CRITICAL EXPONENT β OF THE TWO-DIMENSIONAL ANTIFERROMAGNET (CH3NH3)2FeCl4

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CRITICAL EXPONENT β OF THE

TWO-DIMENSIONAL ANTIFERROMAGNET

(CH3NH3)2FeCl4

H. Keller, W. Kündig, H. Arend

To cite this version:

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JOURNAL D E PHYSIQUE Colloque C6, supplkment au no 12, Tome 37, Dicembre 1976, page C6-629

CRITICAL EXPONENT

/?

OF

THE TWO-DIMENSIONAL

ANTIFERROMAGNET (CH,

NH3), FeCl,

(*)

H. KELLER and W. KUNDIG Physics Institute, University of Zurich

and H. AREND

Laboratory of Solid State Physics, ETH-Zurich, Switzerland

R6sum6. - Le (CH3NH3)2FeC14, une substance antiferromagnetique a quasi deux dimensions, a 6te etudie par effet Mossbauer. Dans le voisinage de la temperature Nee1 TN le champ hyperfin peut &tre decrit par la relation H(T) x (1 - T/TN)P, oh B est l'exponent critique qui depend du modele envisage. L'ajustement des mesures pour 2 x 10-4 < 1

-

T/TN < 10-2 conduit

a B = 0,146 h 0,005 et a TN = 94,46 f 0,02 K. Cette valeur de est en bon accord avec les valeurs qui ont kt6 prkdites pour les syst6mes a deux dimensions.

Abstract.

-

The quasi two-dimensional antiferromagnet (CHsNH3)zFeCld has been investigated by the Mossbauer effect. Near the Nee1 tempeqature TN, the hyperfine field may be described by the power law H(T) x (1

-

T / T ~ ) ~ , where B is a model-dependent critical exponent. A fit to the data in the temperature range 2 x 10-4 < 1

-

T/TN < 10-2 yields /3 = 0.146 f 0.005 and

TN

= 94.46 f 0.02 K. This b-value compares favorably with the value predicted for two-dimensional systems.

1. Introduction.

-

Compounds of the form

(CnHz, + ,NH,),FeCl, (n = 1, 2, 3,

...)

are good

examples of two dimensional magnetic systems [I]. In these compounds, FeC1,-octahedra are arranged in layers separated by organic chains (Fig. 1). For the investigated compound (CH3NH,)zFeC14, the distance between the Fez+ ions in the plane is 5.1

A,

and the separation of the layers is 9.6 h;. Knorr et al. [2] found two structural phase transitions : a continuous order-disorder transition from a high-temperature tetragonal to an orthorhombic phase at 328 K and a discontinuous transition to a low-temperature tetragonal modification at 231 K. Above the NBel temperature (TN = 94.5 K), the Mossbauer spectra show a pure quadrupole splitting. Below TN, both magnetic dipole and electric quadrupole interactions are seen. If one assumes that the hyperfine field H(T) is propor- tional to the sublattice magnetization M ( T ) , one may write near TN : H(T) oc (1

-

TITN)@. The validity of the power law is investigated in this paper, and the experimentally determined critical exponent

fi

is compared with various models.

2. Theory.

-

Magnetic phase transitions are

described by several models. These models consider localized spins with the dimensionality n (n = 1, 2, 3)

(*) Supported by the Schweizerische National fonds.

FIG. 1. -Idealized structure of (CH3NH3)2FeC14 (ref. 121).

and a simplified magnetic interaction J on a d-dimensional lattice (d = 1, 2, 3). The Hamiltonian of such a system may be written,

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where the summation has to be taken over the nearest neighbour spins. For various models (Ising, X Y .

Heisenberg) exact or approximate power law solutions for the thermodynamic quantities have been obtained in the critical region. The Mossbauer effect is a very sensitive method with which to study magnetic phase transitions. Under the usual assumption that the hyperfine field H(T) is proportional to the spontaneous magnetization M(T), one may write for temperatures just below the Curie or Ntel-temperature Tc [3, 41 :

where H(0) is the hyperfine field at T = 0 K, D is a normalization factor and j? is the critical exponent. The critical exponents do not depend explicitly on the magnitude of the magnetic interaction J. This may be explained by the so-called universality principle, which says, that magnetic systems with the same lattice- and spin-dimensionality will exhibit the same exponents 131. The universality principle is well supported by various theoretical and experimental considerations.

