cenas e coisas 3

J.

Phys.

(1988)

France 49

813-817

MAI

1988,

813

Classification

Physics 64.70K

Abstracts 76.30

-

EPR in

-

77.80

Mn2+ doped betaine calcium chloride dihydrate single crystals

J. L. Ribeiro (1), J. C. Fayet (2), J. A. Almeida (1) and M. R. Chaves

(1) (2) (3)

Emery (2), M. Pdzeril (2), J. Albers (3), A. Klöpperpieper (3),

(1)

C.F.U.P. (INIC), Universidade do Porto, 4000 Porto, Portugal Université du Maine, route de Laval, 72017 Le Mans, France Universität des Saarlandes, 6600 Saarbrücken, F.R.G.

(Requ

le 7 décembre 1987,

accepté le

2

f6vrier 1988)

Dans ce travail nous présentons une étude de RPE dans le BCCD dopé au Mn2+ . Les mesures ont Résumé. été effectuées entre 10 K-300 K dans la bande de fréquences 9,45 GHz avec un champ magnétique qui varie de 0 à 104 G. À la température ambiante les résultats sont décrits par un hamiltonien qui explique l’anisotropie observée. Les axes magnétiques principaux des défauts sont identifiés par rapport aux axes critallographiques du système. Les spectres aux basses températures permettent l’identification des différentes phases commensurables et incommensurables du BCCD. 2014

In this paper some results concerning an EPR study of Mn2+ doped BCCD crystals are reported. Abstract. The measurements were done in the temperature range of 10 K-300 K using an X-band frequency of 9.45 GHz and a magnetic field in the range 0-104 G. The high temperature data can be described by a simple Hamiltonian which allows the understanding of the anisotropy of the spectra. The principal magnetic axes of the defects are identified in the crystallographic coordinate system. At low temperatures the analysis of the structure of the hyperfine lines for a particular favourable direction of the applied magnetic field allows the visualisation of several phase transitions to different commensurate and incommensurate phases. 2014

Introduction.

Betaine

changing continuously between 0.320 and 0.285. Below this temperature down to 125 K the modulation remains commensurate (q 2/7). For 125 > T > 116 K a second incommensurate phase occurs in which the wave vector changes continuously between 0.285 and 0.25. At lower temperatures the commensurate phases q = 1/4, q = 1/5 and q = 1/6 are observed in the temperatures ranges 116 to 73 K, 73 to 47 K and T 47 K, respectively. This behaviour can be described as an incomplete devil’s staircase. In this paper we report a study of Electronic Paramagnetic Resonance of Mn2 + doped BCCD crystals. Mn2 + ions replace Ca2 + in the crystalline structure. The doped crystals were grown from a solution with a molar ratio of Mn2 + /Ca2 + of the order of 10- 3. In the first part the EPR spectrum of the high temperature reference phase is shortly described. The principal magnetic axes of the defects are identified and a simplified spin Hamiltonian allows

vector

calcium

chloride

dihydrate-

(CH3)3NCH2COO-CaCI2-2 H20- crystals, grown by isothermal solvent evaporation [1, 2], exhibit at temperature an orthorhombic structure described by the space group Pnma [3]. The unit cell, with the dimensions a = 10.97 A, b 10.15 A, c = 10.82 A, has four molecules. The structure of this phase is shown in figure 1. At lower temperatures the system undergoes a sequence of structural phase transitions to different structures modulated along c [4]. The temperature dependence of the modulation wave vector is described in reference [4]. Between 164 K and 127 K the modulation is incommensurate with the wave room

=

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:01988004905081300

=

814

b) Experimental spectra for Hllb (a) and for In the first case all the centers in the unit cell (b). HII Zmag are equivalent and the spectrum is rather simple showing a typical S 5/2, I = 5/2 structure. In the second case the four molecules form two sets of nonequivalent centers which produce a superposition of resonances. Fig.

2.

