-rich La2Ni04. We plan to examine the short-range correlation effects further on a triple-axis instrument. We should finally note that the absence of antiferromagnetic ordering is not surprising in light of the lowtransition temperature for the HTT-LTO phase transformation. In La2Ni04+&, T, =650 K when 5=0; in the &0.06, T, decreases from 200 to 50 K. A range 0. 01 simple linear extrapolation of those data to large 5 provides an estimate of critical nonstoichiometry parameter 5, =0.065 for which AF ordering disappears. An analogous estimate for x yields the critical value x, =0. 15. At this concentration pronounced logarithmic time dependence of magnetization is being observed (cf. Fig. 2) and ascribed to an onset of two-dimensional spin-glass behav-
'
(5
ior. V. POLARIZED-NEUTRON
IV. SEARCH FOR MAGNETIC ORDER dependence of the susceptibility (Fig. suggests that antiferromagnetic ordering occurs at —18 K. Accordingly, we were surprised to find no direct evidence for long-range magnetic order in a number of scans with both crystals A and D. In particular, crystal D is sufficiently large that we estimate that any ordered moment is ~0. 1 p~. This assumes that the antiferromagnetic order would give peaks at reciprocallattice points such as (1,0, 1), (1,0, 3), etc. , which is the case in pure La2Ni04 and La2Cu04. We have also made scans along a series of reciprocal lattices lines such as (h, 0, 0) (h, 0, 1), and (1,0, l) and found no evidence for any extra scattering below 18 K. We should record here that very weak extra intensity can be detected at the (1,0, 1), (1,0, 3) etc. , positions below the HTT~LTO transition at 120 K. These intensities have a T dependence similar to that shown in Fig. 3. Since these reAections are forbidden in the Bmab space group, one is tempted to ascribe them to antiferromagnetism, although they appear at a much higher temperature than the peak in the susceptibility (Fig. 1}. However, we believe these peaks arise from multiple-scattering effects between the strong F-type reAections and the new superlattice rejections that appear in the LTO phase. Since the latter are absent in the HTT phase, no coupling of beams can produce intensity at the (1,0, 1) position except below 120 K. We found, for example, that the peak at the (1,0, 1) was some 30 times more intense than that at (1,0, 3). This ratio is incompatible with any Ni2+ form
The temperature
1) strongly
451
~Ni04
factor, which would predict a ratio of —1.4. As already noted by Freltoft et al. the measurement of any intrinsic intensity at these points, such as (1,0, 1), requires a careful analysis of the multiple scattering, and our measurements
100
0
La& SSro
EXPERIMENTS
A series of polarized-neutron-scattering experiments was carried out to obtain magnetic form factors needed to obtain spin-density contours for unpaired electrons that respond to an external magnetic field. In these experiments the intensity of the neutron beam undergoing Bragg reAection by the sample is monitored when the neutrons are polarized parallel and antiparallel to the applied field. Neutron scattering involves two components: the normal nuclear interactions, as well as magnetic scattering by the lattice of partially oriented paramagnetic moments in the applied magnetic field. The ratio of the intensities measured for the two neutron-polarization orientations, termed the Gipping ratio, is given by
R
=(N+M) l(N —M)
where N and M are the nuclear and magnetic structure factors at the hkl value of the Bragg reAection. From a determination of R one obtains the ratio y =M/X: since N(hkl} is known from the structural analysis reported in Sec. IV, M(hkl) can be determined. The Fourier transform of M(hkl) then yields information on the magnetization density. A complete set of Gipping ratios for the first 28 F-type (i.e. , hkl all even or all odd) refiections with significant intensity up to sine/A, =0. 5 A ' was measured for both crystals A and D. In the case of crystal A, the measurements were performed at 0.707 A only, and only the 18 strongest reAections were measured; in all cases, 2 —4
LANDER, BRO%N, STASSIS, GOPALAN, SPALEK, AND HONIG
452
equivalent reAections were measured. For crystal D, data were taken at 0.843, 0.707, and O. S4S A. Measurements on different crystals and with different neutron wavelengths allow a good test of extinction, which we find refinement and some agrees with the unpolarized-neutron measure of control over multiple scattering. The processing of, and corrections to, the data are fully explained in our work on La2Ni04 and will not be repeated here. SufFice it to say that we believe we have a high-quality data set and the values of the observed magnetic structure factors Mp(hkl) given in Table II represent a weighted average of four values taken under different experimental conditions, with each independent value being the average of equivalent measurements. The corrections for the diamagnetism have been made as in the pure compound and are a11 ~0. 4 m p~, which is less than the standard deviations. Contamination of the experimental data by A. /2 neutrons was corrected by using the relation
-4
y„„=y, b, (1+ap), where y is the ratio of the magnetic to nuclear structure study of TABLE II. Results of the polarized-neutron La, ,Srp 2NiO~ at T =20 K, H =4. 6 T, H~~b. All numbers refer to 1 formula unit. X is the nuclear structure factor, (1+aP) is the correction for A, /2 contamination, Mo is the observed magnetic structure factor. Standard deviations in parentheses refer to the least significant digit. The values with asterisks have not been used in the Fourier maps.
