We report the results of neutron powder diffraction studies on the spin-chain
compound Ca3CoRhO6 in the temperature range 3 to 293 K. Bragg peaks due to
magnetic ordering start appearing below about 100 K. The most interesting
observation is that there is a diffuse magnetic peak superimposed over the
strongest magnetic Bragg peak. The diffuse magnetic intensity is observed below
as well above 100 K. This finding provides a new insight into the physics of
this compound as though the low-dimensional magnetic interaction coexists with
long range magnetic order - a novel situation among quasi one-dimensional
oxides.Comment: accepted by Eur. Phys. Let

Loewenhaupt, M.

Niazi, A.

Sampathkumaran, E. V.

Schaefer, W.

English

arXiv

We report the results of neutron powder diffraction studies on
the spin-chain compound $\chem{Ca_{3}CoRhO_{6}}$ in the temperature
range from 3 to 293$\un{K}$. Bragg peaks due to magnetic ordering
start appearing below about 100$\un{K}$. The most interesting
observation is that there is a diffuse magnetic peak superimposed
over the strongest magnetic Bragg peak. The diffuse magnetic
intensity is observed below as well as above 100$\un{K}$. This
finding provides a new insight into the physics of this compound
as though the low-dimensional magnetic interaction coexists with
long-range magnetic order —a novel situation among
quasi–one-dimensional oxides

M. Loewenhaupt

W. Schäfer

A. Niazi

E. V. Sampathkumaran

EDP Sciences OAI-PMH repository (1.2.0)

Evidence for the coexistence of low-dimensional 
 magnetism and long-range order in

We report the results of neutron powder diffraction studies on the spin-chain compound 



Ca3CoRhO6 in the temperature range from 3 to 293 K. Bragg peaks due to magnetic ordering start 



appearing below about 100 K. The most interesting observation is that there is a diffuse magnetic peak superimposed over the 



strongest magnetic Bragg peak. The diffuse magnetic intensity is observed below as well as above 100 K. This finding provides a new 



insight into the physics of this compound as though the low-dimensional magnetic interaction coexists with long-range magnetic 



order-a novel situation among quasi-one-dimensional oxides

Schäfer, W.

