- Email: [email protected]
Inelastic and spin-echo neutron scattering studies of the dynamics in the quasi 2d planar antiferromagnet BaNi2(PO4)2
Physica B 156 & 157 (1989) North-Holland, Amsterdam
298-300
INELASTIC AND SPIN-ECHO NEUTRON SCATTERING STUDIES IN THE QUASI 2d PLANAR ANTIFERROMAGNET BaNi,(PO,), L.P. REGNAULT’, C. LARTIGUE’, J.F. J. ROSSAT-MIGNOD’ and J.Y. HENRY’
LEGRANDj,
‘Centre d’Etudes Nucliaires, DRFISPh-MDN, X.5 X. 3804I Grenoble ‘Hahn-Meitner-lnstitut, D-Berlin 39, Fed. Rep. Germany ‘lnstitut Laue Langevin. 1% X, 38042 Grenoble Cede.r. Frunce
We have BaNi,(PO,)z quasi-elastic
x=-c.I;js;s,+Dc(s:)‘, ‘.I
B. FARAGO’. C‘edex. France
performed accurate inelastic neutron scattering experiments on the using both conventional triple-axis and neutron spin-echo spectrometers. contributions have been studied in the vicinity of the phase transition.
The search for nonlinear (e.g. vortex-type) excitations in quasi-2d planar systems has been the subject of relatively few experimental studies [l-3], the main reason being certainly the lack of good prototype for this kind of system. In previous papers we have shown that the compound BaNi,(PO,), could realize a very good approximation of the 2d planar model. The crystallographic structure of this compound can be described by a stacking of honeycomb magnetic planes well separated from each other. The magnetic properties, deduced from magnetization, susceptibility, specific heat and neutron scattering experiments are well understood by considering the following Hamiltonian [2]:
I
with the (negative) intraplanar exchange constants J,=-2.2K, 1,=0.3K, J,=-S.SK, the interplanar one J’ =-0.005 K and the (planar) anisotropy parameter D ~7.3 K. Due to the absence of frustration on the lattice, we expect this AF system to behave similarly to its F counterpart. In particular the scenario of vortexantivortex pairs unbinding above a finite temperature T,, [4] is expected to take place. Three important consequences have been predicted, which can be checked experimentally. The first one concerns the existence of an exponential divergence of the in-plane (IP) correlation 0921-4526/89/$03.50 @ Elsevier Science Publishers (North-Holland Physics Publishing Division)
length,
OF THE DYNAMICS
according
to
quasi-2d planar antiferromagnet The behaviours of spin-wave and
the
relation
[4]:
t(T)
=
A exp(B(T/T,., - I)“‘), with A = 1 A and B = rrl2 near T,,. Such a behaviour has been found in BaNi,(PO,), [2] with A = 0.6 A, B = 1.6 and T - (0.96-0.97) T,, with an actual transition tezperature (TN) slightly increased by J’. The second prediction of the KT transition concerns the existence of a jump in the stiffness constant of long wavelength spin waves (SW) at T KT, in the limit hw = 0 [5]. The renormalization of the SW velocity is expected to be smoother as soon as hw becomes larger, in particular in the range of frequencies accessible to inelastic neutron scattering (INS) [6]. The experimental data on BaNi,( show a rather sudden disappearance of small wavevector excitations. This is well illustrated by the fig. 1, in which we have reported typical scans in energy at q, = 0.01 and q, = 0.02, recorded at several temperatures below and above the transition temperature (T, = 23.95 2 0.05 K). These experiments have been performed on the triple-axis spectrometer (TAS) 4Fl installed on a cold beam of the Orphee reactor. We observe a progressive renormalization of the SW energy up to TIT, = 0.98, above which the renormalization and especially the damping increase more rapidly. No inelastic peak can be detected above TN. Only a broad contribution centered around w = 0 is observed, which shows that the spins must fluctuate rapidly in these ranges of wavevector and temB.V.
L.P. Regnault et al.
