Journal of the Physical Society of Japan
Vol. 70, No. 5, May, 2001, pp. 1222–1225

Letters

High-Field Magnetization and Neutron Diﬀraction Studiesof One-Dimensional Compound Ca3 CoRhO6
Seiji Niitaka* , Hiroshi Kageyama1 , Kazuyoshi Yoshimura, Koji Kosuge,
Shinji Kawano2 , Naofumi Aso3 , Akihiro Mitsuda1 ,Hiroyuki Mitamura1 and Tsuneaki Goto1
Department of Chemistry, Graduate School of Science, Kyoto University, Kyoto 606-8502

1 Institute for Solid State Physics, University of Tokyo, Kashiwanoha, Kashiwa, Chiba 277-8581
2 Research Reactor Institute, Kyoto University, Kumatori, Sennan, Osaka 590-0494

3 Neutron Scattering Laboratory, Institute for Solid State Physics, University of Tokyo, Shirakata 106-1,Tokai-mura, Ibaraki 319-1106(Received November 2, 2000)

High-ﬁeld magnetization and neutron diﬀraction measurements were performed on the onedimensional compound Ca3 CoRhO6 . The long-range ordered state was ﬁrst observed below
90 K. A plateau at 1/3 of the saturation magnetization was observed in the magnetization curveat 70 K, indicating ferrimagnetic alignment of the ferromagnetic Ising chains. We also observeda large hysteresis originating from a spin freezing of ferromagnetic chains in the magnetization
curve at 4.2 K. Based on the results of high-ﬁeld magnetization and neutron diﬀraction measurements, a possible magnetic structure is discussed in terms of the spin frustration on thetriangular lattice.
KEYWORDS: one-dimensional magnetic chain, triangular lattice, Ising spin system, frustration, Ca3 CoRhO6 , ferrimagnetic structure, partially disordered antiferromagnetic state

We have recently reported the synthesis, crystal
structure and magnetic properties of Ca3 CoRhO6 ,1)
which belongs to A3 ABO6 -type compounds (A =Ca, Sr, Ba; A = Cu, Ni, Zn,· · · ; B = Ir, Pt, Ru,· · · ) with
the K4 CdCl6 structure.2) The structure of Ca3 CoRhO6
consists of one-dimensional (1-D) chains of alternating
face-sharing CoO6 trigonal prisms and RhO6 octahedra.
The chains are separated by calcium cations, forminga triangular lattice in the c plane. The distance between the nearest neighbor chains is 5.313 Å, about twice
as long as the intrachain spacing between Co and Rh,
2.682 Å. Therefore, Ca3 CoRhO6 has a structural similarity to ABX3 -type compounds, for example, CsCoCl3 andCsCuCl3 in the respect that chains consisting of magnetic ions are arranged on a triangular lattice, which isexpected to show interesting magnetic characteristics ofa 1-D chain and/or a triangular lattice. Ca3 CoRhO6 has
the positive Weiss temperature of 150 K, suggesting thatthe intrachain exchange interaction is ferromagnetic andrelatively strong compared with that of ABX3 -type compounds.1) It should be noted in the case of Ca3 CoRhO6that each chain has a diﬀerent phase of the atomic sequence from three nearest-neighbor chains by 1/6 along
the c axis (the chain direction) and from the other threeby 2/6 along the same axis.
The temperature dependence of the magnetic susceptibility M/H of Ca3 CoRhO6 1) (see the inset of Fig. 5)
is very complex and similar to those of isostructural
Sr3 NiIrO6 3) and Ca3 CoIrO6 ;4) [1] the values of M/Hdepend on H below T1 (90 K for Ca3 CoRhO6 , 70 K for
Sr3 NiIrO6 , 80 K for Ca3 CoIrO6 ), and [2] there is a sharp