43
factors, a=Ip(A, /2)/Ip(A, ), is the ratio of the incident A, /2 beam to that of the A, neutron beam, and
P= [X(A, /2)/X(A, )] where N represent the nuclear structure factors of the planes dift'racting either the 1,/2 or A, beam. In our case, a=S X 10 since Alters were used at each wavelength and p can be readily calculated. ap is normally less than 0. 1 but in some cases exceeds 0.2. In case of an ap greater than 0. 1, we have not used the value of Mo in the comparison with model calculations, although these values are plotted in Fig. 4. We believe the larger error bars include those in correcting for X/2, but further uncertainties can arise from multiple scattering. The fact that consistent experimental results are obtained with three different wavelengths is already a guarantee against 1arge multiple-scattering effects, but at these short wavelengths it is not conclusive. We have therefore plotted the peak heights normalized by N versus sinO. This curve should approximately follow the instrumental resolution function. The only refIections deviating significantly from this curve are those marked with asterisks in Table II. Presumably most of this deviation arises from the A, /2 contribution but, since the efFects may also reflections are weak, multiple-scattering be significant. These data are not used in the calculation of the Fourier maps. The values of Mo are plotted versus sinO/A, in Fig. 4. The dashed curve is the best fit to a spherically symmetric Ni + form factor. The intercept at sinO/A. =O yields the magnetic moment and the refinement gives
sinO/A,
(1+aP)
hkl
2,0,0 4,0,0 1, 1, 1 3, 1, 1 5, 1, 1
0,0,2 2, 0,2 4, 0,2 1, 1,3 3, 1,3 5, 1,3
0,0,4 2, 0,4 4,0,4 1,1,5 3, 1,5 0,0,6 2, 0, 6 4, 0, 6 1, 1,7 3 17
0,0, 8 2,0, 8 4,0, 8 0,0, 10 2,0, 10 1, 1, 11
0,0, 12
0. 187 0.374 0. 138 0.298 0.479 0.081 0.204 0.383 0. 179 0.319 0.492 0. 161 0.247 0.407 0.241 0.358 0.242 0.306 0.446 0.312 0.409 0.323 0.373 0.494 0.403 0.445 0.463 0.489
2.625 4.750 0.490
0.465 0.418 1.261 1.025 1.255 1.275 1.312 1.375 0.258 1.995
1.017 1.004 1.033 1.031 1.030 1 1 1
1.045 1
0.248 2.453
1.028 1.477 1.008 1.513 1.001
2.398
1
3.925 1.675 3.725 0.364 0.365 2.501 0.392
1
2.500 0.923 1.113 3.525 1.860
1.006 1
1.203 1.190 1.006 1.225 1.004 1.003 1.002 1.005 1.003
35: 29.0(5) 15.8(8) 26. 1(12) 17.3(12) 6.5(10) 29.3(5) 23.8(8) 15.1(8) 25.5(10) 18.0(10)
9.8(13) 29.5(20)' 21.5(8) 10.5{20)* 24. 1(8) 16.5(8) 23.3(8) 17.8(8) 10.8(12) 14.3(20) *
9.5(20)' 16.8(10) 8.3(20) * 7.0(12) 10.1(12) 7.5(10) 7.5(10) 8.8{12)
30-
(La) s Srp 2) Ni 04 T=2OK, H=4. 6T
x
Hlj b
250 20 E
x
~ 15E 10-
t
I
I
I
0.1
0.2
0.3
Q4
sin
e/P
(A
')
0.5
FIG. 4. Induced magnetic moment as a function of sinO/k for (La& 8Sro~)NiO4. Open circles are experimental results, solid circles are reflections which have large 10%) corrections for A, /2 and may also su8'er from multiple scattering. The arrow on the ordinate scale marks the total moment determined in a magnetization experiment. The dashed curve gives the best + form factor, model (1). The crosses correspond to fj.t to a Ni model (3) in Table III.