I Inelastic neutron scattering studies of BaNi,(PO&
perature (typically ho ~320 PeV at q, =0.02 and TIT, = 1.044). Thirdly, central peaks (CP) have been predicted to appear above T,, as a signature of the motion of free vortices. Met-tens et al. [7] have given expressions for the IP and OP dynamic structure factors, assuming a gas of freely moving well-defined vortices. The IP fluctuations are described in their (classical) theory by a square Lorentzian function: ,=( q, w) - r3yZ/(o 2 + r2( 1 + (
(2)
Fig. 1 gives evidence for the growth of such central peaks around T, and around the Bragg line positions. From polarized INS experiments performed on the neutron spin-echo (NSE) spectrometer IN11 this CP appears to be mostly associated with the IP fluctuations, the OP fluctuations (S”( q, w)) being about 20 times smaller than the former. The analysis of scans in energy at q, =O.Ol and TIT, = 1.01 (fig. 1) reveals rather a Lorentzian profile, with a characteristic width r = 50 -+ 10 l.r,eV in contradiction with eq. (2). A similar result is obtained from the scan at q, = 0.02 and TIT, = 1.044, with a much higher fluctuation rate r = 160 ? 30 FeV, which shows that SW dynamics are dominant above q = 0.03. To determine more precisely the dynamic structure factor ??“( q, o) around q = 0, we have performed accurate experiments on a single crystal using the NSE technique. In principle this allows
299
us to determine directly the q and time dependent structure factor Y( q, t). The experiments have been done using the IN11 NSE machine installed at the ILL reactor, set up to have a resulting resolution in q Aq = 0.05 r.1.u. at A, = 5.5 A. This allows one to obtain information on intensity integrated Y”(t) = the in 4, J SXX(q, t) dq = SXX(r= 0, t). Eq. (2) predicts an exponential behaviour YXX(t) - exp( - rt). We give in fig. 2 the time dependence of the integrated scattering measured at several temperatures below and above TN, for a scattering vector Q = (1, 0, 1.2). Clearly a simple exponential function of time is not able to account for the experimental data, especially near the transition. Restricting ourselves to relaxation phenomena near a quasi 3-d transition, we have fitted our data from the more complex function .Y”(t) = (1 - A) exp(-qt) + A exp(-lY,t). The resulting parameters r,, IY,and A are reported in fig. 3 as a function of temperature. From the variation of A, one can guess that the slow exponential (r, 10 ueV) is associated to the (3d) critical fluctuations , whereas the first exponential (r, 50-100 PeV) should correspond to the (basically 2d) contribution observed in the INS experiments. The case r2 = 0 seems excluded from measurements, not reported in fig. 2, at longer times which show that 9”“(t) = 0 for t > 0.5 ns at T = T,. Quite surprisingly we conclude a strong jhctuating character even at q = 0 (typically: r, / IJ] -0.05 at TN), which is not very well reproduced by the (classical) theory. The rather IO'
10-I 0
Energy (meV)
Fig. 1. Temperature netic scattering.
and wave vector dependences
a02
0.04
Time
of mag-
Fig. 2. Time dependence
0.08
0.1
( ny;
of the inplane mode. The full curves correspond to fits as described in the text.
L. P. Regnault
et al. I Inelastic
neutron
scattering
studies
of BaNi2(P0,),
the experimental system BaNi,(PO,),, we may assume for these excitations a rather small density IZ, (since n, - l/c’) and a rather large velocity U (since r - U/e*), which seems incompatible with the “massive” vortex-type excitations. Similar conclusions have been reached in the isomorphous helimagnet BaCo,(AsO,), [2].
References
Ill
23
25
24
Temperature Fig. 3. Temperature amplitude of Y(t).
dependences
(K
1
of fluctuation
rates
and
smooth temperature dependence of r, is also inconsistent with the strong (exponential) behaviour predicted in ref. [7]. The problem is now to reconcile the large correlation length together with the large fluctuation rate r, observed just above TN. If nonlinear excitations play a role in
K. Hirakawa, H. Yoshizawa, J.D. Axe and G. Shirane. J. Phys. Sot. Japan 52 (1983) 19. PI L.P. Regnault, J.P. Boucher, J. Rossat-M&nod, J. Bouillot, R. Pynn, J.Y. Henry and J.P. Renard, Physica B 136 (1986) 329. P. Day, E. Janke and R. Pynn. J. Magn. [31 M.T. Hutchings, Magn. Mat. 54-57 (1986) 673. and D.J. Thouless. J. Phys. C 6 (1973) [41 J.M. Kosterlitz 1181. 151 D.R. Nelson and J.M. Kosterlitz, Phys. Rev. Lett. 39 (1977) 1201. [61 R. Cote and A. Griffin, Phys. Rev. B 34 (1986) 6240. Mertens, A.R. Bishop, G.M. Wysin and C. [71 F.G. Kawabata. Phys. Rev. Lett. 59 (1987) 117.