Publications of the IAS Fellows

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Europhysics Letters PREPRINT
Evidence for the coexistence of low-dimensional magnetism
and long-range order in Ca3CoRhO6
M. Loewenhaupt1, W. Scha¨fer2, A. Niazi3 and E.V. Sampathkumaran3
1 Institut fu¨r Festko¨rperphysik, Technische Universita¨t Dresden, 01062 Dresden, Ger-
many
2 Mineralogisch-Petrologisches Institut, Universita¨t Bonn, 53115 Bonn, Germany
3 Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai-400 005, India
PACS. 61.12.Ld – neutron diffraction.
PACS. 75.25.+z – spin arrangements in magnetically ordered materials.
PACS. 75.40.-s – short range order.
Abstract. – We report the results of neutron powder diffraction studies on the spin-chain
compound Ca3CoRhO6 in the temperature range 3 to 293 K. Bragg peaks due to magnetic
ordering start appearing below about 100 K. The most interesting observation is that there
is a diffuse magnetic peak superimposed over the strongest magnetic Bragg peak. The diffuse
magnetic intensity is observed below as well above 100 K. This finding provides a new insight
into the physics of this compound as though the low-dimensional magnetic interaction coexists
with long range magnetic order – a novel situation among quasi one-dimensional oxides.
Introduction. – The pseudo low-dimensional insulators have been of constant interest
among physicists and chemists [1] for the past few decades as the interplay between intra-
chain and inter-chain interactions has been found to result in novel magnetic anomalies [2].
Till to-date, in all such compounds, the presence of weak inter-chain magnetic coupling results
in eventual loss of the identity of the chains, thereby paving the way for three dimensional
magnetic ordering at low temperatures. In this article, we report the temperature dependent
neutron diffraction data for a quasi one-dimensional compound, Ca3CoRhO6, which appar-
ently has the signatures of the correlations within a chain coexisting with long range magnetic
order, thereby providing a novel situation in this direction of research. The compound un-
der investigation crystallizes in the K4CdCl6-type rhombohedral structure (space group R3¯c).
This class of compounds, (Sr,Ca)3MXO6 (M,X = a metallic ion, magnetic or non-magnetic),
have started attracting attention in recent years due to the presence of spin-chains (M −X)
separated by Sr/Ca ions (see refs. [3] to [16] and references cited therein) and the magnetic
chains form a triangular lattice (with an inter-chain spacing of 5.313 A˚ in the present com-
pound). In this structure, there is face-sharing of octahedra of X ions and trigonal prisms of
M ions. Of these, the title compound is of special interest. On the basis of previous neutron
diffraction data [16], it was inferred that this compound can be classified a ”Partially Disor-
dered Antiferromagnet (PDA)” – a novel magnetic structure very rarely encountered [16] in
magnetism. In this magnetic structure, there is a temperature range (below the paramagnetic
c© EDP Sciences
2 EUROPHYSICS LETTERS
state) in which the chains at the apices of the hexagon are antiferromagnetically coupled to
each other, whereas the one at the center of the hexagon is left incoherent; as the temper-
ature is lowered further, the incoherent chains can undergo spin-glass freezing (as proposed
for the present case [16]) or couple ferrimagnetically with other chains. It has been found
that dc magnetic susceptibililty (χ) exhibits a complex behavior at temperatures below 300 K
(refs. [14] and [15]), reflecting the existence of different temperature regions: there is a broad
maximum in the plot of χ versus T around 100 to 150 K, with an isothermal magnetization
behavior highly non-linear with the magnetic field in the intermediate T -range (40 - 90 K),
but tending to a constant (zero-field-cooled) χ at still lower temperatures. However, ac sus-
ceptibililty exhibits a broad feature in the range 40 - 70 K with an unusually strong frequency
dependence, implying more exotic magnetic behavior of this compound, thereby warranting
further investigations for better understanding [15]. Motivated by this situation, we have sub-
jected this compound to more careful neutron diffraction investigations as compared to those
reported in ref. [16], the new results of which are reported in this article. It is worthwhile
stating that, in sharp contrast to the situation in this material, the analogous Fe compound
exhibits a simple magnetic behavior [14] with a magnetic ordering temperature around 15 K.
Sample Preparation. – The polycrystalline specimen of Ca3CoRhO6 was synthesized by
a conventional solid state route. Stoichiometric amounts of high purity (>99.9%) CaCO3,
CoO and Rh powder were thoroughly mixed. Then the mixture was calcined at 900 C for
one day. The prereacted powder was then finely ground, pelletized and heated at 1200 C
for about 10 days with few intermediate grindings. The x-ray diffraction pattern confirmed
that the sample was single phase. Neutron powder diffraction measurements were performed
at the constant wavelength thermal neutron instrument SV7 at the DIDO research reactor
in the Forschungszentrum Ju¨lich [17] using the diffractometers SV7-a and SV7-b with neu-
tron wavelengths of 1.095 A˚ and 2.332 A˚, respectively. Both instruments are equipped with
JULIOS-type linear scintillation detectors. The sample was contained in a vanadium cylinder
of 8 mm diameter and 30 mm height and inserted in a helium refrigerator cryostat equipped
with vanadium windows. Full long-term diffraction patterns were collected at 293, 100, and
3 K in the short wavelength configuration (λ = 1.095 A˚) and at 4 K and 293 K using the long
wavelength of 2.332 A˚. Short-term runs were performed in the temperature regime between
3 K to 250 K for both wavelengths.
Results and discussion. – We show in fig. 1 the temperature dependence of the raw
diffraction patterns in the low-angle region with the long wavelength. We have carried out
crystal structure data analysis by full-pattern Rietveld refinements using Fullprof [18]. A two-
step data handling was applied to the magnetic structure analysis using (1) a modified version
of the program Profan [19] and (2) the full-matrix least squares program IC-POWLS [20].
Profan fits pre-selectable profile functions, e.g. Gaussian or Lorentzian, into measured peaks
