Magnetic specific heat of the low-temperature phase of rubidium manganese hexacyanoferrate

Chemical Physics Letters 388 (2004) 379–383 www.elsevier.com/locate/cplett

Magnetic specific heat of the low-temperature phase of rubidium manganese hexacyanoferrate Hiroko Tokoro a, Shin-ichi Ohkoshi a,b,*, Tomoyuki Matsuda a, Toshiya Hozumi a, Kazuhito Hashimoto a,* a

Research Center for Advanced Science and Technology, The University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8904, Japan b PRESTO, JST, 4-1-8 Honcho Kawaguchi, Saitama, Japan Received 19 January 2004; in final form 24 February 2004 Published online:

Abstract In the specific heat measurement of RbI MnIII [FeII (CN)6 ] (MnIII ; S ¼ 2, FeII ; S ¼ 0), an anomalous peak due to a long-range magnetic ordering was observed at 11.0 K (Tp ). The magnetic transition entropy (DSmag ) and enthalpy (DHmag ) were evaluated from the magnetic specific heat (Cmag ) to be 11.8
0.9 J K1 mol1 and 125
9 J mol1 , respectively. A detailed analysis of Cmag , DSmag , DHmag , and Tp has shown that the present magnetic phase is a three-dimensional Heisenberg-type ferromagnetic lattice of MnIII sites with an exchange coupling constant of +0.5 cm1 . The ferromagnetic ordering is ascribed to the valence delocalization mechanism. Ó 2004 Elsevier B.V. All rights reserved.

1. Introduction Prussian blue analogs, MA [MB (CN)6 ] (MA and MB : transition metal ions), have drawn attention due to their unique magnetic functionalities [1–3]. The magnetic ordering of Prussian blue analogs is described in terms of a superexchange mechanism [4,5] through cyanide ligands [6–15]. In the materials of this series, only the superexchange interactions between the nearest neighbor metal ions (MA –NC–MB ) operate [10,11]. Contributions from the second nearest neighbor sites can be neglected due to
the long distances between the spin sources (10 A) (MA –NC–MB –CN–MA ). Hence, magnetic coupling between the spin sources can be designed in Prussian blue analogs. We have proposed on this basis (a) magnetic phenomena such as two compensation temperatures [11], an inverted hysteresis loop [16] and (b) magnetooptical phenomena such as photomagnetism [17–19], Faraday effect [15,20], and magnetization-induced second harmonic generation [21]. We have also reported *

Corresponding authors. Fax: +81-3-5452-5083. E-mail addresses: [email protected] (S. Ohkoshi), [email protected] (K. Hashimoto). 0009-2614/$ - see front matter Ó 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2004.03.029

that rubidium manganese hexacyanoferrate, RbMn [Fe(CN)6 ], shows a temperature-induced phase transition with a large thermal hysteresis loop of 73 K [22] and ascribed it to the metal-to-metal charge-transfer from MnII to FeIII and the Jahn–Teller distortion of the produced MnIII . The electronic states of its hightemperature (HT) and low-temperature (LT) phases are MnII (t32g e2g ; S ¼ 5=2)–NC–FeIII (t52g ; S ¼ 1=2) and MnIII (e2g b12g a11g ; S ¼ 2)–NC–FeII (b22g e4g ; S ¼ 0), respectively (Fig. 1a). A synchrotron radiation X-ray powder structural analysis showed the crystal structure of the
LT phase is tetragonal I 4m2 with a ¼ b ¼ 7:08627ð31Þ A
[23]. The characteristic feature and c ¼ 10:52677ð55Þ A of the LT phase is its low-temperature magnetic behavior. Magnetic measurements with a superconducting quantum interference device (SQUID) magnetometer showed that the LT phase exhibits ferromagnetism with a Curie temperature (TC ) of 11.3 K (Fig. 1b). However, understanding of this ferromagnetic ordering is difficult since diamagnetic FeII sites in an alternating fashion connect the MnIII spin sites, which should prevent longrange magnetic ordering. This peculiar ferromagnetism resembles that of Prussian blue, FeIII [FeII (CN)6 ]0:75  3.5H2 O (TC ¼ 5:6 K) [24,25]. The latter ferromagnetism

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platform at 99
1% during the measurements. Since the systematic error due to inaccuracies of the relaxation method used in the PPMS device against adiabatic method was reported to be ±5.0% of Cp [26] and the observed deviations in repeated measurements was ±2.0%, their simple sum (±7.0%) was assumed for the experimental uncertainty of Cp in this measurement.