298-300
INELASTIC AND SPIN-ECHO NEUTRON SCATTERING STUDIES IN THE QUASI 2d PLANAR ANTIFERROMAGNET BaNi,(PO,), L.P. REGNAULT’, C. LARTIGUE’, J.F. J. ROSSAT-MIGNOD’ and J.Y. HENRY’
LEGRANDj,
‘Centre d’Etudes Nucliaires, DRFISPh-MDN, X.5 X. 3804I Grenoble ‘Hahn-Meitner-lnstitut, D-Berlin 39, Fed. Rep. Germany ‘lnstitut Laue Langevin. 1% X, 38042 Grenoble Cede.r. Frunce
We have BaNi,(PO,)z quasi-elastic
x=-c.I;js;s,+Dc(s:)‘, ‘.I
B. FARAGO’. C‘edex. France
performed accurate inelastic neutron scattering experiments on the using both conventional triple-axis and neutron spin-echo spectrometers. contributions have been studied in the vicinity of the phase transition.
The search for nonlinear (e.g. vortex-type) excitations in quasi-2d planar systems has been the subject of relatively few experimental studies [l-3], the main reason being certainly the lack of good prototype for this kind of system. In previous papers we have shown that the compound BaNi,(PO,), could realize a very good approximation of the 2d planar model. The crystallographic structure of this compound can be described by a stacking of honeycomb magnetic planes well separated from each other. The magnetic properties, deduced from magnetization, susceptibility, specific heat and neutron scattering experiments are well understood by considering the following Hamiltonian [2]:
I
with the (negative) intraplanar exchange constants J,=-2.2K, 1,=0.3K, J,=-S.SK, the interplanar one J’ =-0.005 K and the (planar) anisotropy parameter D ~7.3 K. Due to the absence of frustration on the lattice, we expect this AF system to behave similarly to its F counterpart. In particular the scenario of vortexantivortex pairs unbinding above a finite temperature T,, [4] is expected to take place. Three important consequences have been predicted, which can be checked experimentally. The first one concerns the existence of an exponential divergence of the in-plane (IP) correlation 0921-4526/89/$03.50 @ Elsevier Science Publishers (North-Holland Physics Publishing Division)
length,
OF THE DYNAMICS
according
to
quasi-2d planar antiferromagnet The behaviours of spin-wave and
the
relation
[4]:
t(T)
=
A exp(B(T/T,., - I)“‘), with A = 1 A and B = rrl2 near T,,. Such a behaviour has been found in BaNi,(PO,), [2] with A = 0.6 A, B = 1.6 and T - (0.96-0.97) T,, with an actual transition tezperature (TN) slightly increased by J’. The second prediction of the KT transition concerns the existence of a jump in the stiffness constant of long wavelength spin waves (SW) at T KT, in the limit hw = 0 [5]. The renormalization of the SW velocity is expected to be smoother as soon as hw becomes larger, in particular in the range of frequencies accessible to inelastic neutron scattering (INS) [6]. The experimental data on BaNi,( show a rather sudden disappearance of small wavevector excitations. This is well illustrated by the fig. 1, in which we have reported typical scans in energy at q, = 0.01 and q, = 0.02, recorded at several temperatures below and above the transition temperature (T, = 23.95 2 0.05 K). These experiments have been performed on the triple-axis spectrometer (TAS) 4Fl installed on a cold beam of the Orphee reactor. We observe a progressive renormalization of the SW energy up to TIT, = 0.98, above which the renormalization and especially the damping increase more rapidly. No inelastic peak can be detected above TN. Only a broad contribution centered around w = 0 is observed, which shows that the spins must fluctuate rapidly in these ranges of wavevector and temB.V.
L.P. Regnault et al.