or peak clusters and individually refines sets of three profile parameters each for peak position
2Θ, half width FWHM, and peak height H. This procedure permits the separation of broad
diffuse magnetic scattering contributions from the pure Bragg peaks and thus the separation
of disorder and long-range order effects, respectively. The refined profile parameters are
used for the calculation of integrated peak intensities. IC-POWLS uses these intensities as
observations for magnetic structure refinement calculations. With our analysis, we confirm
that Ca3CoRhO6 crystallizes in the rhombohedral space group R3¯c with the lattice constants,
a = 9.214(2) A˚ and c = 10.742 (2) A˚ at 293 K, in good agreement with those from x-ray
diffraction [15]. The atomic site occupations are Ca in 18e (x,0,1/4), Co in 6a (0,0,1/4), Rh in
6b (0, 0, 0) and O in 36f (x, y, z). As the temperature is lowered below 100 K, a prominent new
line appears in the pattern around 15.5 deg scattering angle attributable [16] to the onset of
M. Loewenhaupt et al.: Evidence for the coexistence of SRO and LRO in Ca3CoRhO63
long-range magnetic ordering. The parameters characterizing the long-range magnetic order
obtained from our analysis of the diffraction data at 4.2 K are tabulated in table I. We obtain
a moment value of 3.7 (4) µB parallel to c per antiferromagnetically ordered Co-ion (4 out of
6 in the unit cell) in fair agreement with the value of 4 µB for Co-ions in a trivalent state and
with high-field magnetization data at 4.2 K and no moment on Rh, in accordance with [16].
We now turn to the point of central importance. A careful look at our raw diffraction
patterns shown in fig. 1 indicated to us that there is in addition to the magnetic Bragg
peak a broad weak peak (”magnetic short-range-order-like”) that is present at all investigated
temperatures, both above and below the long-range magnetic ordering temperature. We have
carefully obtained the patterns at several temperatures for the shorter wavelength (1.095 A˚)
and the typical patterns obtained are shown in fig. 2 for 3, 100, and 293 K. The strongest
magnetic reflection (100) is clearly visible at 2Θ = 8 deg as a superstructure reflection at
3 K and a diffuse intensity enhancement at 100 K (figs. 2 and 3). This is visible even in
the diffraction patterns measured with increased resolution using a neutron wavelength of
2.332 A˚(fig. 4). It may be noted that in the latter case there is a clear separation of the
(110) and (012) Bragg reflections when compared to the low resolution data of fig. 2 and the
strongest magnetic peak at 2Θ = 16.5 deg is superimposed by a broad diffuse share (dotted
line) as obtained by peak profile fits using two Gaussian-type curves. In order to highlight
the features due to the diffuse part, we have fitted the curves (for short wavelength) around
2Θ = 8 deg to a superposition of two Gaussians with different widths (one of them resolution
limited), as shown in fig. 3.
In figs. 5, 6, and 7 we present the temperature dependence of the relevant parameters
(intensity, width and position, respectively) of the diffuse peak, apart from showing the tem-
perature dependence of the intensity related to the long-range magnetic order.
The most remarkable feature is that the diffuse peak intensity persists in the entire tem-
perature range of investigation as though the magnetic ions (Co-3 and Co-6, see table I)
responsible for this peak are only weakly coupled to those undergoing long-range magnetic
ordering (Co-1, Co-2, Co-4, and Co-5). The only influence of long-range magnetic order-
ing appears to narrow this peak marginally and to pull out some intensity below 100 K. A
closer inspection of the temperature dependence of the intensity of the diffuse peak (fig. 5)
is quite revealing. The peak intensity increases as the temperature is lowered below 300 K,
attaining a maximum around 100 to 150 K, followed by a decrease at lower temperatures.
This qualitatively mimics the behavior of χ expected for antiferromagnetic correlations in
one-dimensional chains [21] and is actually observed in the χ data. The reader may see in
fig.1 of ref. [15] the tendency for the flattening of χ in the range 100 - 150 K as though there
is a Bonner-Fischer-type peak and the fall of χ below 100 K is presumably intercepted by the
enhancement of χ due to the onset of long range magnetic order. Thus, the present neutron
data is able to distinctly delineate the features due to long-range magnetic ordering and the
intra-chain effects. We therefore believe that the so-called ”incoherent chains” described in
the introduction retain their individuality (”isolated intra-chain interactions”) down to low
temperatures. The width of the broad diffuse peak underneath the strongest magnetic Bragg
reflection (100) (compare fig. 6) has been used for an estimation of the correlation length at
4 K. The estimation is based on the reciprocal relation between cluster size D [A˚] and peak
half width broadening FWHM [deg] according to
D =
λ · 57.3
cosΘ · FWHM
(1)
By taking the actual experimental parameters (neutron wavelength λ = 1.096 A˚, central
diffuse peak position 2Θ = 7.4 deg and FWHM = 2.75 deg after correction for instrumental
4 EUROPHYSICS LETTERS
resolution), the calculation results in a characteristic value of 23 A˚ for the linear extension
of the antiferromagnetic chain segments that coexist with the long-range magnetic order. In
the region without long-range order, i.e. above 100 K, the diffuse peak is somewhat broader,
hence the characteristic length for the one-dimensional cluster size is correspondingly smaller
(16 A˚). Thus, the influence of long-range magnetic order is to increase the correlation length.
The position-shift of the diffuse peak with decreasing temperature to larger scattering angles
(see fig. 7) indicates the reduction of short-range correlations from larger distances and/or
larger numbers of Co atoms (nearest, next nearest and even more neighbors) to a smaller
number and finally to only Co-3 and Co-6 atoms with an inter-atomic distance of 6.415 A˚.
However, because of the limitation of the diffuse experimental data in Q-space (only one
maximum of the scattering function is observed) the data cannot be used for the calculation
of a pair-correlation function.
Conclusion. – From a detailed neutron diffraction investigation we find direct evidence
for the coexistence of isolated intra-chain interactions and long-range magnetic ordering due
