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Critical spin dynamics in Rb2CrCl4: A nearly two-dimensional easy-plane ferromagnet
Journal of Magnetism and Magnetic Materials 54-57 (1986) 673-674 CRITICAL
SPIN
DYNAMICS
673
IN RbzCrCI4: A NEARLY
TWO-DIMENSIONAL
EASY-PLANE
FERROMAGNET M.T. HUTCHINGS
*, P. D A Y +, E. J A N K E
+ a n d R. P Y N N
++
* Materials" Physics and Metallurg3' Division, A E R E Harwell, Dideot, Oxon O X I I ORA, UK + Inorganic Chemistry Laboratory, South Parks Road, Oxford OXI 3QR, UK + + lnstitat Laue-Langevin, BP 156 Centre de Tri, 38042 Grenoble, France
High resolution inelastic neutron scattering measurements of the critical long wavelength spin fluctuations within the easy plane of Rb2CrCl 4 have been made near T. = 52.2 K. The scattering comprises both spin waves and a central, quasielastic. component, and its variation with wavevector and temperature has been investigated.
R u b i d i u m c h r o m o u s chloride, Rb2CrC1 n, is one of a few k n o w n ionic, optically transparent, ferromagnets, ordering at T~. = 52.2 K. The crystal structure, Cmca, is a cooperative J a h n Teller anti-ferrodistortive superstructure of that of K 2 N i F 4 in which the magnetic C r 2 + ( 3 d ) 4 ions, with S = 2, lie in p l a n a r square arrays with very weak coupling to adjacent layers [1]. Since the Cr 2+ ion positions m a y be described by the K z N i F 4 structure we shall here refer all indices to the related I 4 / m m m unit cell, which has lattice constants of a 0 = 5.086 A a n d c 0 = 15.715 ,~ at 4.5 K. The d o m i n a n t interaction is the ferromagnetic exchange between the nearest n e i g h b o u r (n.n.) ions in the planes, and single ion terms confine the spins to lie in these planes [2]. A weak third n.n. i n t e r p l a n a r exchange interaction, of -- 1 0 - 4 of that between n.n., causes the spins to order in three dimensions [3d] at Tc. However m a n y of the magnetic properties are two dimensional [2d] in character. A l t h o u g h the true spin structure is a slightly (~< 5 °) c a n t e d ferrimagnet [1], the spin wave behaviour m a y be well described by a collinear model in which the d o m i n a n t single ion term confines the spins to the (001) planes and a weaker uniaxial term aligns them in ( 1 1 0 ) directions [2]. The quasistatic critical scattering of Rb2CrC14 has been studied on the same crystal as used for the m e a s u r e m e n t s reported here [3], a n d exhibits a crossover from [2d] to [3d] b e h a v i o u r between ( Tc - 1 ) K a n d ( Tc + 3) K. A b o v e 55 K the critical scattering is confined to rods of intensity along [001]. The variation of the bulk magnetisation with magnetic field a n d temp e r a t u r e has also been investigated recently [4]. The experiments reported here were m a d e on a single crystal of ~ 0.27 cm 3 which was encapsulated in a helium filled a l u m i n i u m can attached to the cold finger of a helium cryostat. T e m p e r a t u r e m e a s u r e m e n t was by m e a n s of a p l a t i n u m resistance thermometer. The high energy resolution necessary was o b t a i n e d on the IN12 3-axis spectrometer at ILL situated on a cold n e u t r o n guide. Pyrolitic graphite m o n o c h r o m a t o r a n d analyser crystals, a n d collimation angles of 30', gave overall energy resolution of 0.050 meV for an incident n e u t r o n 0304-8853/86/$03.50
wavelength of 5.03 ,~.. A cooled beryllium filter in the incident b e a m minimised second-order c o n t a m i n a t i o n . The instrumental resolution function [5] was carefully measured using the (002) a n d (004) Bragg reflections. The m e a s u r e m e n t s were m a d e at temperatures between 20 a n d 85 K using constant-k i, constant-Q, scans of energy transfer at values of q in the [~'~'0] direction corresponding to ~"= (0, 0, 2.9). We here define Q = k i - k f , where k i ( k f ) are the incident (final) n e u t r o n wavevector and q = Q - ~'. We define the energy transfer as h~0 = E i - E f , where E i ( E f ) is the initial (final) n e u t r o n energy. T~ was determined to be (52.231 _+ 0.010) K from the t e m p e r a t u r e dependence of the (002) Bragg reflection. Since the nuclear incoherent cross section of C1 gives rise to an elastic peak in the scattering, this was carefully measured and together with a constant b a c k g r o u n d subtracted from the measured intensity. A typical scan is shown in fig. 1. As Q was nearly parallel to [001], the observed scattering was due to spin fluctuations within the (001) planes. However, fluctuations parallel and perpendicular to the easy direction in
30C
±
r
F
Rb2Cr[l~
°1oo
§ z
-, • ,
e-0"2
.