High-temperature phase

(a)

Mn(II)d5 -NC- Fe(III)d5 S= 5/2 S= 1/2 231 K

304 K

Low-temperature phase Mn(III)d4 -NC- Fe(II)d6 S= 2 S= 0

3. Results and discussion 3.1. Specific heat

1500

3

-1

Magnetization (G cm mol )

(b)

The Cp value increased gradually with temperature and reached a maximum 27.1 J K1 mol1 at 11.0 K (denoted here as Tp ), as shown in Fig. 2. Then it dropped suddenly to 17.5 J K1 mol1 , and increased gradually. The dependence of the Cp values on the external magnetic field is shown in Fig. 3, where the Tp peaks are found to shift to a higher temperature as the external magnetic field is increased (see Table 1).

FCM REM

1000

500

ZFCM 0 0

5

10 15 Temperature (K)

20

Fig. 1. (a) Electronic states of the HT and LT phases, (b) magnetization vs temperature plots of the LT phase by SQUID measurement: ( ) field-cooled magnetization (FCM) at B0 ¼ 10 G; () zero fieldcooled magnetization (ZFCM) at B0 ¼ 10 G; (s) remnant magnetization (REM) data for RbI MnIII [FeII (CN)6 ].



3.2. Entropy and enthalpy of magnetic transition Since RbMn[Fe(CN)6 ] is an insulating magnetic system, the Cp value is described as a sum of the contributions from lattice vibration, Clat , short-range magnetic ordering, Cshort , and long-range magnetic ordering, Clong Cp ¼ Clat þ Cshort þ Clong :

is explained by a particular ferromagnetic coupling mechanism (so-called the valence delocalization mechanism). However, this type of ferromagnetic coupling has not been reported in other magnetic cyano-bridged metal assemblies. The specific heat (Cp ) of RbI MnIII [FeII (CN)6 ] was measured in the present study to interpret the magnetic ordering of the LT phase, and the dimensionality of magnetic lattice and the exchange coupling constant of this ferromagnetic ordering are discussed.

ð1Þ

Clat , is described by a polynomial function of temperature with odd powers [27,28] Clat ¼ aT 3 þ bT 5 þ cT 7 þ dT 9 þ eT 11 þ    ;

ð2Þ

2

and Cshort is described by AT [29]. We have fitted the Cp data in the region between 15 K ( ¼ 1:4  Tc ) and 30 K ( ¼ 2:7  Tc ) by the contributions of Clat þ Cshort , in the light of analyses reported in other systems [30,31]. The derived coefficients, including estimated uncertainties

40

Tp -1

30

-1

Cp (J K

RbMn[Fe(CN)6 ] was prepared as powder using by the method reported in [22]. Cp measurements were conducted by a relaxation method using a Quantum Design 6000 physical property measurement system (PPMS). The powder sample for the Cp measurements was pressed into a pellet (2.00 mg). The LT phase, RbI MnIII [FeII (CN)6 ], was prepared in a PPMS device by cooling at a rate of )0.5 K min1 . This rate is reported to be slow enough to prepare this phase [19,22]. The temperature increment was set to 0.5% for each Cp measurement. The Cp data were collected maintaining the thermal contact between the sample and the sample

mol )

2. Experimental

20

10

0

0

5

10 15 20 Temperature (K)

25

30

Fig. 2. Plots of Cp vs T in the zero external magnetic field: (sÞ experimental and (—) derived Clat curve based on Eq. (2).

H. Tokoro et al. / Chemical Physics Letters 388 (2004) 379–383 Table 2 Derived coefficients in Clat and Cshort a

0T 0.05 T 0.10 T 0.20 T 0.30 T 0.50 T 1.00 T 2.00 T 3.00 T

-1

-1

CP (J K mol )

(a) 40

30

20

381

10

Coefficient

Value

a b c d e A

9.0(7)  103 J K4 mol1 )2.8(2)  105 J K6 mol1 4.5(3)  108 J K8 mol1 )3.7(3)  1011 J K10 mol1 1.2(1)  1014 J K12 mol1 1.1(1)  103 J K mol1

a

See Eq. (2).

0 0

5

10 15 20 Temperature (K)

25

(b) 30 0T 0.05 T 0.10 T 0.20 T 0.30 T 0.50 T 1.00 T 2.00 T 3.00 T

-1

CP (J K mol )

25

-1

20 15 10 5 6

8

10 12 14 Temperature (K)

16

Fig. 4. Plots of Cmag vs log T .

Fig. 3. (a) Plots of Cp vs T in the presence of the external magnetic field B0 , (b) enlarged plots of (a).

The estimated values of DSmag and DHmag for RbI MnIII [FeII (CN)6 ] are 11.8
0.9 J K1 mol1 and 125
9 J mol1 , respectively.