()
MAGNETIC AND STRUCTURAL STUDY OF
43
La& SSro
(xyo) section
34.5(7) my~. This corresponds to a susceptibility (at H =4. 6 T) of 4.2(1) X 10 emu/mol, a value below that of 5 X 10 emu/mol found at low field in Fig. 1. We anticipate that the magnetic moment of a spin glass should not vary linearly with the applied field. Indeed, recent measurements by Johnston have shown that at 4.6 T and to p = 31. 1 corresponds 20 K the magnetization of a high-field susceptibility m p/I /mol, yielding 4.02X10 emu/mol, in satisfactory agreement with the value based on Fig. 4. The large moments encountered in La 8Srp 2Ni04 should be compared to the much smaller values of 6 m p~ in LazNi04 and with a moment p = 1.5 m p~ for Cu in LazCu04 in fields of 4 —6 T. The larger moment is useful in arriving at information discussed in Sec. VI. The uncertainties in data statistics, nuclear structure factors, extinction, and multiple scattering are estimated to be roughly 0.5 m pz in these structures, corof in susceptibility to an uncertainty responding 60X10 emu/mol. The quantities of greatest interest are the asphericity and bonding effects, which normally amount to no more than 10% of the total amount: thus, 20 m pz to one must have total moments of magnitude ensure that the moments associated with bonding effects exceed the experimental uncertainties.
453
2Ni04
/
X
1/2
(b)
&
(xxz} section
1/2
/
/ /
/
/
I
/
I
/
I
I
I
I I I
/
I
/
/
/ / /
/ /
)
I I
I
/ /
I
/
/
VI. OBSERVED AND MODEL MAGNETIZATION DISTRIBUTIONS
/
/
/
/
/ I
As in our previous work on pure La2Ni04, we consider densities corresponding to the differences between our observed magnetization distributions and various model distributions. Thus, we calculate first the best fit of Mo to a spherical Ni + form factor and then calculate M, (hkl). The coefficients for the Fourier difference map are [Mo(hkl) — M, (hkl)]. These coeKcients are multiplied by a weighting function which averages the resultant density over a cube of edge length 0.5 A, and rejections not measured are given zero weight. In this way, the well-known errors arising from series termination are largely avoided. A significance map may be calculated from the standard deviations and then the contours adjusted so that about one interval contour is significant. Such maps are shown in Figs. 5(a) and 5(b) and the parameters are given in Table III. For a free-atom Ni + the
y
—5. 9. It is important to keep
in mind the small value of these differences and that the Ni + form factor is a relatively good fit to the data (Fig. 4). The maximum at the Ni position for the M, map corresponds to contours so that the effects in the difference maps are at the few per cent level. Nevertheless, there are a number of significant features: (1) There is a positive density at the Ni site surrounded by a negative density, (2) a large positive feature near the La site, and (3) a positive density at the O(2) position. Features (1) and (2) are essentially independent and may be treated separately. Feature (1) may possibly arise from an orbital moment, from covalency, or from a real contraction of the Ni + atomic wave functions. The simplest way to change the spatial extent of the Ni + (Q), which is represented here by a single term ( jo ), is to add a term in ( j2 ) so that
-90
f
I 'I
0 (x xo)
-1/4
+1/4
(Mo — M, )
FIG. 5. Difference Fourier sections using Ni spherical form factor, model (1). The significance level (deduced from the experimental uncertainties) is —1 contour, the zero contour is suppressed. The difference Fourier has been aver0 aged over a cube of 0.5 A. Solid (dashed) contours correspond to positive (negative) region in the difference map. The atom symbols are ~ Ni, ~ La, A O(1), and 4 O(2).