-
o'•
o o°
. •
-0.I
0 ENERGY TRANSFER (meV)
Fig. 1. Scattering at Q = ( - O . O ] ,
-0.01,
•
•",.
01 2.9), T = 5 1 . 0 8
.
02 K,
× observed counts, • - c o u n t s after background and incoherent elastic contribution subtracted. Solid line is best fit to data of central Lorentzian (long dash) and sharp spin wave (short dash) functions convolved with resolution function (see text).
© E l s e v i e r S c i e n c e P u b l i s h e r s B.V.
M.T. Hutchings et al. / Critical spin dvnanlics in Rb_,CrCI4
674
-~
T
T
T--~w
(~
q=0.0262~-'
q=0 0349A ~,.~
040-
,
o.o0
t\
40
-
\
-
-
60 TEMPERATURE (K) Fig. 2. Renormalisation of spin wave energy with temperature at q values in [~'~'0] direction measured relative to (0, 0, 2.9). The inset shows the measured low q spin wave energy dispersion in [f~'0] at 6 K. 45
these planes c a n n o t be distinguished. At temperatures well below T sharp spin waves are observed at all q, with a gap at q = 0 of 0.1 meV at 5 K. As the t e m p e r a t u r e increases the low wavevector spin waves renormalise anomalously falling more rapidly t h a n H a r t r e e - F o c k theory predicts [2]. Near T~ there is clear evidence of the presence of a central c o m p o n e n t to the scattering, unusual for a ferromagnet. The data were analysed using the F I T S Q W routine, which convolves parametrised forms of the scattering function S ( Q , w) with the resolution function, and fits the resulting expression to the data. The best fits were o b t a i n e d by taking two c o n t r i b u t i o n s to S ( Q , ,0): the first from ' s h a r p ' spin waves which had no measureable b r o a d e n i n g (i.e. < 0.002 meV) at all q and T, as calculated by the R E S F L D routine [6], and the second from a central Lorentzian c o m p o n e n t of the form S(Q,,~)-If(Q)
x
12
(1
h,~B e h'4~) k u T
F (1"2+,02 ) ( K Z + q 2)
Here f ( Q ) is the form factor, h~o the energy transfer, - 1 / k B T , I" is the Lorentzian half width, and ~ the correlation length within the plane given empirically by ~ 2 = ~0 + at2~ above Tc a n d ~ = ~0 below To. t = ( T T~), K o = 7 . 3 × 1 0 3~ i a=2.2×10 s,~ ~. and v = 0.83 [3]. The non-zero K0 is due to [3d] effects. A typical fit to the d a t a is s h o w n in fig. 1, where the two convolved c o n t r i b u t i o n s are plotted The different lineshape of the spinwave c o n t r i b u t i o n on energy loss a n d gain is due to 'focussing' effects of the resolution ellipsoid, The spin wave energy renormalisation for low wavevectors, q < 4% of the zone b o u n d a r y , is shown in fig. 2 where it
is seen that there is a rapid drop in energy, at progressively higher temperatures as q increases. The central peak width F increases with q at each t e m p e r a t u r e where data were taken, varying approximately linearly with q at T < T~ a n d quadratically at T > T~. F increases only slightly with t e m p e r a t u r e increase, a n d is non-zero (0.014 meV) at T~ at q = 0, most p r o b a b l y due to [3d] effects. Full details of the data analysis and results will be presented in a future publication. The observation of a central peak c o m p o n e n t to the scattering a n d the a b r u p t spin wave renormalisation near T~, are two interesting features of the critical scattering from Rb2CrCI 4. The m e a s u r e m e n t s were m a d e relative to the [2d] rod, away from the [3d] Bragg reflection, a n d it should be noted that [3d] effects are observed in the quasistatic scattering in the temperature region of the rapid renormalisation. However somewhat similar renormalisation effects observed in K 2CuF 4 have been tentatively attributed to [2d] X - Y behaviour [7]. It is not yet clear what is the cause of this a n o m a l o u s renormalisation in Rb2CrC14. This work was supported in part by the SERC and a Harwell E M R grant. We t h a n k W.G. Stirling for helpful discussions. [1] E. Janke, M.T. Hutchings, P. Day and P.J. Walker, J. Phys. C 16 (1983) 5959. [2] M.T. Hutchings, J. Als-Nielsen, P.A. Lindgard and P.J. Walker, J. Phys. C 14 (1981) 5327. [3] J. Als-Neilsen and M.T. Hutchings, in preparation. [4] C. Cornelius, P. Day, P.J. Fyne, M.T. Hutchings and P.J. Walker, J. Phys. C (1985) to be published. [5] B. Dorner, Acta Cryst. A28 (1972) 319. [6] E.J. Samuelsen, Structural Phase Transitions and Soft Modes eds. E.J. Samuelsen, E. Andersen and J. Fedder (Oslo Universitetsforlaget, 1971)p. 189. [7] K. Hirakawa, H. Yoshizawa, J.D. Axe and G. Shirane, J. Phys. Soc. Japan 52 (1983) 4220.
