VOLUME 79, NUMBER 17

PHYSICAL REVIEW LETTERS

27 OCTOBER 1997

Mössbauer Observation of the Quantum Levels of Fe31 Ions Dopedin 1D Ising Ferromagnet Ca3Co2O6
H. Kageyama,1 S. Kawasaki,2 K. Mibu,2 M. Takano,2 K. Yoshimura,1 and K. Kosuge1
1Division of Chemistry, Graduate School of Science, Kyoto University, Kyoto 606–01, Japan
2
Institute for Chemical Research, Kyoto University, Uji, Kyoto 611, Japan(Received 23 June 1997)

We have measured the Mössbauer effect of 57 Fe31 sS ­ 5y2d ions doped in a 1D Ising ferromagnet
Ca3Co2O6. The spectra with hyperfine fields corresponding to the exchange polarized Fe electron
spins with mz ­ 65y2, 63y2, 61y2 are first observed in the magnetically dense system for T # 20 K,
suggesting slow magnetic relaxation at the Fe31 sites. The key lies in the large difference between
magnetic characters of the host (Ising) and impurity (Heisenberg) spins, making the impurity spins
extremely isolated in the host 1D Ising spin system. [S0031-9007(97)04334-2]
PACS numbers: 75.20.Hr, 76.80. + yMany compounds with the general formula A03 ABO60(A ­ Sr, Ca, . . . , A ­ Ni, Cu, Zn, . . . , B ­ Ir, Pt, . . .)have been synthesized, and the magnetic properties havebeen investigated from the viewpoint of one-dimensional(1D) magnetism [1]. Ca3Co2O6 contains chains made ofalternating face-sharing CoO6 octahedra (Co1) and CoO6
triagonal prisms (Co2) [2]. These chains are widely
separated from each other by Ca ions. Another featureof the structure is that the chains form a triangular lattice,from which spin frustration effect might be expected ifthe interchain interaction is antiferromagnetic.
Magnetic properties of Ca3Co2O6 were investigatedby Aasland et al. [3] and the present authors [4] independently. It was found that the intrachain interaction
is ferromagnetic. The compound, moreover, exhibits aferrimagnetic ordering of the ferromagnetic chains at low
temperatures due to the antiferromagnetic interaction between ferromagnetic chains in a triangular net along the caxis. As is mentioned in Ref. [4], the ferrimagnetic state
indicates that the Co ion has Ising spin character. According to neutron diffraction, the moments of the Co ions aresuggested to be 0.08mB and 3.00mB for Co1 and Co2,respectively. Together with this fact, our magnetization
measurements using an oriented sample [5] strongly indicate that Co1 is nonmagnetic while Co2 is magnetic witha magnetic moment of 4mB .
This study was carried out to elucidate the static anddynamic properties of the magnetically ordered states using Mössbauer spectroscopy for Ca3(Co0.99 57Fe0.01)2O6.
We have succeeded in observing well-resolved nuclear
hyperfine structures corresponding to the electronic levels smz ­ 6 52 , 6 32 6 12 d of 6 S ion, 57 Fe31 for T # 20 K.
This is quite an unusual case: In magnetically dense systems, an individual electron spin changes its z component
at an approximate rate of Jyh̄ (J: exchange interaction),
which is fast enough to make a nuclear spin feel a time
averaged effective field. In the present case, however, because the magnetic character of the host (Ising) and theimpurity (Heisenberg) spins are considerably different, theimpurity spin is extremely isolated and thus can be treatedas an “isolated paramagnetic moment.” Another prominent result is that the spectra for T $ 30 K show an increasing relaxation rate of electronic spins as temperature
increases, but it is still slow even at room temperature compared to the time window of the Mössbauer experiment.
The 1% 57Fe-doped Ca3Co2O6, i.e., Ca3(Co0.99 57Fe0.01)2O6, was prepared by a citrate sol-gel precursor technique.
The detailed procedures have been described in Ref. [3].
Another sample with the same composition was preparedusing a conventional solid state reaction [4]. Both samples
gave almost the same magnetization curves and Mössbauer
spectra, indicating the successful preparation of thesamples. From the magnetization measurements onCa3(Co0.99Fe0.01)2O6 as a function of temperature andmagnetic field, it has been concluded that the doping of57
Fe does not disturb the intrinsic properties of Ca3Co2O6significantly. Mössbauer spectra were measured on powdered samples in a temperature range 4.2 # T # 293 K
with a conventional spectrometer in transmission geometry. A room temperature g-ray source of 57Co dissolvedin Rh matrix was used. An a-Fe absorber was used atroom temperature to calibrate the Doppler velocity V andalso as the standard for the isomer shift IS.
The spectra clearly showed that the magnetic relaxation
time depends on temperature. The Mössbauer absorption
spectra of Ca3(Co0.99 57Fe0.01)2O6 for T # 20 K are shownin Fig. 1. The spectrum at 4.2 K is resolved into twocomponents (components 1 and 2) and the spectra at
8, 13, and 20 K are resolved into three components(components 1, 2, and 3) using a least square fitting
program. Lorentzian line shapes with the line width of
0.30 mmys are assumed. The fitted hyperfine parameters
were summarized in Table I. It is noted that the hyperfine field Hhf points parallel to the c axis because
the Co spins are directed strongly to the Ising spin
axis, i.e., the c axis of the crystal. It appears that theelectric field gradient is also directed in the z direction,
which agrees with the principal axis of the crystal