drop at T2 reaching nearly zero (35 K for Ca3 CoRhO6 ,21 K for Sr3 NiIrO6 , 32 K for Ca3 CoIrO6 ) in zero ﬁeldcooling (ZFC) measurements, and the M/H does notdrop in ﬁeld cooling (FC) measurements. Hence, it isconsidered that these three compounds have similar magnetic properties which can be attributed to the 1-D chain
and/or the triangular lattice and possibly the alternating arrangement of two diﬀerent ions. Nyugen and Loyeconsidered that the abrupt drop in M/H of Sr3 NiIrO6is ascribed to a transition to the spin singlet state in theZFC process.3) Their neutron diﬀraction measurements
at 10 K and 30 K for Sr3 NiIrO6 indicate neither a structural change nor additional Bragg peaks, suggesting theabsence of a magnetic superstructure. As for Ca3 CoIrO6 ,the magnetic susceptibility has been reported only byKageyama et al.4) Thus still little is known about theground states and the phase transitions of these threecompounds.
In order to elucidate the above-mentioned unusual
magnetic behaviors, we have performed high-ﬁeld magnetization and powder neutron diﬀraction measurementsof Ca3 CoRhO6 . The main ﬁndings are that the M –H
curve at 70 K shows a plateau at 1/3 of the saturation
magnetization and that four magnetic Bragg reﬂections
indicating a magnetic ordering were observed below 90 K.
The polycrystalline sample of Ca3 CoRhO6 was prepared by a solid state reaction from starting materials CaCO3 (99.99%), CoO(99.99%), and Rh(>99.95%).
They were mixed in a stoichiometric proportion, pressed
into pellets, and calcined in air at 1173 K for one day.
Then the sample was heated at 1473 K in air for one
week with several intermediate grindings. Field-oriented∗ E-mail: niitaka@kuchem.kyoto-u.ac.jp1222

LettersFig. 1. Magnetization curves of Ca3 CoRhO6 at 70 K in pulsed
magnetic ﬁelds up to 18.7 T. The arrows along the curves indicate the directions of the ﬁeld sweeps. The inset represents thelow-ﬁeld region in the magnetization curve for H  c.

samples for high-ﬁeld magnetization measurements wereprepared by solidifying the powder dispersed in epoxy
resin Stycast 1226 under the magnetic ﬁeld of 8 T atroom temperature. X-ray diﬀraction measurement conﬁrmed the alignment of the polycrystalline samples along
the hexagonal c axis. High-ﬁeld magnetization measurements were carried out for the ﬁeld-oriented samples by an induction method in a pulsed high magnetic
ﬁeld up to 18.7 T at 70 K and 42 T at 4.2 K. The duration of the pulsed ﬁeld was 12 ms, roughly corresponding to (∆H/∆t) = 3.1 T/ms at 70 K, and 7.0 T/ms at
4.2 K. Powder neutron diﬀraction measurements wereperformed using the HQR diﬀractometer installed atJRR-3M Guide Hall in Japan Atomic Energy ResearchInstitute. The wavelength of the incident neutrons was
2.467 Å. The data were collected in the 2θ range of 10◦
to 60◦ at an interval of 0.1◦ in the temperature range
of 4–155 K under an applied magnetic ﬁeld of 0–2 T.
The powder neutron diﬀraction patterns of two magnetic
structures were calculated using Rietan.5)
In Fig. 1 we show the magnetization curves of the ﬁeldoriented samples in pulsed magnetic ﬁelds up to 18.7 T
at 70 K between T2 and T1 . There is a large diﬀerence
between the magnetization for H  c, M and that forH ⊥ c, M⊥ . The value of M at 18.7 T is 4.05µB /f.u.,eight times as large as that of M⊥ at 18.7 T, 0.53µB /f.u.
This indicates the Ising spin nature of this system. M⊥
shows linear ﬁeld dependence up to 18.7 T. On theother hand, M exhibits a plateau around 4 T reaching
4µB /f.u. at 15 T as seen in the inset of Fig. 1. The valueof the magnetization at 4 T is 1.39µB /f.u., corresponding
to 1/3 of the saturation magnetization. The plateau at
the value of 1/3 of the full moment implies a ferrimagnetic alignment of ferromagnetic spin chains supportedby the positive Weiss temperature.1)
Figure 2 shows magnetization curves in pulsed mag-1223

Fig. 2. Magnetization curves of Ca3 CoRhO6 at 4.2 K in pulsed
magnetic ﬁelds up to 42 T. The arrows along the curves indicate
the directions of the ﬁeld sweeps.

