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N. M. R. STUDY OF PHASE TRANSITIONS IN PEROVSKITES CRYSTALS
G. Bonera, F. Borsa, A. Rigamonti
To cite this version:
G. Bonera, F. Borsa, A. Rigamonti. N. M. R. STUDY OF PHASE TRANSITIONS IN PEROVSKITES CRYSTALS. Journal de Physique Colloques, 1972, 33 (C2), pp.C2-195-C2-197.
�10.1051/jphyscol:1972266�. �jpa-00215002�
JOURNAL DE PHYSIQUE Colloque C2, suppliment au no 4, Tome 33, Avril 1972, page C2-195
N. M. R. STUDY OF PHASE TRANSITIONS IN PEROVSKITES CRYSTALS
G. BONERA, F. BORSA and A. RIGAMONTI Istituto di Fisica dell'universith di Pavia, 27100 Pavia, Italy
Rksumh. - Les rbsultats preliminaires relatifs aux taux de relaxation spin rbseau de Nb93 et Na23 dans KNbO3 et NaNb03 sont presentes ici. Nous discutons les resultats B lalumi6redes diffb- rentes thkories dynamiques critiques associees a l'existence modes doux qui induisent les transitions de phase. Nous obtenons des renseignements sur la nature des mouvements critiques.
Abstract. - Preliminary results of Nb93 and Naz3 spin-lattice relaxation rates in KNb03 and NaNbO3 are presented. The results are discussed in the light of different critical dynamics associat- ed to the soft modes that drive the phase transitions : some elucidating information about the nature of the critical motions are obtained.
The interaction of the nuclear quadrupole moment with the crystal electric field gradient Vjk couples the nuclear spin system with the lattice. A magnetic resonance experiment is the best tool to study this interaction and to obtain the static electric field gra- dient (through splitting and/or shifts in the N. M. R.
spectrum) and also its time fluctuations (through spin- lattice relaxation measurements).
In the neighbourhood of a phase transition the relevant temperature dependence in the atomic motions is the one associated to the critical dynamics. The displacement of the i-th atom with respect to the equili- brium position in the high-temperature phase can be written :
where the time average < 6,(t) > = 0. By expanding the efg component with respect to ui one can write :
where
+ Bi : < > (la)
i
and
While q i = < ui(t) > is zero in the high-temperature phase, it is a function of the order parameter in the distorted phases ; Si(t) can be expressed in terms of the Fourier components 6, and its power spectrum can be related through the fluctuation-dissipation theorem to the generalized dielectric susceptibility ~ ( q , o).
In the perovskite crystals, due to the cubic symmetry of the high-temperature phase vjOk = 0 and the only contribution to the quadrupole coupling can arise from the term < 6' > in eq. (la), which produces a shift in the resonance line proportional to the real part of the susceptibility at w = 0. In the distorted phase since q i can be expressed as a function of the order parameter q, Vjk can be related to the first powers of q : therefore from the features of the N. M. R. spectrum the temperature behavior of the order parameter can in principle be investigated [I], [2].
The fluctuating part of the efg ((eq.) (Ib)) produces quadrupole spin-lattice relaxation ; the term linear in 6(t) works through a << direct )) mechanism in which a nuclear spin makes a transition among two Zeeman levels m and m + p (p = 1 or 2) and a quantum lattice excitation ha, or 2 hwL (w, Larmor frequency) is produced or absorbed ; the term quadratic in G(t) can induce nuclear relaxation through a Raman process with simultaneous occurrence of two lattice excitations who differ by ho, or 2 ha,. Due to the strong damping that generally characterizes the soft modes in perovskite crystals the relaxation should be driven by the direct process (*) and the quadrupole spin-lattice relaxation rate W,,,,, can be evaluated [3] in the framework of a classical lattice theory. Then :
where Q,,, is the matrix element of the quadrupole moment operator and J(puL) is the spectral density
(*) A proof of this assumption could be the lack of critical contribution in the Nb93 spin-lattice relaxation at the 2: 915 OK
structural transition in NaNbO3, where the direct contribution is ineffective.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1972266
C2-196 G. BONERA, F. BORSA AND A. RIGAMONTI
at the transition frequency of the efg functions V,(V, = V,, + i v y , and V, = +(Vxx - Vyy) +, iVxy).
In the R. P. A. approximation we found :
where
SE = C Af A:" exp[ - iq. Rill
il
can be considered as a structure factor )) that depends from the symmetry of the critical motion. The exact evaluation of the above expression is in general very difficult ; for an immediate comparison of the theory and the experiments we can write the spectral density in the approximate form :
where we have assumed that the dissipative part of the generalized susceptibility is dominated by the critical motion associated to the soft mode and Sp is the corres- ponding structure factor.
In order to study the nature and the critical dyna- mics of the phase transitions in perovskite type crystals we have performed resonance and relaxation measure- ments on Na2, and Nbg3 in NaNbO, and KNbO,. In these crystals purely structural, antiferroelectric and ferroelectric transitions occur, driven by soft modes involving both the off-center motions of the B atom and rotational motions of the BO, octahedra. The experiments were performed by pulse techniques in the temperature range 77-1 100 OK ; the measurements reported have a preliminary character since no suffi- ciently large single crystals were available to us.