3258© 1997 The American Physical Society

0031-9007y97y79(17)y3258(4)$10.00

VOLUME 79, NUMBER 17

PHYSICAL REVIEW LETTERS

27 OCTOBER 1997TABLE I. Mössbauer parameters of the high-spin Fe31 ionsin Ca3Co2O6 for T # 20 K.
T(K)

4.2

81320

FIG. 1. Mössbauer spectra of 57 Fe31 in Ca3Co2O6 for T #20 K. The theoretical hyperfine structures for the three crystalfield states are shown at the bottom of the figure.

field gradient at a site with the trigonal symmetry.
The IS of 0.52 mmys and the quadrupole splitting QSs­ e2 qQy2d of 21.23 mmys are almost identical forcomponents 1–3, where eq and Q denote the electric field
gradient and the nuclear quadrupole moment, respectively.
We can conclude that the Fe ions are distributed at a
crystallographically equivalent site, that is, either at theoctahedral site (Co1) or the trigonal prism site (Co2).
Since IS of high-spin Fe31 compounds lies between 0.2–
0.6 mmys in general, it is reasonable to identify thepresent case as high-spin Fe31 . Considering the large
value of QS, the Fe ion is possibly doped in the trigonal
prism site with lower local symmetry.
The most prominent features are that the hyperfine fieldfor each component is independent of temperature andthat the ratio of the effective magnetic fields Hhf is almost
5:3:1 (see Table I). From these facts, it is concluded
that components 1–3 correspond to the electronic energy
levels of the high-spin Fe31 s6 Sd, namely, mz ­ 6 52 , 6 23 ,and 6 12 , respectively. Such spectra have been observed
only for magnetically dilute materials with slow magnetic
relaxation, in which the electron spin-electron spin (S-S)
interaction is exceedingly small [6–9]. This is the firstobservation of Mössbauer subspectra corresponding to theIS(mmys)

QS(mmys)Hhf(kOe)

I(%)

62

50.52

21.23

512

92.8

62

30.52

21.21

310

7.2

62

1·········

062

50.52

21.23

510

80.4

62

30.53

21.23

306

14.2

62

1

0.45

21.16

107

5.4

62

50.52

21.24

510

66.8

62

30.52

21.25

306

22.1

62

1

0.50

21.29

102

11.1

62

50.52

21.23

509

54.3

62

30.53

21.24

305

26.9

10.51

21.27

103

18.8

Componentmz

123123123123

62

quantum levels of Fe31 in a magnetic material having
long range magnetic order.
In the presence of Hhf due to the electron spins,
the hyperfine Hamiltonian Hhf of a nuclear spin I isexpressedHhf ­ Sz AIz ­ gN mN Hhf Iz ,(1)