Fig. 3. Neutron powder diﬀraction patterns of Ca3 CoRhO6 observed at 4 K, 40 K, and 120 K and the calculated neutron powderdiﬀraction patterns for ferrimagnetic and PDA (F-PDA) structures on the assumption that Co and Rh have the magnetic moments of 3µB /f.u. and 1µB /f.u., respectively. Indexing of theobserved peaks is based on the chemical unit cell. The additional magnetic peaks are marked by asterisks.

netic ﬁelds up to 42 T at 4.2 K below T2 . M⊥ increases
linearly, reaching 0.64µB /f.u. at 42 T. Although the values of M below 28 T are about the same as those ofM⊥ , M shows a steep increase above 28 T and reaches
4µB /f.u., corresponding to the saturation magnetization
at 70 K. A plateau is not observed in M at 4.2 K unlikethat at 70 K. We can see a distinct hysteresis in M , indicating a hard magnetization process against an external

1224

LettersFig. 4. Schematic illustration of (a) ferrimagnetic structure and(b) partially disordered antiferromagnetic structure projected on
the c plane. Plus and minus signs indicate the directions of themoments in the ferromagnetic Ising chains. Zero(0) represents
either + or − at random.

ﬁeld due to spin freezing. This hard process agrees wellwith the spin glass behavior seen in M/H below T2 .1)
The powder neutron diﬀraction patterns of Ca3 CoRhO6
measured at 4 K, 40 K, and 120 K are shown in Fig. 3.
Four additional Bragg peaks at 17.7◦ , 35.9◦ , 41.4◦ and48.2◦ were observed in the patterns obtained at 4 K and40 K, indexed as (100), (200), (112), and (210) basedon the chemical unit cell, respectively. These peaks areascribed to a magnetic ordering because powder X-ray
diﬀraction does not show any indication of structuralphase transition down to 10 K. This is the ﬁrst timethe existence of magnetic ordering has been conﬁrmed
among Ca3 CoRhO6 , Sr3 NiIrO6 , and Ca3 CoIrO6 . It also
indicates that Sr3 NiIrO6 and Ca3 CoRhO6 have diﬀerent magnetic structures, although the temperature dependence of M/H of Sr3 NiIrO6 is similar to that ofCa3 CoRhO6 .
The four magnetic peaks may be explained in termof a ferrimagnetic structure by the comparison between
the powder neutron diﬀraction patterns at 4 K and 40 K
and the calculated powder neutron diﬀraction patternof the ferrimagnetic structure as seen in Fig. 3. In thecalculation of the diﬀraction pattern, Co and Rh wereassumed to have the magnetic moments of 3µB /f.u. and1µB /f.u., respectively. This assumption is based on thesaturation magnetization, 4µB /f.u. and the bond valencecalculation.1) The ferrimagnetic structure projected on
the c plane is illustrated in Fig. 4(a). All the moments are aligned along [001] and ferromagnetic coupling
dominates within the chains. These ferromagnetic Ising
chains are ordered ferrimagnetically in the c plane. This
ferrimagnetic structure is the same as the magnetic structure of Ca3 Co2 O6 at low temperatures,6) consistent withthe 1/3 plateau observed at 70 K in M , the Ising spin
nature, and the high relative intensity of the (100) magnetic reﬂection.
Figure 5 represents the temperature dependence of the(100) peak intensity at H = 0 T, I0T , at H = 2 T for
ZFC, I2T-ZFC , and at H = 2 T for FC, I2T-FC . The
temperature dependence of I0T exhibits no anomaly atT2 . We estimated the long-range ordering temperature,
TN by ﬁtting I0T between 50 K and 85 K to the following
formula,I0T = A(1 − T /TN )β + I0 ,Fig. 5. Temperature dependences of peak intensity of (100) reﬂection. Solid circles denote I0T , open squares I2T-ZFC , andcrosses I2T-FC . The inset shows the temperature dependencesof the magnetic susceptibilities M/H of Ca3 CoRhO6 measured
at H = 1, 3, and 5 T.