Table 1 Tp values in the presence of the magnetic field B0

3.3. Type of long-range magnetic ordering

B0 (T)

Tp (K)

0 0.05 0.10 0.20 0.30 0.50 1.00 2.00 3.00

11.0 11.0 11.2 11.3 11.4 11.5 11.9 13.8 15.2

(±7.4%) from experiment (±7.0%) and curve fitting (±2.3%), are listed in Table 2. The solid line in Fig. 2 shows the Clat curve. The magnetic specific heat, Cmag ¼ Cshort þ Clong , is obtained by subtracting Clat from Cp , as shown in Fig. 4. The magnetic transition entropy, DSmag , and enthalpy, DHmag , can be obtained from Z T DSmag ¼ Cmag d lnT ; ð3Þ 0

and DHmag ¼

Z

T

Cmag dT : 0

ð4Þ

Since the Tp value of 11.0 K agrees with the TC value of 11.3 K derived from a SQUID measurement, the anomalous peak at Tp can be ascribed to a magnetic phase transition. The DSmag value of 11.8
0.9 J K1 mol1 is close to the value calculated for the ordering of magnetic spins on the MnIII (S ¼ 2) sites for RbI MnIII [FeII (CN)6 ] given by R lnð2S þ 1Þ ¼ 13:4 J K1 mol1 , where R is the gas constant. Thus, the origin of this magnetic phase transition can be attributed to the long-range magnetic ordering of the MnIII sites. The temperature dispersion of DSmag allows determination of the dimensionality of magnetic ordering, i.e., two- or three-dimensional (2- or 3-D) magnetic lattice. When the value of DSmag is divided into two terms, such as the magnetic entropy values below Tp ðDSmag-lower Þ and above Tp ðDSmag-upper Þ, it is known that the ratio of DSmag-lower =DSmag for the magnetic lattices of 3-D Ising, 2-D Ising, and 3-D Heisenberg-types are 81%, 44%, and 62%, respectively [32]. The ratio of DSmag-lower =DSmag in the present system is now found to be 65(3)% (Fig. 4). Therefore, in this framework the magnetic ordering of the LT phase is likely to be the 3-D Heisenberg-type magnetic ordering. Note that magnetic

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anisotropy is expected to appear in this system because the crystal structure of the LT phase is tetragonal instead of cubic. This magnetic anisotropy may make a small influence on the comparison between the observed value of 65% with the theoretical value of 62%. Whether the long-range magnetic ordering of a target material is ferromagnetic or antiferromagnetic can be determined by analyzing Cmag at very low-temperature using the spin-wave theory. The specific heat due to the spin-wave excitation, CSW , is expressed by [33] Csw ¼ aT d=n ;

ð5Þ

where d stands for the dimensionality of magnetic lattice and n is the exponent in the dispersion relation: n ¼ 1 for antiferromagnets and n ¼ 2 for ferromagnets. We have fitted the Cmag values in the region between 2.8 and 4.7 K to Eq. (5) (Fig. 5) and estimated the parameter of d=n to be 1.51(11). This d=n value is in reasonable agreement with that predicted for the magnetic ordering of the LT phase, i.e., the 3-D ferromagnet, where d ¼ 3 and n ¼ 2. The observed shifts in the Tp values in-field Cp data, 11.0 K (0 T) ! 15.2 K (3.00 T) displayed in Fig. 3, also suggest the ferromagnetic character. Since the shift in Tp to higher temperature is characteristic of ferromagnetic transitions [34], the trend of the in-field Cp values observed in the present study gives direct evidence for that magnetic ordering of the LT phase is ferromagnetic. 3.4. Exchange coupling constant Although diamagnetic FeII is bridged to MnIII in an alternative fashion, this system shows a 3-D Heisenbergtype ferromagnetic ordering. The exchange coupling constant, J , of this ferromagnet can be evaluated in the following manner. The a value derived from Eq. (5) is related to the J value. In CSW for a 3-D ferromagnet, the coefficient a is described by [35]

1 5Rfð5=2ÞCð5=2Þ a ¼ pffiffiffi 16p2 S 3=2 2



kB J

3=2 ;