where Sz is the z component of the electronic spin operator, A is the hyperfine interaction tensor, and Iz is thez component of the nuclear spin operator I, gN is the nuclear gyromagnetic ratio, and mN is the nuclear magneton.
By electron-nuclear double resonance of 57 Fe31 in MgO[10], the value of Hhf has been accurately determined,Hhf ­ 220Sz kOe. It is widely known that this relation isapplicable to other dilute Fe31 compounds [6–8]. In thepresent material, the similar value of Hhf ­ 204Sz kOe
was obtained. This proportional relationship without any
constant term indicates the absence of any transfer hyperfine field. In other words, the hyperfine field originatesfrom the Fermi contact interaction, i.e., the polarization of
the s electrons of Mössbauer atom due to the interaction
with the unpaired d electrons at the same atom. Furthermore, a well-resolved hyperfine structure of mz ­ 6 12 ,which in general corresponds to Hhf ­ 110 kOe, has notbeen observed so far by the Mössbauer method, partly because the mz ­ 6 12 states greatly admix with other states[7,8]. It is remarkable that the spectrum corresponding tomz ­ 6 12 can be resolved well. See the spectrum at 20 K
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VOLUME 79, NUMBER 17PHYSICAL REVIEW LETTERSin Fig. 1; the line c arises mainly from mz ­ 6 12 . One
can also confirm the presence of this contribution by comparing the intensity of line b with that of line a or line d.
Hereafter, we consider two extremes: magneticallydilute and dense systems. For the magnetic materials
having a high density of magnetic ions, for example
metallic iron or a-Fe2O3, where S-S interaction is verylarge [11], Sz in Eq. (1) is replaced by kSz l (the zcomponent of the effective electronic spin) and the valueof kSz l decreases with temperature: In the case of theitinerant electron systems, the magnitude of the momentof spin itself varies with temperature. Even in the caseof the localized electron system, owing to the fast S-S
relaxation rate compared with the nuclear precession timeof a nuclear spin, kSz l is the thermal average of the mzstates obeying the mean-field theory.
On the other hand, for the dilute magnetic materials
such as a solid solution of 0.08% Fe in corundum [7–9], resolved paramagnetic hyperfine structures of thequantum levels of Fe31 ion are observable. The hyperfine
field originating from each mz state is independent oftemperature. The requirement of the observation is that
the S-S and electron spin-lattice (phonon) relaxation timeof the Mössbauer ion is sufficiently long compared withthe precession time of the nuclear spin.
The observation of the hyperfine structures of high-spin
Fe31 must be attributed to the large difference of magnetic character between the host (Ising) and the impurity(Heisenberg) spins. Theoretical treatment of the localized
impurity spin state in antiferromagnets and ferromagnets
are given in Ref. [12], and the references therein, in which
the localized spin wave mode around the impurity was calculated. Experimentally, Date et al. observed the impurity
spin resonance for the Ising spin systems such as CoCl2 ?
2H2 O and FeCl2 [13]. According to their discussion, theFe spin with a small anisotropy energy interacts with theneighboring Co spins through relatively weak exchange interactions. On the other hand, since the strongly coupled
Co spins are Ising-like, the spin reversal energy or the spincluster excitation energy of the host spin system lies muchhigher than the Fe spin energy so that the impurity spinstate can be regarded as an extremely isolated, low-lying
localized state for the sake of obeying the energy conservation rule. Thus, one can treat the impurity Fe spin as an“isolated paramagnetic moment” in the ordered host spin
system. In this case, the electronic spin levels of Fe31 are,to a good approximation, described as the six levels splitby the molecular field produced by surrounding Co ions, asdiscussed later. Consequently, the situation of Ca3(Co0.99Fe0.01)2O6 is similar to the case of the magnetically dilute
materials in the sense that energy exchange hardly occurs
not only between the Fe spins but also between the Fe andthe host spins.
Next, we turn our attention to the relative populationsof mz ­ 6 52 , 6 23 , and 6 12 states. The temperature variations of the relative area intensities I shown in Fig. 2 sug3260

27 OCTOBER 1997

FIG. 2. Temperature dependence of the relative intensities ofthree components corresponding to jmz j ­ 52 , 32 , and 12 . Calculated intensity ratios are shown for a given Hmf : broken lines,Hmf ­ 70 kOe; solid lines, 100 kOe; dotted lines, 130 kOe.
Inset: Electronic levels for high-spin Fe31 s6 S, L ­ 0d vs Hmf .

gest that the molecular field Hmf splits the six electroniclevels of Fe31 , and each mz level is populated according
to the probability psmz d ­ N exps2gmB Hmf mz ykB T d,where N is a normalization constant and kB is the Boltzmann constant. Hmf comes from the intra- and interchain
exchange interaction and the dipolar interactions between
the Fe and the surrounding Co spins. The inset of Fig. 2shows the Zeeman splitting of the mz levels as a functionof Hmf . Here, the crystalline field effect is neglected because it is much smaller than the magnetic effect in thepresent case [8]. For a particular value of Hmf , we calculated the population distribution for each mz level, where
the g value is assumed to be 2. As shown in Fig. 2, thebest fit is obtained when Hmf ­ 100 6 10 kOe, giving
the Zeeman splitting of gmB Hmf ­ 9.4 cm21 .
The temperature variation of the Mössbauer spectrum
measured in the temperature range 30 # T # 293 K isshown in Fig. 3. Resolved hyperfine structures of Fe31
were still observed at 30 and 34 K in a paramagnetic region, but these spectra are broadened due to the relaxationof the electronic spins. As the temperature increases, theobserved spectrum becomes broader, indicating that the relaxation rate becomes faster. An asymmetry in the spectrum is observed at room temperature, which shows thatthe relaxation time is still slow within the time windowof the Mössbauer method. We emphasize here that suchslow relaxation phenomena have not been studied by electron spin resonance.
In order to estimate the characteristic time t of fluctuation of Hhf in the presence of quadrupole interaction, we use the Blume and Tjon Hamiltonian [14]