f(Q)=(j )+c (j
)
j;)
where ( are Bessel transforms of the single-electron density. ' Assuming that g is near to 2.0 (almost quenched orbital moment), it is straightforward to show that, for a transition-metal atom,
c, =(g —2)/g . In NiO, g =2. 2, so we might expect c2-0. 1. In fact, the best fit yields c2=0. 25(10) with y reduced to 5.0. This
larger value of cz is perhaps not surprising since, in NiO, Alperin' found c2-0. 8, corresponding to a considerable contraction of the free-atom Ni + wave functions. Feature (2) is the positive susceptibility at the La site, which gives 1.7(4) mIM/I per La atom, corresponding to a susceptibility of 2. 1(5) X 10 emu/mol. We should note that, as in our previous study of pure La2Ni04, we have
454
LANDER, BROWN, STASSIS, GOPALAN, SPALEK, AND HONIG
used a Ni + form factor to model the induced moment at the La site. The g sum now drops to 3.0. We do not have sufhcient data to determine the individual La form factor, but it is not a free-atom 5d form factor, which falls very rapidly to zero. ' The resulting values of M, are given in Table III and plotted as crosses in Fig. 4. The difFerence map with these modifications is shown in Fig. 6. Clearly, no significant features remain in the basal (xy) plane. At first sight this is surprising, as we had hoped to be able to establish the e symmetry of Ni +, where we would expect the two unpaired electrons 2— r d orbitals. This would be the to be in x — y and 3z expectation for Ni + octahedrally coordinated by oxygen with the o. antibonding states based on the Ni e orbitals and the t2 states filled. With electrons in the e orbitals, the form factor should be aspherical, but if the x — y
43
r orbitals have equal population, the aspheriand 3z — cal components involved are the spherical harmonics of order 4 involving terms in (j&). (Note that the x — y orbitals have their maxima along the x and y axis. With respect to the crystallographic axes used here, we must rotate a and Il by 7r/4 to conform to the usual notation. ) These terms primarily afFect the form factor only at relatively high scattering angles, e.g. , for sin0/A, 0. 45 A where our data (Fig. 4) are not of suScient precision. The efFect of e symmetry is well illustrated in Alperin's study' of NiQ, in which accurate data out to sinO/A, -O. 8 A ' were collected. In Table III we include a column giving an e occupation as compared to a spherical distribution. This difFerence is clearly less than the standard deviations of our data. The basal plane of the difFerence map, Fig. 6(a), shows also that there is no
)
TABLE III. Comparison of observed Mo with different modes M, for (La, ,Sr&, ) Ni04 induced form
factor. (1) Spherical Ni'+, (2) spherical Ni
++cl(j2), (3) as (2) but adding La moment, (4) change from (3) with e~ symmetry instead of spherical for Ni +, and (5) change from (3) when additional contribution for covalency between Ni and O(2) is included. Note that (4) and (5) are not least-squares fits but are for demonstration, see text. The induced total moment as measured by magnetization is 33.1 p~. The asterisks indicate reAections not used in the least squares because of possible errors in correcting for A, /2. M, (mp~) for diA'erent models o
(m