to inter-chain interactions from the rest of the chains in a spin-chain system, Ca3CoRhO6.
This is a fascinating finding in the field of quasi one-dimensional magnetism.
∗ ∗ ∗
Technical assistance by R. Skowronek in performing the neutron diffraction experiments
is gratefully acknowledged.
REFERENCES
[1] See, for instance, Lines M.E.,Phys. Rev. B, 131 (1963) 546, and Achiwa N., J. Phys. Soc. Jpn.,
27 (1969) 561.
[2] For a recent literature, see, for instance: Hase M., Teresaki I., and Uchinokura K., Phys.
Rev. Lett., 70 (1993) 3651; Yamaura K., Huang Q., and Takayama-Muromachi E., Phys.
Rev. B, 64 (2001) 184428; Tsukada I., Sasago Y., Uchinokura K., Zheludev A., Maslov
S., Shirane G., Kakurai K., and Ressouche E., Phys. Rev. B, 60 (1999) 6601 and references
therein.
[3] Irons S.H. et al., Phys. Rev. B, 61 (2000) 11594.
[4] Nguyen T.N. and zur Loye H.-C., J. Solid State Chem., 117 (1995) 300; Nguyen T.N. et
al., Chem. Mater., 6 (1994) 1642.
[5] Niazi A., Sampathkumaran E.V., Paulose P.L., Eckert D., Handstein A., and Mueller
K.-H., Solid State Commun., 120 (2001) 11; cond-mat/0107069.
[6] Niazi A., Sampathkumaran E.V., Paulose P.L., Eckert D., Handstein A., and Mueller
K.-H., Phys. Rev. B, 65 (2002) 064418.
[7] Neubacher M. and Mu¨ller-Buschbaum Hk., Z. Anor. allg. Chem., 607 (1992) 124.
[8] Westerberg E. et al., Phys. Rev. B, 55 (1997) 12578.
[9] Frischmuth B. et al., Phys. Rev. B, 60 (1999) 3388.
[10] Furusaki A. et al., Phys. Rev. Lett., 73 (1994) 2622.
[11] Nguyen T.N. et al., Science, 271 (1996) 489.
[12] Mahesh Kumar M. and Sampathkumaran E.V., Solid State Commun., 114 (2000) 643.
[13] Paulose P.L., Mahesh Kumar M., Majumdar Subham and Sampathkumaran E.V., J.
Phys.: Condens. Matter, 12 (2000) 8889.
[14] Niitaka S., Kageyama H., Kato M., Yoshimura Y., and Kosuge K., J. Solid State Chem.,
146 (1999) 137.
[15] Sampathkumaran E.V. and Niazi A., Phys. Rev. B, 65 (2002) 180401.
M. Loewenhaupt et al.: Evidence for the coexistence of SRO and LRO in Ca3CoRhO65
[16] After having started this investigation we came across two neutron diffraction reports by Ni-
itaka S. et al., (J. Phys. Soc. Jpn., 70 (2001) 1222 and Phys. Rev. Lett., 87 (2001) 177202) on
the Ca3CoRhO6 sample. Our results establishing long range magnetic ordering are the same as
those reported in these articles. However, it is not straightforward to draw our main conclusion
on the basis of the previously reported data as such a conclusion requires a direct observation
and careful tracking of the diffuse peak at closer temperature intervals, not only below 100 K,
but also above this temperature in the paramagnetic state. The present work also enables us to
obtain the correlation lengths. In these respects, the results reported in the present article are
new.
[17] Scha¨fer W., Jansen E., Skowronek R., and Kirfel A., Physica B, 234-236 (1997) 1146.
[18] Rodriguez-Carvajal J., Physica B, 192 (1993) 55; Fullprof-version 1999.
[19] Merz P., Jansen E., Scha¨fer W., and Will G., J. Appl. Cryst., 23 (1990) 444; version
modified by Jansen E. 1999 (unpublished).
[20] Kockelmann W., Jansen E., Scha¨fer W., and Will G., IC-POWLS: A Program for Calcu-
lation and Refinement of Commensurate and Incommensurate Structures using Powder Diffrac-
tion Data, Report Ju¨l-3024, Forschungszentrum Ju¨lich, 1995.
[21] Bonner J.C. and Fischer M.E., Phys. Rev., 135 (1964) A640.
6 EUROPHYSICS LETTERS
Table I – Parameters of the antiferromagnetic structure of Ca3CoRhO6 at 4.2 K.
magnetic atom position in chemical cell moment orientation magnetic moment [µB ]
Co-1 2/3, 1/3, 0.0833 + (parallel to c) 3.7(4)
Co-2 0 , 0 , 0.25 - (anti-parallel to c) 3.7(4)
Co-3 1/3, 2/3, 0.4167 not ordered 0
Co-4 2/3, 1/3, 0.5833 + (parallel to c) 3.7(4)
Co-5 0 , 0 , 0.75 - (anti-parallel to c) 3.7(4)
Co-6 1/3, 2/3, 0.9167 not ordered 0
M. Loewenhaupt et al.: Evidence for the coexistence of SRO and LRO in Ca3CoRhO67
In
te
ns
ity
 / 
10
3
1
2
3
4
2 Theta [deg]
20 30 40 50
Tem
perature [K]
50
100
150
200
250
Fig. 1 – Temperature dependence of diffraction patterns of Ca3CoRhO6 measured with a neutron
wavelength of 2.332 A˚.
8 EUROPHYSICS LETTERS
3 K
100 K
293 K
10
0
2 Theta [deg]
10 20 30 40 50
In
te
ns
ity
Fig. 2 – Comparison of Ca3CoRhO6 diffraction patterns measured at 3 K, 100 K, and 293 K us-
ing a neutron wavelength of 1.095 A˚. The strongest magnetic reflection (100) is clearly visible as
superstructure reflection at 3 K and as a diffuse intensity enhancement at 100 K.
M. Loewenhaupt et al.: Evidence for the coexistence of SRO and LRO in Ca3CoRhO69
10
0
3 K - 293 K
3 K - 100 K
100 K - 293 K
2 Theta [deg]
4 6 8 10 12
In
te
ns
ity
Fig. 3 – Magnetic reflection (100) of fig. 2 in an expanded scale according to its appearance in the
temperature difference patterns. Profile fits (lines) show that the peak at 3 K is composed of a
Gaussian (resolution limited) Bragg peak resulting from long-range magnetic order and a diffuse
share which also exists at 100 K.
10 EUROPHYSICS LETTERS
2 Theta [deg]
10 20 30 40 50
In
te
ns
ity
11
0
01
2
20
2
21
1
11
3
30
0
12
2
10
4
10
0/
01
0/
1− 1
0
1− 1
2/
10
2/
01−
2
02
0/
20
0/
2− 2
0
1− 2
2/
11
2/
2− 1
2
21−
2/
1− 1−
2/
12−
2
22−
2/
02
2/
2− 0
2
1− 3
0/
21
0/
3− 1
0
2− 3
0/
3− 2
0/
12
0
21
2/
2− 3
2/
1− 2−
2
3− 2
2/
31−
2/
13−
2
T = 293 K
T = 4 K
Fig. 4 – Comparison of the diffraction patterns of Ca3CoRhO6 measured with increased resolution at
293 K (crystal structure indexing) and at 4 K using a neutron wavelength of 2.332 A˚. Note the clear
separation of the (110) and (012) Bragg reflections if compared to the low resolution data of fig. 2.
The strongest magnetic peak at 2Θ = 16.5 deg is superimposed by a broad diffuse share (dotted line)
as obtained by peak profile fits using two Gaussian-type curves. The temperature difference pattern
(4 K - 293 K, bottom) shows the pure long-range magnetic Bragg scattering after subtraction of the
diffuse part.
M. Loewenhaupt et al.: Evidence for the coexistence of SRO and LRO in Ca3CoRhO611
Fig. 5 – Temperature dependence of the integrated (100) magnetic Bragg intensity and of the diffuse
intensity of Ca3CoRhO6 (measured with λ = 1.095 A˚) after subtraction of a constant background
assuming Gaussian line shapes for both lines.
Fig. 6 – Temperature dependence of the line width (FWHM ) of the diffuse peak of Ca3CoRhO6.
12 EUROPHYSICS LETTERS
Fig. 7 – Temperature dependence of the angular position of the diffuse peak of Ca3CoRhO6 assuming
a Gaussian line shape.