-

=

Molecular structure of BCCD (top) and the unit Fig. 1. cell of the high temperature reference phase (bottom) showing the positions of the four molecules. Mn2 + replaces Ca2 + at the center of the distorted octahedron generated by the Cl-03’, Cl’-03 and 01-02 chemical axis (from Ref. [3]). -

centers. In figure 2a the experimental fo H//b is shown. For this particular spectrum direction of the applied magnetic field the spectrum is simple and only five fine structure lines (S 5/2) splitted into six hyperfine lines (I = 5/2) can be clearly observed. The crystallographic b axis is a principal magnetic axis common to the two sets of resonant centers. The five spin resonances are located at 1 717 G, 2 283 G, 3 033 G, 3 850 G and 5 548 G. The average hyperfine splitting is of the order of 90 G. A super hyperfine structure due to the two equivalent protons of the two water molecules can also be resolved. With the magnetic field applied in the ac plane the most enlarged spectrum is observed for the directions H HO * ( ± cos (39), 0, cos (51)) (Fig. 2b). If we consider only a reduced spin Hamiltonian bo 2 0° + b2 02 this means that these directions correspond to the principal magnetic axes of two nonequivalent centers [5]. The third principal directions are therefore defined on the ac plane by the vectors (± sin 39, 0, sin 51). Figure 3 shows a projection on the ac plane of two BCCD molecules. It is clear that the principal magnetic axes of the defect are approximately defined by the projections of Mn- Cl and Mn- 0 chemical axes on the ac plane and by the orthogonal direction b. Without considering second order effects due to the hyperfine coupling As.I it is possible to describe reasonably well the observed behaviour by the Hamiltonian (5) :

equivalent

=

the description of the observed anisotropic behaviour and the calculation of the spin energy levels as a function of the applied magnetic field. In the second part, the results concerning the lower temperature region will be reported. The detailed structure which appears on the initial hyperfine lines is particularly sensitive to the several phase transitions, revealing in addition the existence of a new phase, non modulated (q 0), at low temperatures. =

=

Experimental. The measurements were done using a Bruker spectrometer with a double axes goniometer allowing a fine orientation of the samples in the applied magnetic field. A X-band frequency of 9.5 GHz was used with a dc magnetic field in the range of 0-104 G. For the low temperature measurements a standard Oxford-Instruments quartz cryostat adaptable to the resonance cavity was used. The temperature was measured with a thermocouple in the coolgas flow, 1.5 cm away from the sample. Due to the hygroscopy of the material the samples were protected with a thin varnish film.

Experimental

results.

As can be seen in figure 1 the unit cell of the reference phase has four molecules forming two non

815

Projection of the Fig. 3. allowing the identification of in this plane. -

on the ac plane principal magnetic axes

structure

the

with

The curves of anisotropy generated by this Hamiltonian agree quite well with the experimental ones and the energy levels can be calculated as functions of the applied magnetic field allowing the identification of the several resonance lines. For the study of some essential features of the sequence of phase transitions it was choosen the simpler orientation H//b. The choice of any other direction for the applied magnetic field would require much more than a nearly visual examination of the lines. The analysis was focused at the temperature dependence of the structure of the hyperfine lines, which is rather sensitive to local changes of symmetry. For simplicity the description of the results will be made by considering simple and representative resonances centered at different values of the magnetic field. Figure 4 displays the temperature dependence of the hyperfine structure centered at 3 850 G between 170 K and 100 K. In figure 4a a typical I 5/2 hyperfine sextuplet is observable. At 158 K the structure becomes incommensurate and each line gives rise to two edge singularities as expected (Fig. 4b), [6]. For T 140 K this structure cannot be described assuming a pure sinusoidal modulation, and a multisoliton regime is observed (Fig. 4c). The P-INC phase transition (at T = 158 K) is marked by the rise of nuclear transitions (Ami ± 1 ) which are particularly evident within the sextuplet (Ami = 0 ) centered at 3 033 G. This means that the BCCD molecules have lost the (010) mirror symmetry and that the displacement mode is antisymmetric with respect to this mirror plane. Therefore the local lineshifts are an even function of the amplitude and a microscopic dipolar moment along b is allowed without prejudice to the macroscopic polarization. T 121 K the distortion wave locks into For 119 2/7. This corresponds the commensurate value q to figure 4d. =

=

=

4.