29.0(5) 15.8(8) 26. 1(12) 17.3(12) 6.5(10) 29.3(5) 23.8(8) 15.1(8) 25.5(10) 18.0(10)
2,0,0 4,0,0 1,1, 1
3, 1, 1 5, 1, 1 0,0,2 2,0,2 4, 0,2 1, 1,3 3~1~3
9.8(13) *29.5(20) 21.5(8)
5, 1,3 0,0,4 2,0,4 4, 0,4 1, 1,5 3, 1,5 0,0, 6 2, 0, 6 4, 0,6 1,1,7 3, 1,7 0,0, 8 2,0, 8 4,0, 8 0,0, 10 2, 0, 10 1,1, 11 0,0, 12
*10.5(20) 24. 1(8) 16.5(8) 23.3(8) 17.8(8) 10.8(12) 14.3(20) *9.5(20) 16.8(10) *8.3(20) 7.0(12) 10.1(12} 7.5(10) 7.5(10) 8.8(12)
x' p~;(m p~
p, )
}
Nl (Jl )Cl pLa (m pg )
(3)
26. 1 13.0 29.5 17.9 7.8 32.7 24.9 12.5 26.7 16.5 7.3 28.0
21.6 11.2 22. 1 14.0 22. 1 17.4
9.3 17.0
11.1 16.3 13.1 7.2 11.4
9.3 8.5 7.6 5.9 34.5(7) 0 0
25. 8 14. 1 28.7 18.6
9.2 31.4 23.5 13.6 26.3 17.3 8.7 27.4 21.9 12.4 22. 3 15.0 22.2 18.1 10.6 17.8 12.3 17.1 14.2 8.6 12.6 10.7 9.9 9.0
5.0 32.9(9) 0.29( 12) 0
28.0 15.0 26.4 17.0 8.3 30.5 23.9 13.0 28. 1 18.2 9.0 24.4 19.4 10.9 22.7 15.1 22. 7 18.4 10.6 15.7 10.8 17.8 14.8 8.9
11.4 9.6 10.3 8.2
3.0 32.5(7) 0.25(9) 1.7(4)
(4)
(5}
0.01 0.08 0.02 0. 16 0.25 0.01 —0.08 —0.09 —0.05 —0. 12 —0.06 0. 11 —0.23 —0.48 —0.03 —0.46 0.40 —0.23 —0.86 0.20 —0.65 0.88 0.00
0.34 0. 15 —0.06 —0. 11 —0.06 —0.84 —0.74 —0.48 —0.61 —0.56 —0.38 0.43 0. 13 —0. 10 0.75 0.38 0.67 0.51 0.24 0.28 0. 12 0.31 0. 19 —0.00 0.28 0.22 0.04 —0.03
—1.05 1.43
0.40 1.12 1.92
43
MAGNETIC AND STRUCTURAL STUDY OF (xyo) section
(a)
La& 8Slo
2Ni04
455
(xxz) section
VL
',
X—
Z
(xxz} section
I I
I
I
(xxo}
+1/4
FIG. 7. Section (xxz) as in Figs. 4 and 5 and showing the different density obtained when a covalent mixing of Ni 3z — r and O(2) p, orbitals is allowed as compared to an e~ orbital population of the two unpaired Ni electrons. The contours are at approximately half the intervals as in Figs. 4 and 5 so that the effect may be better illustrated.
(xxo}
+1/4
FIG. 6. The same difFerence map sections as in Fig. 4 except that model (3) including a cz( ) term and a positive La term is used for M, .
j,
significant density at the O(l) site. However, feature (3), the positive density at O(2) and the negative eKects along the Ni-O(2) bond, does provide evidence for transfer of moment to O(2), suggesting that the covalent mixing is greater for the 3z — r orbitals than for the x — set. To some idea of the density get y which might result from such covalency, we have calculated the structure factors for the magnetic scattering by introducing the covalency through ( PNi
+ ~4
( o)) 2/
A
d,
where PN; involves a Ni + , orbital and Poizi involves an oxygen 2p, orbital, and A is the normalization factor. We have used a convolution technique and tried several different values of A, . The structure factors are the sum of three parts, a transition-metal part, a ligand, and an overlap part, but the parts contributing to the difference density are the ligand and overlap parts plus a negative contribution from the aspherical part of the transition-metal density transferred to the ligand; the sum of these contributions for k=0. 2 is illustrated (Fig. 7). With this value of A, the "covalent" density reproduces the positive density in the O(2) site quite well, but assigns an insufficient negative density in the "overlap"
region. Some further interaction leading to expansion of the nickel wave function to increase the Ni-O(2) overlap is needed to account for the data. This may imply s-d mixing on nickel.