Evidence for the coexistence of low-dimensional magnetism and long-range order in Ca<SUB>3</SUB>CoRhO<SUB>6</SUB>

Indian Academy of Sciences

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Europhysics Letters PREPRINT
Evidence for the coexistence of low-dimensional magnetism
and long-range order in Ca3CoRhO6
M. Loewenhaupt1, W. Schäfer2, A. Niazi3 and E.V. Sampathkumaran3
1 Institut für Festkörperphysik, Technische Universität Dresden, 01062 Dresden, Ger-
many
2 Mineralogisch-Petrologisches Institut, Universität Bonn, 53115 Bonn, Germany
3 Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai-400 005, India
PACS. 61.12.Ld – neutron diffraction.
PACS. 75.25.+z – spin arrangements in magnetically ordered materials.
PACS. 75.40.-s – short range order.
Abstract. – We report the results of neutron powder diffraction studies on the spin-chain
compound Ca3CoRhO6 in the temperature range 3 to 293 K. Bragg peaks due to magnetic
ordering start appearing below about 100 K. The most interesting observation is that there
is a diffuse magnetic peak superimposed over the strongest magnetic Bragg peak. The diffuse
magnetic intensity is observed below as well above 100 K. This finding provides a new insight
into the physics of this compound as though the low-dimensional magnetic interaction coexists
with long range magnetic order – a novel situation among quasi one-dimensional oxides.
Introduction. – The pseudo low-dimensional insulators have been of constant interest
among physicists and chemists [1] for the past few decades as the interplay between intra-
chain and inter-chain interactions has been found to result in novel magnetic anomalies [2].
Till to-date, in all such compounds, the presence of weak inter-chain magnetic coupling results
in eventual loss of the identity of the chains, thereby paving the way for three dimensional
magnetic ordering at low temperatures. In this article, we report the temperature dependent
neutron diffraction data for a quasi one-dimensional compound, Ca3CoRhO6, which appar-
ently has the signatures of the correlations within a chain coexisting with long range magnetic
order, thereby providing a novel situation in this direction of research. The compound un-
der investigation crystallizes in the K4CdCl6-type rhombohedral structure (space group R3̄c).
This class of compounds, (Sr, Ca)3MXO6 (M, X = a metallic ion, magnetic or non-magnetic),
have started attracting attention in recent years due to the presence of spin-chains (M − X)
separated by Sr/Ca ions (see refs. [3] to [16] and references cited therein) and the magnetic
chains form a triangular lattice (with an inter-chain spacing of 5.313 Å in the present com-
pound). In this structure, there is face-sharing of octahedra of X ions and trigonal prisms of
M ions. Of these, the title compound is of special interest. On the basis of previous neutron
diffraction data [16], it was inferred that this compound can be classified a ”Partially Disor-
dered Antiferromagnet (PDA)” – a novel magnetic structure very rarely encountered [16] in
magnetism. In this magnetic structure, there is a temperature range (below the paramagnetic
c© EDP Sciences
2 EUROPHYSICS LETTERS
state) in which the chains at the apices of the hexagon are antiferromagnetically coupled to
each other, whereas the one at the center of the hexagon is left incoherent; as the temper-
ature is lowered further, the incoherent chains can undergo spin-glass freezing (as proposed
for the present case [16]) or couple ferrimagnetically with other chains. It has been found
that dc magnetic susceptibililty (χ) exhibits a complex behavior at temperatures below 300 K
(refs. [14] and [15]), reflecting the existence of different temperature regions: there is a broad
maximum in the plot of χ versus T around 100 to 150 K, with an isothermal magnetization
behavior highly non-linear with the magnetic field in the intermediate T -range (40 - 90 K),
but tending to a constant (zero-field-cooled) χ at still lower temperatures. However, ac sus-
ceptibililty exhibits a broad feature in the range 40 - 70 K with an unusually strong frequency
dependence, implying more exotic magnetic behavior of this compound, thereby warranting
further investigations for better understanding [15]. Motivated by this situation, we have sub-
jected this compound to more careful neutron diffraction investigations as compared to those
reported in ref. [16], the new results of which are reported in this article. It is worthwhile
stating that, in sharp contrast to the situation in this material, the analogous Fe compound
exhibits a simple magnetic behavior [14] with a magnetic ordering temperature around 15 K.
Sample Preparation. – The polycrystalline specimen of Ca3CoRhO6 was synthesized by
a conventional solid state route. Stoichiometric amounts of high purity (>99.9%) CaCO3,
CoO and Rh powder were thoroughly mixed. Then the mixture was calcined at 900 C for