Sequence of hyperfine structures of the resocentered at 3 850 G for Hllb, between 170 K and 100 K. Spectra a) to h) correspond to T 170 K (Pphase), T = 152 K, T = 135 K (INC-phase 1), T 120 K (COM-phase 2/7), T = 118 K, 116 K, 113 K (INCphase 2) and T = 100 K (COM-phase 1/4), respectively. Fig.

-

nance

=

=

The second incommensurate phase appears in the T 119 K. The temperature dependence of a hyperfine sextuplet in this region is described in figure 4e, f, g. A typical lineshape corresponding to a pure sinusoidal modulation is never observed clearly and some additional singularities in the spectral density are observed. This can be due to either an additional symmetry breaking or to metastable q 2/7 regions. As the temperature decreases the spectrum changes indicating a multisoliton regime percursor of the commensurate q = 1/4 phase (Fig. 4g). Figure 4h shows a typical spectrum observed for the q = 1/4 commen-

temperature range 112

=

phase. phase and at lower temperatures, this particular resonance is obscured by the overlap of adjacent hyperfine lines. The low field resonance at surate

In this

1 717 G, which is less sensitive becomes suitable for the continuation of the analysis at lower temperatures. Figure 5a and 5b show the equivalent spectra for the q 2/7 and q = 1/4 commensurate phases which are identical to those already described. Figure 5c and 5d display the hyperfine lines at =

816

5. Structure of the initial hyperfine lines for the low temperature commensurate phases : a) corresponds to 120 K, b) to 100 K, c) to T 65 K and d) to 40 K for the resonance centered at 1 717 G. The experimental (full lines) and computer constructed curves using equal components with the same intensity, shape and width (dotted lines) are shown ; in c), the last two lines belong to the adjacent hyperfine structure ; in d) the last four lines are not significant due to the confuse overlap with the adjacent structure.

Fig. T

-

=

=

to reference [4], two different commensurate phases should be expected. As can be seen in figure 5a, 5b and 5c the change of the modulation wave vector in the different low temperature commensurate phases is reflected on the structure of the hyperfine lines, with the exception of the q = 1/6 phase which cannot be clearly resolved (Fig. 5d). The structure in figure 5a can be fitted by the superposition of seven single lines, i.e. 2/7. A sharp change leads to the 7/2 * 2 from q structure in figure 5b, which at first sight represents a quadruplet (q = 1/4). The computer reconstruction clears out extra unresolved doublets. A second sharp modification leads to the structure in figure 5c (q =1/5 ) which is obscured by the partial overlap between adjacent hyperfine lines. The computer reconstruction clears out a set of five doublets. Figure 5d shows a typical hyperfine line observed in the temperature range for which the q = 1/6 commensurate phase is reported to exist [4]. As can be seen no sharp change in the structure is observed. The computer reconstruction (dotted line) shows only five doublets, being possible that the extra one is merged on the adjacent lines. At about T = 15 K the spectrum changes drastically as can be seen in figures 6a (full structure) and 6b (detail of the sharpest line). From figure 6a and by comparison with figure 4a, we may infer that the size of the initial cell is restored (Z 4, q 0), but with a low symmetry. Indeed satellite lines associated to nuclear transitions (Amit ± 1 ) indicate that b is

temperatures where, according

=

=

=

=

Hyperfine structure just below T = 15 K : the full hyperfine structure of the resonance centered at 1717 G ; in b) the reconstruction of an intense line (Ami = 0 ) reveals an underlying quadruplet. Fig. 6. a) shows

-

no

longer a magnetic axis.