where A is the coeﬃcient of the temperature dependent
term, β the critical exponent, and I0 the constant term.
The obtained TN is 89.9 ± 2.9 K, in good agreement withT1 .
I2T-ZFC exhibits unusual temperature dependence fora simple ferrimagnet. Although the values of I2T-ZFC arethe same as those of I0T below 30 K, I2T-ZFC increases
sharply at 30 K on heating. Note that the abrupt increases of I2T-ZFC and the susceptibilities M/H for ZFC
occur at about the same temperature. The values ofI2T-ZFC above 50 K are about twice as large as thoseof I0T . The TN estimated from I2T-ZFC by the abovementioned method is 90.8 ± 3.1 K, consistent with theTN estimated from I0T . One can see the diﬀerence between I2T-ZFC and I2T-FC below 40 K.
One explanation for the origin of the increase in
I2T-ZFC at 30 K may be that spin glass regions between
predominant ferrimagnetic regions are changed into domains of the ferrimagnetic structure by the magnetic ﬁeld
against the random freezing. Based on this explanation,the observed increase in I2T-ZFC at 30 K implies anomalously large volume of spin glass regions inconsistent withthe Ising spin nature of Ca3 CoRhO6 , although the possibility of this case cannot be ruled out.
Here we propose the following model that can explain
the increase at 30 K in I2T-ZFC more suitably. Below
90 K, the ferromagnetic spin chains in Ca3 CoRhO6 arepartially ordered antiferromagnetically. In other words,
the partially disordered antiferromagnetic (PDA) stateis realized below 90 K. In the PDA state as illustratedin Fig. 4(b), 2/3 of the ferromagnetic Ising chains orderantiferromagnetically with each other and the remaining

LettersFig. 6. Schematic magnetic phase diagram for T and H. P, theparamagnetic state; F, the ferromagnetic state; FR, the ferrimagnetic state; PDA, the partially disordered antiferromagneticstate; F-PDA, the frozen PDA state.

1/3 are left incoherent with the other chains. The shortrange ferromagnetic order is well developed even withineach incoherent chain. The 1/3 incoherent ferromagnetic chain originates from the cancellation of the antiferromagnetic exchange interactions with the six nearest
neighbor chains and the entropy eﬀect. The incoherent
ferromagnetic chains ﬂuctuate by means of the propagation of the domain walls. Below 30 K, a spin freezing of
the incoherent ferromagnetic chains occurs, resulting ina frozen PDA (F-PDA) state. In the F-PDA structure,
2/3 of the ferromagnetic chains order antiferromagnetically similar to the case above 30 K and the momentsin the 1/3 incoherent ferromagnetic Ising chains freeze
randomly due to a ﬁnite activation energy for the spininversion in ferromagnetic Ising chains. The randomly
frozen Ising spin chains have much lower magnetic susceptibility than the ﬂuctuating chains. This accounts forthe sharp drop of the magnetic susceptibility at 30 K. We
show a rough magnetic phase diagram of Ca3 CoRhO6 inFig. 6. The two critical ﬁelds at 2 T and 4 T in the phase
diagram are roughly estimated from the magnetization
curve at 70 K in M .
It is theoretically indicated by molecular ﬁeld approximation7) and Monte Carlo simulation8) that a PDA
phase equivalent to that of our model appears in the triangular Ising lattice with an antiferromagnetic nearest
neighbor interaction together with a weak ferromagnetic
second neighbor interaction. GdInCu4 is given as a casein which incoherent spins in a PDA state freeze at lowtemperatures.9)
We brieﬂy examine the results mentioned above fromthe viewpoint of our model. The 1/3 plateau at 70 K
in M originates from a ferromagnetic alignment of the1/3 incoherent chains, leading to the ferrimagnetic struc-1225