VII. SUMMARY The neutron-scattering experiments on La& &Sro 2Ni04 single crystals have shown that the magnetic susceptibility peak in the g, b depicted in Fig. 1 does not correspond to the onset of long-range antiferromagnetic ordering. From preliminary unpublished measurements, and in analogy to the cuprate system, we suggest that the strong two-dimensional magnetic short-range correlations develop in the basal plane which "freeze" at low temperature. The induced magnetization density shows a number of unusual features. Perhaps the most important aspect is that there appears to be almost no interesting sects in the ab plane. This is quite surprising in view of our expectation of covalency between the Ni + d(x — y ) orbital and the oxygen p and p orbitals. It is an element of these studies that is not well understood. So far, theoretical studies have not distinguished between the AF and induced spin density, but in all cases have emphasized the importance of the hybridization involving the d (x — y ) orbitals. In recent experiments involving the AF spin in LazNi04, large such effects in the ab plane density have been found. This makes it even more dificult to understand why they are absent in the induced spin density. On the other hand, significant effects are found along the c axis. Although the experimental data are not of sufficient accuracy to distinguish between a spherical Ni + and a complete e state (i.e. , one unpaired electron
LANDER, BROWN, STASSIS, GOPALAN, SPALEK, AND HONIG
—r orbitals), there is clearin each of the x — y and 3z an overall contraction of the Ni + wave function. A ly similar situation was found in NiO. ' ' In our case the magnetization experiment gives 33.1 mph for M(0, 0, 0), which is in reasonable agreement with the forward extrapolation of the total amount of 32.5(7) +2 X 1.7(4) =35.9(11) m ps from the neutron experiments (see Table III). The effects along the c axis include a positive susceptibility at the La site of 200(50) X 10 emu/mol and, at a somewhat lower degree of uncertainty, covalency effects between the Ni and O(2) atoms. The covalency effects actually give rise to a positive contribution of 7 m ps to M(0, 0, 0) so that the total amount in the unit cell is 32.5 — 0. 7+2(1.7) =35.2(11) m ps. The La effect is larger by a factor of 2 than that found in our previous study of pure LazNi04, but the Ni suscep-
-0.
T. Freltoft et al. , Phys. Rev. B 37, 137 (1988). C. Stassis et al. , Phys. Rev. B 38, 9291 (1988). G. H. Lander et al. , Phys. Rev. 8 40, 4463 (1989).
4D. J. Buttrey et al. , J. Solid State Chem. 54, 407 (1984). ~G. Y. Guo and W. M. Temmermann, Phys. Rev. B 40, 285 (1989). J. D. Jorgensen et al. , Phys. Rev. 8 40, 2187 (1988). 7J. Rodriguez-Carvajal et al. , Phys. Rev. B 38, 7148 (1988). 8J. M. Delgado et al. , Phys. Rev. B 37, 9343 (1988). R. J. Cava et al. , Phys. Rev. B 35, 6716 (1987). 'oA. J. Schultz et al. , Physica C 157, 301 (1989). ' P. Boni et al. Phys. Rev. 8 38, 185 (1988). , T. R. Thurston et al. , Phys. Rev. B 39, 4327 (1989). J. D. Axe et al. , Phys. Rev. Lett. 62, 2751 (1989). ~4L. Pintschovius et al. , Phys. Rev. B 40, 2229 (1989).
43
-6.
tibility has increased by a factor of Band-structure calculations suggest that some of the La 5d states are mixed with oxygen wave functions and may be polarized, but a quantitative study has not been made. It is interesting in this regard that no La effect can be seen in the AF form factor; in this respect, the La susceptibility is clearly induced by the applied magnetic field. ACKNOWLEDGMENTS
We would like to thank Bruce Harmon for a number vf interesting discussions and David Johnston for sharing his results with us. Work at Purdue was sponsored by the National Science Foundation (Grant No. DMR 86 16533 AO2) and that at Ames Laboratory by the Department of Energy.
~~Y. Endoh et al. , Phys. Rev.
For example, R.
J.
B 37, 7443 (1988). and G. Shirane,
Birgeneau
in Physical Properties of High Temperatu-re Superconductors, edited by D. M. Ginsberg (World-Scientific, Singapore, 1989), Vol. I, p. 151 —211, and references therein. ' G. Aeppli and D. J. Buttrey, Phys. Rev. Lett. 61, 203 (1988). R. E. Watson and A. J. Freeman, Phys. Rev. 120, 1125 (1960). i H. A. Alperin, Phys. Rev. Lett. 6, 55 (1961). M. Blume, Phys. Rev. 124, 96 (1961). 2 T. O. Brun and G. H. Lander, Phys. Rev. Lett. 23, 1295 (1969); R. M. Moon et al. , Phys. Rev. B 5, 997 (1972) See, for example, P. J. Brown, Chem. Scr. 26, 433 (1986). 2 T. C. Leung et al. , Phys. Rev. B 37, 384 (1988). "X. L. Wang et al. , Bull. Am. Phys. Soc. 35, 720 (1990); J. Appl. Phys. (to be published). ~