I Inelastic neutron scattering studies of BaNi,(PO&
perature (typically ho ~320 PeV at q, =0.02 and TIT, = 1.044). Thirdly, central peaks (CP) have been predicted to appear above T,, as a signature of the motion of free vortices. Met-tens et al. [7] have given expressions for the IP and OP dynamic structure factors, assuming a gas of freely moving well-defined vortices. The IP fluctuations are described in their (classical) theory by a square Lorentzian function: ,=( q, w) - r3yZ/(o 2 + r2( 1 + (
(2)
Fig. 1 gives evidence for the growth of such central peaks around T, and around the Bragg line positions. From polarized INS experiments performed on the neutron spin-echo (NSE) spectrometer IN11 this CP appears to be mostly associated with the IP fluctuations, the OP fluctuations (S”( q, w)) being about 20 times smaller than the former. The analysis of scans in energy at q, =O.Ol and TIT, = 1.01 (fig. 1) reveals rather a Lorentzian profile, with a characteristic width r = 50 -+ 10 l.r,eV in contradiction with eq. (2). A similar result is obtained from the scan at q, = 0.02 and TIT, = 1.044, with a much higher fluctuation rate r = 160 ? 30 FeV, which shows that SW dynamics are dominant above q = 0.03. To determine more precisely the dynamic structure factor ??“( q, o) around q = 0, we have performed accurate experiments on a single crystal using the NSE technique. In principle this allows
299
us to determine directly the q and time dependent structure factor Y( q, t). The experiments have been done using the IN11 NSE machine installed at the ILL reactor, set up to have a resulting resolution in q Aq = 0.05 r.1.u. at A, = 5.5 A. This allows one to obtain information on intensity integrated Y”(t) = the in 4, J SXX(q, t) dq = SXX(r= 0, t). Eq. (2) predicts an exponential behaviour YXX(t) - exp( - rt). We give in fig. 2 the time dependence of the integrated scattering measured at several temperatures below and above TN, for a scattering vector Q = (1, 0, 1.2). Clearly a simple exponential function of time is not able to account for the experimental data, especially near the transition. Restricting ourselves to relaxation phenomena near a quasi 3-d transition, we have fitted our data from the more complex function .Y”(t) = (1 - A) exp(-qt) + A exp(-lY,t). The resulting parameters r,, IY,and A are reported in fig. 3 as a function of temperature. From the variation of A, one can guess that the slow exponential (r, 10 ueV) is associated to the (3d) critical fluctuations , whereas the first exponential (r, 50-100 PeV) should correspond to the (basically 2d) contribution observed in the INS experiments. The case r2 = 0 seems excluded from measurements, not reported in fig. 2, at longer times which show that 9”“(t) = 0 for t > 0.5 ns at T = T,. Quite surprisingly we conclude a strong jhctuating character even at q = 0 (typically: r, / IJ] -0.05 at TN), which is not very well reproduced by the (classical) theory. The rather IO'
10-I 0
Energy (meV)
Fig. 1. Temperature netic scattering.
and wave vector dependences
a02
0.04
Time
of mag-
Fig. 2. Time dependence
0.08
0.1
( ny;
of the inplane mode. The full curves correspond to fits as described in the text.
L. P. Regnault
et al. I Inelastic
neutron
scattering
studies
of BaNi2(P0,),
the experimental system BaNi,(PO,),, we may assume for these excitations a rather small density IZ, (since n, - l/c’) and a rather large velocity U (since r - U/e*), which seems incompatible with the “massive” vortex-type excitations. Similar conclusions have been reached in the isomorphous helimagnet BaCo,(AsO,), [2].
References
Ill
23
25
24
Temperature Fig. 3. Temperature amplitude of Y(t).
dependences
(K
1
of fluctuation
rates
and
smooth temperature dependence of r, is also inconsistent with the strong (exponential) behaviour predicted in ref. [7]. The problem is now to reconcile the large correlation length together with the large fluctuation rate r, observed just above TN. If nonlinear excitations play a role in
K. Hirakawa, H. Yoshizawa, J.D. Axe and G. Shirane. J. Phys. Sot. Japan 52 (1983) 19. PI L.P. Regnault, J.P. Boucher, J. Rossat-M&nod, J. Bouillot, R. Pynn, J.Y. Henry and J.P. Renard, Physica B 136 (1986) 329. P. Day, E. Janke and R. Pynn. J. Magn. [31 M.T. Hutchings, Magn. Mat. 54-57 (1986) 673. and D.J. Thouless. J. Phys. C 6 (1973) [41 J.M. Kosterlitz 1181. 151 D.R. Nelson and J.M. Kosterlitz, Phys. Rev. Lett. 39 (1977) 1201. [61 R. Cote and A. Griffin, Phys. Rev. B 34 (1986) 6240. Mertens, A.R. Bishop, G.M. Wysin and C. [71 F.G. Kawabata. Phys. Rev. Lett. 59 (1987) 117.