As shown in

figure 6b, the

unresolved intense lines (demi = 0 ) may represent that all the four quadruplet which would indicate hand On the other sites in the cell are unequivalent. the superhyperfine structure of the protons is again resolved on other lines, which is indicative of a well ordered lattice. an

817

Discussion. Our results show that Mn2 + replacing Ca2 + in the crystal structure is a good EPR probe for the study of the structural phase transitions in BCCD. The room temperature spectra can be understood by considering the lower order quadrupolar terms for the crystal field and the principal magnetic axes of the Mn2 + defects can be reasonably well related with chemical axes in the molecular structure. At low temperatures the spectra show important changes in correlation with phase transition sequence. The first worthnote point in the analysis of the results concerns the values of the different critical temperatures, which are found to be slightly shifted from those reported in [1, 3] for the pure system. In order to check a possible effect of the Mn 2, impurities on the values of these temperatures we try to confirm these shifts by other studies. Preliminar measurements of pyroelectric coefficients and dielectric constants on samples with the same molar rate of Mn 2+ /Ca2 + did not reveal any appreciable changes in the critical temperatures for the higher temperature phase transitions P -+ INCl -+ q 2/7 -+ INC2. For the other transitions, the values found are not quite reproducible [2] and therefore no firm conclusion can be drawn. It is possible that the observed differences may be partially due to experimental limitations on the measurement of the absolute values of the tempera=

ture.

In the first incommensurate phase the analysis of the hyperfine lines shows that a pure sinusoidal regime is observed over a large temperature range indicating that the pinning of the distortion wave by the Mn impurities is not relevant. The analysis of the hyperfine structure allows also the identification of several commensurate phases. When the modulation wave vector takes a rational value q m/n each non-equivalent center splits in, at most, n different centers. If the amplitude of the =

distortion is small compared with the reference unit cell dimensions and if the magnetic field is applied in a suitable symmetry direction of the reference structure (as it is the case here with H//b) this splitting can be equivalently described as a modulated line shift given by :

wherei refers to the number of the unit cell. Applying this simple expression one can account for the position of the lines satisfactorily by assuming four magnetically equivalent sets of seven centers for H//b and q 2/7. For q = 1/4 this simple model does not hold neither for the line positions nor for 2/7 and q = 1/4 exhibit their number. The phases q therefore essential differences in agreement with the existence of small spontaneous polarizations along b for q 2/7 and along a for q = 1/4 [1, 2]. The transition from q = 1/4 to q = 1/5 can be observed by the rise of an extra doublet in the hyperfine superstructure, which reflects the increase of the unit cell. At lower temperatures, the progressive overlap between the different adjacent hyperfine lines, already observed within the phase q 1/5, prevents a simple evidence of the transition to the phase q 1/6. An additional transition to a nonmodulated phase at low temperatures, not reported in [4], was clearly observed. This new phase produces a sharp change of the spectrum and each intense hyperfine line reveals an underlying quadruplet showing the nonequivalence of the four sites in the restored unit cell. =

=

=

=

=

Acknowledgments. The authors are greatly indebted to Dr. A. Leble (Lab. de Spect. du Solide, Univ. du Maine) for the program used to simulate the spectra and to Prof. Dr. H. E. Mfser (Univ. of Saarlandes) for stimulating discussions.

References

[1] ROTHER, H.J., ALBERS, J., KLÖPPERPIEPER, A., Ferroelectrics 54 (1984) 107. A., ROTHER, H. J., ALBERS, J., KLÖPPERPIEPER, [2] MÜSER, H. E., Jpn. J. Appl. Phys. 24 Suppl. 242 (1985) 829. [3] BRILL, W., SCHILDKAMP, W., SPILKER, J., Z. Kristallgr. 172 (1985) 281.

[4] BRILL, W., EHSES, K. H., Jpn. J. Appl. Phys. 24 Suppl. 24-2 (1985) 826. [5] ABRAGHAM, A., BLEANEY, B., Electron Paramagnetic Resonance of Transition Ions (Clarendon Press, Oxford) 1970. BLINC, R., Phys. Rep. 79 (1981) 331. [6]