one day. The prereacted powder was then finely ground, pelletized and heated at 1200 C
for about 10 days with few intermediate grindings. The x-ray diffraction pattern confirmed
that the sample was single phase. Neutron powder diffraction measurements were performed
at the constant wavelength thermal neutron instrument SV7 at the DIDO research reactor
in the Forschungszentrum Jülich [17] using the diffractometers SV7-a and SV7-b with neu-
tron wavelengths of 1.095 Å and 2.332 Å, respectively. Both instruments are equipped with
JULIOS-type linear scintillation detectors. The sample was contained in a vanadium cylinder
of 8 mm diameter and 30 mm height and inserted in a helium refrigerator cryostat equipped
with vanadium windows. Full long-term diffraction patterns were collected at 293, 100, and
3 K in the short wavelength configuration (λ = 1.095 Å) and at 4 K and 293 K using the long
wavelength of 2.332 Å. Short-term runs were performed in the temperature regime between
3 K to 250 K for both wavelengths.
Results and discussion. – We show in fig. 1 the temperature dependence of the raw
diffraction patterns in the low-angle region with the long wavelength. We have carried out
crystal structure data analysis by full-pattern Rietveld refinements using Fullprof [18]. A two-
step data handling was applied to the magnetic structure analysis using (1) a modified version
of the program Profan [19] and (2) the full-matrix least squares program IC-POWLS [20].
Profan fits pre-selectable profile functions, e.g. Gaussian or Lorentzian, into measured peaks
or peak clusters and individually refines sets of three profile parameters each for peak position
2Θ, half width FWHM, and peak height H. This procedure permits the separation of broad
diffuse magnetic scattering contributions from the pure Bragg peaks and thus the separation
of disorder and long-range order effects, respectively. The refined profile parameters are
used for the calculation of integrated peak intensities. IC-POWLS uses these intensities as
observations for magnetic structure refinement calculations. With our analysis, we confirm
that Ca3CoRhO6 crystallizes in the rhombohedral space group R3̄c with the lattice constants,
a = 9.214(2) Å and c = 10.742 (2) Å at 293 K, in good agreement with those from x-ray
diffraction [15]. The atomic site occupations are Ca in 18e (x,0,1/4), Co in 6a (0,0,1/4), Rh in
6b (0, 0, 0) and O in 36f (x, y, z). As the temperature is lowered below 100 K, a prominent new
line appears in the pattern around 15.5 deg scattering angle attributable [16] to the onset of
M. Loewenhaupt et al.: Evidence for the coexistence of SRO and LRO in Ca3CoRhO63
long-range magnetic ordering. The parameters characterizing the long-range magnetic order
obtained from our analysis of the diffraction data at 4.2 K are tabulated in table I. We obtain
a moment value of 3.7 (4) µB parallel to c per antiferromagnetically ordered Co-ion (4 out of
6 in the unit cell) in fair agreement with the value of 4 µB for Co-ions in a trivalent state and
with high-field magnetization data at 4.2 K and no moment on Rh, in accordance with [16].
We now turn to the point of central importance. A careful look at our raw diffraction
patterns shown in fig. 1 indicated to us that there is in addition to the magnetic Bragg
peak a broad weak peak (”magnetic short-range-order-like”) that is present at all investigated
temperatures, both above and below the long-range magnetic ordering temperature. We have
carefully obtained the patterns at several temperatures for the shorter wavelength (1.095 Å)
and the typical patterns obtained are shown in fig. 2 for 3, 100, and 293 K. The strongest
magnetic reflection (100) is clearly visible at 2Θ = 8 deg as a superstructure reflection at
3 K and a diffuse intensity enhancement at 100 K (figs. 2 and 3). This is visible even in
the diffraction patterns measured with increased resolution using a neutron wavelength of
2.332 Å(fig. 4). It may be noted that in the latter case there is a clear separation of the
(110) and (012) Bragg reflections when compared to the low resolution data of fig. 2 and the
strongest magnetic peak at 2Θ = 16.5 deg is superimposed by a broad diffuse share (dotted
line) as obtained by peak profile fits using two Gaussian-type curves. In order to highlight
the features due to the diffuse part, we have fitted the curves (for short wavelength) around
2Θ = 8 deg to a superposition of two Gaussians with different widths (one of them resolution
limited), as shown in fig. 3.
In figs. 5, 6, and 7 we present the temperature dependence of the relevant parameters
(intensity, width and position, respectively) of the diffuse peak, apart from showing the tem-
perature dependence of the intensity related to the long-range magnetic order.
The most remarkable feature is that the diffuse peak intensity persists in the entire tem-