Since there are no exact solutions for most model systems (except for the 2d-Ising model), various appro- ximation methods (series expansions, renormalization group approach [5], etc.) have been developed to calculate the critical exponents. Table I summarizes some of the theoretically predicted p-values. The

P-

values show a strong dependence on the lattice dimensionality d, and a weaker dependence on the spin dimensionality n. For most models the critical region for the power law behaviour is limited to 1

-

TITc < 4 x [6]. Erroneous exponents result when one disregards this very stringent temperature requirement.

Critical exponent j? as predicted by various models Spin-dimensionality Lattice-dimensionality d n d = 2 d = 3

-

Ising n = 1 0.125 0.31 XY n = 2 0.13 f 0.03 ( 7 0 . 3 3 Heisenberg n = 3

-

0.36

(a) 2d XY-model with quartic anisotropy (ref. [17]).

A list of compounds approximating Ising, XY and Heisenberg interactions (ferro- and antiferromagnetic) and with lattice dimensionality d = 1,2, 3) was given

by de Jongh and Miedema [7]. A quasi two-dimensional magnetic system such as (CH,NH,),FeCI,, which is characterized by weakly coupled layers may be described by a Hamiltonian given by Liu and Stanley [8].

where J and J' = R J are the intra- and inter-layer coupling constants. In an ideal two-dimensional system,

.R

= 0.

3. Experimental.

-

Single crystals of

were prepared by dissolving stoichiometric amounts of FeCI, .4 H 2 0 and CH3NH3Cl under argon in a mini- mal amount of slightly acidified water at 60 OC. Traces of Fe3+ were removed by the addition of a small amount of Fe-powder. The hot solution was filtered into a glass ampoule which was then sealed and cooled slowly to room-temperature in a watefilled Dewar vessel. The crystals obtained were dried and stored under argon. The single crystals had typical dimensions of 70 mm2 x 0.4 mm. The powder samples were prepared by crushing single crystals, which were then mixed with plexiglas powder in order to obtain a random distribution of the crystallites. The very hygroscopic compound was sealed into plastic sample holders under an argon atmosphere.

The Mossbauer spectra were measured with a standard constant acceleration drive using 57Co diffused into Pd as a source. A flow cryostat with a

silicon diode temperature sensor provided long-term temperature stability of 50 mK. The absolute accuracy

CHRNNEL NUMBER ,so

1.00 . P 9

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CRITICAL EXPONENT B OF THE TWO-DIMENSIONAL ANTIFERROMAGNET C6-631 of the measured sample temperature was estimated to

be better than 1 K.

Mossbauer spectra of various samples were measured as a function of temperature in the range 6-300 K (Fig. 2) [9-111. Above the NCel temperature TN, pure quadrupole spectra were observed. Evidence of the phase transition [2] at 231 K was searched for in the quadrupole splitting and the center shift of powder samples (Fig. 3). No indication of this transition was

TEMPERATURE ( K )

FIG. 3. - Quadrupole splitting and center shift of (CH3NH&FeC14 measured above TN.

found. The center shift shows a linear temperature dependence above TN :

The observed shift is mainly due to the second order Doppler effect [I 11. Single crystal quadrupole spectra taken perpendicular to the Fe-layers showed two lines with an intensity ratio of 1 : 3. This indicates that the axis of the electric field gradient (EFG) is parallel to the c-axis. The poly- and single crystal spectra below TN were fitted by a general Mossbauer eigenvalue program [12]. The results of the fit are as follows :

H(0) = 280

2

3 kOe $ eQ V,, = 2.58

+

0.04 mm/s

8 = 85

+

lo y = 0.00

+

0.05.

H(0) is the hypxfine field extrapolated to 0 K. The temperature dependence of H(T) is shown in figure 4. The quadrupole interaction

3

eQV,, is almost temperature-independent, and corresponds to the quadrupole splitting observed, just above TN (Fig. 3). 8 is the polar angle of the hyperfine field in the EFG prin-

0

0 20 40 60 80 100

TEMPERATURE (K)

FIG. 4. - Hyperfine field as a function of temperature. The dashed line corresponds to the measured points and the solid line to the calculated power law behaviour (see insert).

cipal axis system and q is the asymmetry parameter of the EFG tensor.

All lines in the spectra were assumed to have the same linewidth. The temperature dependence of the linewidth near TN is presented in figure 5. The width (FWHM) in the antiferromagnetic phase corresponds almost to the width of the source (0.227 mm/s). In the paramagnetic state, a slight broadening due to self- absorption of the intense lines is observed. Significant broadening due to critical fluctuations and sample inhomogeneities are seen near T,.