ture. The powder neutron diﬀraction patterns at 4 K and
40 K can be explained qualitatively by the PDA (F-PDA)
structure similar to the ferrimagnetic structure as seenin Fig. 3. It should be noted that the calculated patternof the F-PDA structure is identical to that of the PDAstructure since the randomly frozen chains do not contribute any Bragg scattering. The unusual temperaturedependence of I2T-ZFC can be explained by a transition
from the F-PDA state to the ferrimagnetic state. Although the thermodynamically stable state at H = 2 T
below 90 K is the ferrimagnetic state as shown in Fig. 6,
2 T is not strong enough to change the F-PDA state into
the ferrimagnetic state below 30 K, so that I2T-ZFC is
the same as I0T below 30 K. Above 30 K, it is possible tochange the system into a ferrimagnetic structure at 2 T.
The magnetic structure factor of the (100) peak in theferrimagnetic structure is larger than that in the F-PDAstructure, resulting in the steep increase at 30 K in thetemperature dependence of I2T-ZFC . In order to conﬁrm
our model, speciﬁc heat, ESR, and NMR measurements
are now in progress.
In conclusion, we have investigated the magnetic properties of Ca3 CoRhO6 by high-ﬁeld magnetization andpowder neutron diﬀraction measurements. The plateau
at 1/3 of the saturation magnetization was observed in
the magnetization curve at 70 K, indicating a ferrimagnetic alignment of ferromagnetic spin chains. Four magnetic Bragg peaks ascribed to a magnetic ordering wereobserved in the powder neutron diﬀraction patterns below 90 K. The existence of magnetic long-range orderinghas been ﬁrst conﬁrmed among three compounds whichshow similar temperature dependences of M/H. We propose a partially disordered antiferromagnetic state as apossible magnetic structure of Ca3 CoRhO6 , of which theincoherent chains freeze randomly below 30 K.
This study was supported by a Grant-in-Aid onpriority area, “Novel Quantum Phenomena in Transition Metal Oxides”, from the Ministry of Education, Science, Sports and Culture, and also partially
supported by a Grant-in-Aid for Scientiﬁc Researchof the Japan Society for the Promotion of Science(11440195, 12740364, 12440195, 12874038).
1) S. Niitaka, H. Kageyama, M. Kato, K. Yoshimura and K. Kosuge: J. Solid State Chem. 146 (1999) 137.
2) G. Bergerhoﬀ and O. Schmitz-Dumott: Z. Anorg. Allg. Chem.
284 (1956) 10.
3) T. N. Nyugen and H.-C. Loye: J. Solid State Chem. 117 (1995)
300.
4) H. Kageyama, K. Yoshimura and K. Kosuge: J. Solid State
Chem. 140 (1998) 14.
5) F. Izumi: The Rietveld Method, ed. R. A. Young (Oxford University Press, Oxford, 1993) Chap. 13; Y.-I. Kim and F. Izumi:
J. Ceram. Soc. Jpn. 102 (1994) 401.
6) S. Aaslamd, H. Fjellvåg and B. Hauback: Solid State Commun.
101 (1997) 187.
7) M. Mekata: J. Phys. Soc. Jpn. 42 (1977) 76.
8) S. Fujiki, K. Shutoh, Y. Abe and S. Katsura: J. Phys. Soc. Jpn.
52 (1983) 1531.
9) H. Nakamura, N. Kim, M. Shiga, R. Kmiec, K. Tomala, E.
Ressouche, J. P. Sanchez and B. Malaman: J. Phys.: Condens.
Matter 11 (1999) 1095.