ð6Þ

where f is Riemann’s zeta function, C is Euler’s gamma function, and kB is the Boltzmann constant. Since the a value obtained from Eq. (5) is 0.17(1) J K5=2 mol1 , the J value is estimated to be +0.55(4) cm1 based on Eq. (6). The DHmag value is also related to the J value in an extension of the molecular-field theory. In this treatment, DHmag due to long-range magnetic ordering is expressed by DHmag S 2 zJ ¼ ; ð7Þ kB R where the number of neighboring magnetic sites, z, is 6 in the present system. The J value is estimated from Eq. (7), using DHmag ¼ 125
9 J mol1 , to be + 0.44(3) cm1 . The application of the superexchange interaction mechanism to the present ferromagnetic ordering is difficult, because the diamagnetic FeII sites are connect with the paramagnetic MnIII sites. One plausible mechanism is the valence delocalization mechanism, in which ferromagnetic coupling arises from the charge-transfer configuration [24]. Day and co-workers [24] explained the ferromagnetism of FeIII [FeII (CN)6 ]0:75  3.5H2 O by the ferromagnetic exchange interaction based on a partial delocalization of the electrons occupying the FeII t2g orbitals to the neighboring high-spin FeIII sites. Since the FeIII in Prussian blue is replaced with MnIII , the same mechanism is feasible in our system. In fact, an intense intervalence transfer (IT) band of the LT phase has been observed at 700 nm as well as the IT band of Prussian blue. In the valence delocalization mechanism, the TC value is related to the valence delocalization coefficient of c as TC / c4 . The c value is given by secondorder perturbation theory as X c¼ ðhw0 jH jwi ihw1 jH jwi i=ðE1  E0 ÞðEi  E0 ÞÞ; ð8Þ i¼2;3

10

where w0 , w1 , w2 , and w3 are the ground (pure MnIII – FeII ) state and the charge-transfer configurations of FeII ! MnIII , FeII ! CN, and CN ! MnIII , respectively, and E0  E3 are their energies. The ferromagnetic exchange coupling is caused by the mixing of these excited charge-transfer configurations with the ground state. The J value of +0.5 cm1 in the present system is three times larger than that of +0.15 cm1 in Prussian blue. This large J value means that RbI MnIII [FeII (CN)6 ] has a large c value; namely, the electrons on the FeII site are delocalized to the MnIII site.

Cmag (J K

-1

-1

mol )

8

6

4

2 Csw

0

2

3

4 5 6 Temperature (K)

7

8

Fig. 5. Experimental plots of Cmag () and the CSW curve (—) calculated from the spin-wave theory for a 3-D ferromagnet using Eq. (5) with d=n ¼ 1:51 and a ¼ 0:17 J K5=2 mol1 .

4. Conclusion An anomalous peak was observed in the specific heat of RbI MnIII [FeII (CN)6 ] at 11.0 K. An analysis of the

H. Tokoro et al. / Chemical Physics Letters 388 (2004) 379–383

magnetic transition entropy and enthalpy has shown that this phase is a 3-D Heisenberg-type ferromagnet. The exchange coupling constant and DHmag are estimated by the spin-wave theory to be +0.55 and +0.44 cm1 , respectively. The magnetic coupling between the MnIII spin sites in this system is prevented by the diamagnetic FeII sites, but the ferromagnetic ordering is achieved by the valence delocalization mechanism. Acknowledgements The present research is supported in part by a Grant for 21st Century COE Program ‘Human-Friendly Materials based on Chemistry’ and a Grand-in-Aid for Scientific Research from the Ministry of Education, Culture, Sports, Science, and Technology of Japan. References [1] S. Ohkoshi, K. Hashimoto, J. Photochem. Phtotobiol. C 2 (2001) 71. [2] M. Verdaguer, A. Bleuzen, V. Marvaud, J. Vaissermann, M. Seuleiman, C. Desplanches, A. Scuiller, C. Train, R. Garde, G. Gelly, C. Lomenech, I. Rosenman, P. Veillet, C. Cartier, F. Villain, Coord. Chem. Rev. 190 (1999) 1023. [3] J.S. Miller, MRS Bull. 25 (2000) 60. [4] J.B. Goodenough, Phys. Rev. 100 (1959) 564. [5] J. Kanamori, J. Phys. Chem. Solids 10 (1959) 87. [6] W.D. Griebler, D. Babel, Z. Naturforsch. B 87 (1982) 832. [7] T. Mallah, S. Thiebaut, M. Verdaguer, P. Veillet, Science 262 (1993) 1554. [8] R.E. William, G.S. Girolami, Science 268 (1995) 397. [9] S. Ferlay, T. Mallah, R. Ouahes, P. Veillet, M. Verdaguer, Nature 378 (1995) 701. [10] S. Ohkoshi, T. Iyoda, A. Fujishima, K. Hashimoto, Phys. Rev. B 56 (1997) 11642. [11] S. Ohkoshi, Y. Abe, A. Fujishima, K. Hashimoto, Phys. Rev. Lett. 82 (1999) 1285. [12] K. Awaga, T. Sekine, M. Okawa, W. Fujita, S.M. Holmes, G.S. Girolami, Chem. Phys. Lett. 293 (1998) 352.

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