FIG. 5. -Temperature dependence of the linewidth near TN.

4. Discussion.

-

Assuming a power law beha-

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C6-632 K. KELLER, W. KUNDIG AND H. AREND

A logarithmic plot of the reduced hyperfine field is shown in figure 6. Comparison with table I shows that the experimentally determined value of

p

is close to those found for a two-dimensional magnetic system. Since the spins are nearly parallel to the layers (6 = 850), an XY-type of interaction between neigh- bouring spins is expected.

FIG. 6. - Logarithmic plot of the reduced hyperfine field H(T)/H(O) against 1-T/TN. The slope of the straight line cor-

responds to the critical exponent /3.

thermal motions [13] (Fig. 1). A similar situation may

occur in the iron compound. Such a distorted octa- hedral symmetry could explain the measured value of 6 = 850. This would be consistent with the explana- tion that the spins are exactly parallel to the layers. A

tilt of 50 out of the layers, however, is not excluded. The 2d-character of the investigated compound is further supported by susceptibility measurements of Willet and Gerstein [14]. The critical exponents for the low-field susceptibility were found to be

y = 1.67 ( T > TN) and y' = 1.60 (T < TN). The 2d-Ising model predicts y = y' = 1.75, while experi- ments [7] on XY-like systems suggest values of y

between 1.5 and 3. In order to test the scaling relation a

+

2 /?

+

y = 2 the critical exponent a of the specific heat must yet be measured.

The present value for

p

is smaller than those given earlier

(p

= 0.23 [lo] and

P

= 0.217

+

0.012 [15]). This may be explained by the fact that these values were determined for reduced temperatures 1

-

TITN

>

2 x lo-', a temperature region not close enough to TN to justify a fit to the power law. The fitted value TN = 94.46

+

0.02 K is in agree- ment with TN = 94.5

+

0.1 K found by the characte- ristic peak in the linewidth (Fig. 5) and TN = 94.9 obtained by susceptibility measurements [14]. For T

>

TN, the critical behaviour of the line broadening

AT (due to critical fluctuations) may be described by a power law with a critical exponent n :

In the temperature range

In the similar compound (CH3NH3),MnC14, the a value of n = 0.91 f 0.46 was found. This values is MnC1,-octahedra and (CH,NH,)-groups are tilted questionable since the power law behaviour may be with respect to the four-fold c-axis and undergo large distorted by sample inhomogeneities.

References

[I] VAN AMSTEL, W. D. and DE JONG, I,. J., Solid State Commun.

11 (1972) 1423.

[2] KNORR, K., JAHN, I. R. and HEGER, G., Solidstate Comnzun.

15 (1974) 231.

[3] HOHENEMSER, C., Proc. of the Mossbauer Conference, Vol. 2, Cracow (1975).

[4] HOHENEMSER, C., KACHNOWSKY, T. and BERG-

STRESSER, T. K., Phys. Rev. B 13 (1976) 3154. [5] FISHER, M. E., Rev. Mod. Phys. 46 (1974) 597.

[6] WIELINGA, R. I?., Progr. LOW Temp. Phys. (North-Holland), Vol. VI, p. 333 (1970).

[7] DE JONGH, L. 3. and MIEDEMA, A. R., Adv. Phys. 23 (1974) 1.

[8] LTU, L. L. and STANLEY, H. E., Phys. Rev. B 8 (1973) 2279. [9] MOSTAFA, M. F. and WILLET, R. D., Phys. Rev. B 4 (1971)

2213.

[lo] SCHURTER,, J. L., BARNES, R. G. and WILLET, R. D., Proc. 20th Conf. on Magnetism and Magnetic Mate- rials, San Francisco (1974).

[ l l ] KELLER, H., K ~ ~ N D I G , W. and AREND, H., Proc. of the Mossbauer Conference, Vol. 1, Cracow (1975). [12] KUNDIG, W., Nuel. Instrum. and Meth. 48 (1967) 219 and

75 (1969) 336.

[13] HEGER, G., MULLEN, D. and KNORR, K., Phys. Stat. Sol. (a) 31 (1975) 455.

[14] WILLET, R. D. and GERSTEIN, B. G., Phys. Lett. 44A (1973) 153.

[IS] KELLER, H., KUNDIG, W. and AREND, H., Helv. Phys. Acta 49 (1976) 148.

[16] KOBEISSI, M. A., SUTER, R., GOTTLIEB, A. M. and HOHE- NEMSER, C., Phys. Rev. B 11 (1975) 2455.