KNbO,. - Referring to the critical contribution in the Nbg3 spin-lattice relaxation (see Fig. 1) which occurs at the cubic-tetragonal transition, let us consider two types of possible critical motions [4] : the Last
FIG. 1. - Nb93 spin-lattice relaxation rate in KNb03 vs T.
mode s2 in which the Nb and 0 ions move together against the K ions and the (( tetragonal>) mode s, + s,
having the same (( structure H of the tetragonal ferro- electric phase. In a point charge model we find, for the critical motions associated to the q = 0 modes : S1 = S2 = 0 both for the Last and for the tetragonal mode, i. e. the modes at q = 0 are not (( active D in producing direct Nbg3 spin-lattice relaxation process.
On the other hand recent neutron scattering experi- ments [5] indicate that a large portion of the branch along the [loo] directions could exhibit softening. This corresponds to a motion weakly correlated along the [100] direction : therefore the structure factors have to be evaluated by considering the contributions from the ions in adjacent (100) planes independently. By taking into account only the interaction with the nearest moving atoms one obtains
for the Last mode s1 10-14 a-8 for the tetragonal mode : S'
-
1.3 x a-8a lattice constant.
NaNbO,. - A large critical contribution to the spin-lattice relaxation (see Fig. 2) occurs only for Na23 nucleus at the
-
915 OK cubic-tetragonal transition.The critical dynamics of this transition involves mainly
FIG. 2. - Na23 spin-lattice relaxation rate in NaNb03 vs T.
Some indicative data for Nb93 relaxation rate are also reported.
rotations of the oxygen octahedra about their tetrad axis [6], [7] ; these collective fluctuations correspond, in a phonon description, to a soft lattice mode I'25 at the R point in the Brillouin zone (q = 3, 3, t). For the atomic motion associated to this mode only, one obtains for ~a~~ and Nb93 : S' = S2 = 0. However, the spin lattice relaxation results can be explained if one assumes the lack of correlation between oxygen rotations in adjacent (001) planes. This assumption is suggested by the anisotropy in the X-ray diffuse scatter- ing [7] and corresponds to a softening of all modes whose q values extend from the R point to the M point (q = 3, 3, 0) in the Brillouin zone.
N. M. R. STUDY OF PHASE TRANSITIONS IN PEROVSKITES CRYSTALS C2-197
In the case of completely uncorrelated rotations from one (001) layer to another, one has
for Na23 S1 E 2 x 10-l5 a-8 for Nbg3 s1 = s 2 = o .
From the experimental results, in the light of the above analysis, the following conclusions can be drawn.
i) The fact that < V . > = 0 in the cubic phase both at the NaZ3 and N$93 sites in NaNbO, and the presence of strong critical contributions to the Na2, spin-lattice relaxation indicate that the disorder in the oxygen positions (that appears from X-ray measure- ments 171) has a dynamical character i. e, there is a critical rotational motion of the NbO, octahedra for T > T,.
ii) The presence of a strong critical relaxation for Na23 and the lack of this contribution for the Nbg3 in the neighbourhood of the high temperature purely structural transition in NaNbO, are consistent with the hypotesis of rotational soft motion of the oxygen octahedra in adiacent (001) planes that are uncorre- lated one from the other.
iii) The tetragonal D soft mode in KNbO, exhibits softening along a large portion of the branch in the [loo] direction.
Finally it must be pointed out that no meaningfull numerical comparison of the relaxation rate and its temperature behavior can be made on the basis of eq. (2), and this not only because eq. (2) can be a too crude approximation. In fact, during the last months, neutron scattering measurements [8] have suggested the existence, near a structural phase transition, of a
(( central mode D i. e. a critical fluctuation characterized by a spectral density centered at w = 0 and width less than the instrumental resolution. Since the spin-lattice relaxation rate is sensitive to the spectral density in the radiofrequency range, it cannot be decided weather the relaxation is dominated by the central mode or the soft mode or both ; spin-lattice relaxation measurements at different resonance frequency (together with attempts to resolve a structure that seems to be present in the critical raising of the relaxation rate) are planned in order to clarify the above point.
References [I] BORSA (F.), CRIPPA (M. L.) and DERIGHETTI (B.), Phys.
Letters, 1971, 34A, 5.
[2] BONERA (G.), BORSA (F.), CRIPPA (M. L.) and RIGA-
MONTI A.), Phys. Rev., 1971, B 4, 52,
[3] BONERA (G.), BORSA (F.) and RIGAMONTI (A.), Phys.
Rev., 1970, B 2, 2784.
BLINC (R.), ZUMER (S.) and LAHAJNAR (G.), Phys. Rev., 1970, B 1,4456.
141 AXE (J. D.), Phys. Rev., 1967, 157,429.
51 NUNES (A. C.), AXE (J. D.) and SHIRANE (G.), to be published.
HARADA (J.), AXE (J. D.) and SHIRANE (G.), Phys. Rev., 1971, B 4, 155.
SHIRANE (G.), AXE (5. D.), HARADA (J.) and L ~ N Z (A.) Phys. Rev., 1970, B 2, 3651.
[6] MULLER (K. A.), BERLINGER (W.) and WALDNER (F.), Phys. Rev. Letters, 1968,21, 814.
[7] DENOYER (F.), COMES (R.) and LAMBERT (M.), Solid State Comm., 1970, 8, 1979.
DENOYER (F.), COMES (R.) and LAMBERT (M.), Acta Cryst., to be published.
[8] RISTE (T.), SAMUELSON (E. J.), OTNES (K.) and FEDER (J.), Nato Advanced Study Institute on (( Soft Modes and Phase Transition n, Geilo April 1971 and
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