VOLUME 79, NUMBER 17

PHYSICAL REVIEW LETTERS

27 OCTOBER 1997

FIG. 4. Temperature dependence of relaxation time and rateof Fe31 in Ca3Co2O6.

of 21.23 mmys. The best fit spectra are shown by thesolid lines in Fig. 3. IS ­ 0.45 mmys at 293 K is smaller
than 0.50–0.51 mmys at lower temperatures, which is dueto the second order Doppler shift. As shown in Fig. 4,the relaxation time increases exponentially with decreasing temperature. The electron spin-lattice relaxation, in
which t increases with temperature, is considered as oneof the relaxation mechanisms. It is noted, however, thatin the case of 0.08% 57Fe in corundom, well-resolved hyperfine structures were still observed at 78 K [7]. Thusin the case of Ca3(Co0.99Fe0.01))2O6, the dynamics of the1D Ising spin ferromagnetic chain would also cause thepresent relaxation effect.
Finally, the authors wish to thank Professor T. Shinjoand Professor N. Hosoito of the Institute for ChemicalResearch, Kyoto University for useful discussion.
FIG. 3. Mössbauer spectra for 30 # T # 293 K. The solidlines are the computed spectra using Blume’s theory [14].

Hhf ­ gN mN hIz fstd, which describes the line shape in
the presence of a fluctuating magnetic field which jumps
at random between the value 1h and 2h, where fstd isa random function of time and it takes a value of either
11 or 21. For 30 and 34 K, the population of the six
levels was calculated by assuming the exchange field isthe same as that at lower temperatures. IS ­ 0.52 mmysand QS ­ 21.23 mmys were used as fixed parameters.
For the purpose of simplifying the analysis and obtaining
an approximate relaxation rate from the line broadening,
we assumed that the three components corresponding toh1 ­ 510 kOe, h2 ­ 307 kOe, and h3 ­ 103 kOe relax independently with the same relaxation time t. Note that
this model is not ideal because in reality faster relaxation
would be expected between the states with jDmz j ­ 61
such as mz ­ 6 52 $ 6 32 rather than the relaxation withjDmz j . 1. For T $ 40 K, we assumed one component
with h ­ 510 kOe and the temperature independent QS[1] T. N. Nguyen and H.-C. zur Loye, J. Solid State Chem.
117, 300 (1995).
[2] H. Fjellvåg et al., J. Solid State Chem. 124, 190 (1996).
[3] S. Aasland, H. Fjellvåg, and B. Hauback, Solid State
Commun. 101, 187 (1997).
[4] H. Kageyama et al., J. Phys. Soc. Jpn. 66, 1607 (1997).
[5] H. Kageyama et al., J. Phys. Soc. Jpn. (to be published).
[6] F. E. Obenshain et al., Phys. Rev. Lett. 14, 365 (1965).
[7] G. K. Wertheim and J. P. Remeika, Phys. Lett. 10, 14(1964).
[8] H. H. Wickman and G. K. Wertheim, Phys. Rev. 148, 211(1966).
[9] J. W. G. Wignall, J. Chem. Phys. 44, 2462 (1966).
[10] P. R. Locher and S. Geschwind, Phys. Rev. 139, A991
(1965).
[11] R. S. Preston, S. S. Hanna, and J. Heberle, Phys. Rev. 128,2207 (1962).
[12] H. Ishii, J. Kanamori, and T. Nakamura, Progr. Theor.
Phys. 33, 795 (1965).
[13] M. Date and M. Motokawa, Phys. Rev. Lett. 15, 854(1965); N. Fujii, M. Motokawa, and M. Date, J. Phys.
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[14] M. Blume and J. A. Tjon, Phys. Rev. 165, 446 (1968).

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