perature range of investigation as though the magnetic ions (Co-3 and Co-6, see table I)
responsible for this peak are only weakly coupled to those undergoing long-range magnetic
ordering (Co-1, Co-2, Co-4, and Co-5). The only influence of long-range magnetic order-
ing appears to narrow this peak marginally and to pull out some intensity below 100 K. A
closer inspection of the temperature dependence of the intensity of the diffuse peak (fig. 5)
is quite revealing. The peak intensity increases as the temperature is lowered below 300 K,
attaining a maximum around 100 to 150 K, followed by a decrease at lower temperatures.
This qualitatively mimics the behavior of χ expected for antiferromagnetic correlations in
one-dimensional chains [21] and is actually observed in the χ data. The reader may see in
fig.1 of ref. [15] the tendency for the flattening of χ in the range 100 - 150 K as though there
is a Bonner-Fischer-type peak and the fall of χ below 100 K is presumably intercepted by the
enhancement of χ due to the onset of long range magnetic order. Thus, the present neutron
data is able to distinctly delineate the features due to long-range magnetic ordering and the
intra-chain effects. We therefore believe that the so-called ”incoherent chains” described in
the introduction retain their individuality (”isolated intra-chain interactions”) down to low
temperatures. The width of the broad diffuse peak underneath the strongest magnetic Bragg
reflection (100) (compare fig. 6) has been used for an estimation of the correlation length at
4 K. The estimation is based on the reciprocal relation between cluster size D [Å] and peak
half width broadening FWHM [deg] according to
D =
λ · 57.3
cosΘ · FWHM
(1)
By taking the actual experimental parameters (neutron wavelength λ = 1.096 Å, central
diffuse peak position 2Θ = 7.4 deg and FWHM = 2.75 deg after correction for instrumental
4 EUROPHYSICS LETTERS
resolution), the calculation results in a characteristic value of 23 Å for the linear extension
of the antiferromagnetic chain segments that coexist with the long-range magnetic order. In
the region without long-range order, i.e. above 100 K, the diffuse peak is somewhat broader,
hence the characteristic length for the one-dimensional cluster size is correspondingly smaller
(16 Å). Thus, the influence of long-range magnetic order is to increase the correlation length.
The position-shift of the diffuse peak with decreasing temperature to larger scattering angles
(see fig. 7) indicates the reduction of short-range correlations from larger distances and/or
larger numbers of Co atoms (nearest, next nearest and even more neighbors) to a smaller
number and finally to only Co-3 and Co-6 atoms with an inter-atomic distance of 6.415 Å.
However, because of the limitation of the diffuse experimental data in Q-space (only one
maximum of the scattering function is observed) the data cannot be used for the calculation
of a pair-correlation function.
Conclusion. – From a detailed neutron diffraction investigation we find direct evidence
for the coexistence of isolated intra-chain interactions and long-range magnetic ordering due
to inter-chain interactions from the rest of the chains in a spin-chain system, Ca3CoRhO6.
This is a fascinating finding in the field of quasi one-dimensional magnetism.
∗ ∗ ∗
Technical assistance by R. Skowronek in performing the neutron diffraction experiments
is gratefully acknowledged.
REFERENCES
[1] See, for instance, Lines M.E.,Phys. Rev. B, 131 (1963) 546, and Achiwa N., J. Phys. Soc. Jpn.,
27 (1969) 561.
[2] For a recent literature, see, for instance: Hase M., Teresaki I., and Uchinokura K., Phys.
Rev. Lett., 70 (1993) 3651; Yamaura K., Huang Q., and Takayama-Muromachi E., Phys.
Rev. B, 64 (2001) 184428; Tsukada I., Sasago Y., Uchinokura K., Zheludev A., Maslov
S., Shirane G., Kakurai K., and Ressouche E., Phys. Rev. B, 60 (1999) 6601 and references
therein.
[3] Irons S.H. et al., Phys. Rev. B, 61 (2000) 11594.
[4] Nguyen T.N. and zur Loye H.-C., J. Solid State Chem., 117 (1995) 300; Nguyen T.N. et
al., Chem. Mater., 6 (1994) 1642.
[5] Niazi A., Sampathkumaran E.V., Paulose P.L., Eckert D., Handstein A., and Mueller
K.-H., Solid State Commun., 120 (2001) 11; cond-mat/0107069.
[6] Niazi A., Sampathkumaran E.V., Paulose P.L., Eckert D., Handstein A., and Mueller
K.-H., Phys. Rev. B, 65 (2002) 064418.
[7] Neubacher M. and Müller-Buschbaum Hk., Z. Anor. allg. Chem., 607 (1992) 124.
[8] Westerberg E. et al., Phys. Rev. B, 55 (1997) 12578.
[9] Frischmuth B. et al., Phys. Rev. B, 60 (1999) 3388.
[10] Furusaki A. et al., Phys. Rev. Lett., 73 (1994) 2622.
[11] Nguyen T.N. et al., Science, 271 (1996) 489.
[12] Mahesh Kumar M. and Sampathkumaran E.V., Solid State Commun., 114 (2000) 643.
[13] Paulose P.L., Mahesh Kumar M., Majumdar Subham and Sampathkumaran E.V., J.
Phys.: Condens. Matter, 12 (2000) 8889.
[14] Niitaka S., Kageyama H., Kato M., Yoshimura Y., and Kosuge K., J. Solid State Chem.,
146 (1999) 137.
[15] Sampathkumaran E.V. and Niazi A., Phys. Rev. B, 65 (2002) 180401.
M. Loewenhaupt et al.: Evidence for the coexistence of SRO and LRO in Ca3CoRhO65
[16] After having started this investigation we came across two neutron diffraction reports by Ni-
itaka S. et al., (J. Phys. Soc. Jpn., 70 (2001) 1222 and Phys. Rev. Lett., 87 (2001) 177202) on
the Ca3CoRhO6 sample. Our results establishing long range magnetic ordering are the same as
those reported in these articles. However, it is not straightforward to draw our main conclusion
on the basis of the previously reported data as such a conclusion requires a direct observation
and careful tracking of the diffuse peak at closer temperature intervals, not only below 100 K,
but also above this temperature in the paramagnetic state. The present work also enables us to
obtain the correlation lengths. In these respects, the results reported in the present article are
new.
[17] Schäfer W., Jansen E., Skowronek R., and Kirfel A., Physica B, 234-236 (1997) 1146.
[18] Rodriguez-Carvajal J., Physica B, 192 (1993) 55; Fullprof-version 1999.
[19] Merz P., Jansen E., Schäfer W., and Will G., J. Appl. Cryst., 23 (1990) 444; version
modified by Jansen E. 1999 (unpublished).
[20] Kockelmann W., Jansen E., Schäfer W., and Will G., IC-POWLS: A Program for Calcu-
lation and Refinement of Commensurate and Incommensurate Structures using Powder Diffrac-
tion Data, Report Jül-3024, Forschungszentrum Jülich, 1995.
[21] Bonner J.C. and Fischer M.E., Phys. Rev., 135 (1964) A640.
6 EUROPHYSICS LETTERS
Table I – Parameters of the antiferromagnetic structure of Ca3CoRhO6 at 4.2 K.
magnetic atom position in chemical cell moment orientation magnetic moment [µB ]
Co-1 2/3, 1/3, 0.0833 + (parallel to c) 3.7(4)
Co-2 0 , 0 , 0.25 - (anti-parallel to c) 3.7(4)
Co-3 1/3, 2/3, 0.4167 not ordered 0
Co-4 2/3, 1/3, 0.5833 + (parallel to c) 3.7(4)
Co-5 0 , 0 , 0.75 - (anti-parallel to c) 3.7(4)
Co-6 1/3, 2/3, 0.9167 not ordered 0
M. Loewenhaupt et al.: Evidence for the coexistence of SRO and LRO in Ca3CoRhO67
In
te
ns
ity
 / 
10
3
1
2
3
4
2 Theta [deg]
20 30 40 50
T
em
perature [K
]
50
100
150
200
250
Fig. 1 – Temperature dependence of diffraction patterns of Ca3CoRhO6 measured with a neutron
wavelength of 2.332 Å.
8 EUROPHYSICS LETTERS
3 K
100 K
293 K
10
0
2 Theta [deg]
10 20 30 40 50
In
te
ns
ity
Fig. 2 – Comparison of Ca3CoRhO6 diffraction patterns measured at 3 K, 100 K, and 293 K us-
ing a neutron wavelength of 1.095 Å. The strongest magnetic reflection (100) is clearly visible as
superstructure reflection at 3 K and as a diffuse intensity enhancement at 100 K.
M. Loewenhaupt et al.: Evidence for the coexistence of SRO and LRO in Ca3CoRhO69
10
0
3 K - 293 K
3 K - 100 K
100 K - 293 K
2 Theta [deg]
4 6 8 10 12
In
te
ns
ity
Fig. 3 – Magnetic reflection (100) of fig. 2 in an expanded scale according to its appearance in the
temperature difference patterns. Profile fits (lines) show that the peak at 3 K is composed of a
Gaussian (resolution limited) Bragg peak resulting from long-range magnetic order and a diffuse
share which also exists at 100 K.
10 EUROPHYSICS LETTERS
2 Theta [deg]
10 20 30 40 50
In
te
ns
ity
11
0
01
2
20
2
21
1
11
3
30
0
12
2
10
4
10
0/
01
0/
1−
10
1−
12
/1
02
/0
1−
2
02
0/
20
0/
2−
20
1−
22
/1
12
/2−
12
21−
2/
1−
1−
2/
12−
2
22−
2/
02
2/
2−
02
1−
30
/2
10
/3−
10
2−
30
/3−
20
/1
20
21
2/
2−
32
/1−
2−
2
3−
22
/3
1−
2/
13−
2
T = 293 K
T = 4 K
Fig. 4 – Comparison of the diffraction patterns of Ca3CoRhO6 measured with increased resolution at
293 K (crystal structure indexing) and at 4 K using a neutron wavelength of 2.332 Å. Note the clear
separation of the (110) and (012) Bragg reflections if compared to the low resolution data of fig. 2.
The strongest magnetic peak at 2Θ = 16.5 deg is superimposed by a broad diffuse share (dotted line)
as obtained by peak profile fits using two Gaussian-type curves. The temperature difference pattern
(4 K - 293 K, bottom) shows the pure long-range magnetic Bragg scattering after subtraction of the
diffuse part.
M. Loewenhaupt et al.: Evidence for the coexistence of SRO and LRO in Ca3CoRhO611
Fig. 5 – Temperature dependence of the integrated (100) magnetic Bragg intensity and of the diffuse
intensity of Ca3CoRhO6 (measured with λ = 1.095 Å) after subtraction of a constant background
assuming Gaussian line shapes for both lines.
Fig. 6 – Temperature dependence of the line width (FWHM ) of the diffuse peak of Ca3CoRhO6.
12 EUROPHYSICS LETTERS
Fig. 7 – Temperature dependence of the angular position of the diffuse peak of Ca3CoRhO6 assuming
a Gaussian line shape.


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Evidence for the coexistence of low-dimensional magnetism and long-range order in Ca3CoRhO6

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