SPIN
DYNAMICS
673
IN RbzCrCI4: A NEARLY
TWO-DIMENSIONAL
EASY-PLANE
FERROMAGNET M.T. HUTCHINGS
*, P. D A Y +, E. J A N K E
+ a n d R. P Y N N
++
* Materials" Physics and Metallurg3' Division, A E R E Harwell, Dideot, Oxon O X I I ORA, UK + Inorganic Chemistry Laboratory, South Parks Road, Oxford OXI 3QR, UK + + lnstitat Laue-Langevin, BP 156 Centre de Tri, 38042 Grenoble, France
High resolution inelastic neutron scattering measurements of the critical long wavelength spin fluctuations within the easy plane of Rb2CrCl 4 have been made near T. = 52.2 K. The scattering comprises both spin waves and a central, quasielastic. component, and its variation with wavevector and temperature has been investigated.
R u b i d i u m c h r o m o u s chloride, Rb2CrC1 n, is one of a few k n o w n ionic, optically transparent, ferromagnets, ordering at T~. = 52.2 K. The crystal structure, Cmca, is a cooperative J a h n Teller anti-ferrodistortive superstructure of that of K 2 N i F 4 in which the magnetic C r 2 + ( 3 d ) 4 ions, with S = 2, lie in p l a n a r square arrays with very weak coupling to adjacent layers [1]. Since the Cr 2+ ion positions m a y be described by the K z N i F 4 structure we shall here refer all indices to the related I 4 / m m m unit cell, which has lattice constants of a 0 = 5.086 A a n d c 0 = 15.715 ,~ at 4.5 K. The d o m i n a n t interaction is the ferromagnetic exchange between the nearest n e i g h b o u r (n.n.) ions in the planes, and single ion terms confine the spins to lie in these planes [2]. A weak third n.n. i n t e r p l a n a r exchange interaction, of -- 1 0 - 4 of that between n.n., causes the spins to order in three dimensions [3d] at Tc. However m a n y of the magnetic properties are two dimensional [2d] in character. A l t h o u g h the true spin structure is a slightly (~< 5 °) c a n t e d ferrimagnet [1], the spin wave behaviour m a y be well described by a collinear model in which the d o m i n a n t single ion term confines the spins to the (001) planes and a weaker uniaxial term aligns them in ( 1 1 0 ) directions [2]. The quasistatic critical scattering of Rb2CrC14 has been studied on the same crystal as used for the m e a s u r e m e n t s reported here [3], a n d exhibits a crossover from [2d] to [3d] b e h a v i o u r between ( Tc - 1 ) K a n d ( Tc + 3) K. A b o v e 55 K the critical scattering is confined to rods of intensity along [001]. The variation of the bulk magnetisation with magnetic field a n d temp e r a t u r e has also been investigated recently [4]. The experiments reported here were m a d e on a single crystal of ~ 0.27 cm 3 which was encapsulated in a helium filled a l u m i n i u m can attached to the cold finger of a helium cryostat. T e m p e r a t u r e m e a s u r e m e n t was by m e a n s of a p l a t i n u m resistance thermometer. The high energy resolution necessary was o b t a i n e d on the IN12 3-axis spectrometer at ILL situated on a cold n e u t r o n guide. Pyrolitic graphite m o n o c h r o m a t o r a n d analyser crystals, a n d collimation angles of 30', gave overall energy resolution of 0.050 meV for an incident n e u t r o n 0304-8853/86/$03.50
wavelength of 5.03 ,~.. A cooled beryllium filter in the incident b e a m minimised second-order c o n t a m i n a t i o n . The instrumental resolution function [5] was carefully measured using the (002) a n d (004) Bragg reflections. The m e a s u r e m e n t s were m a d e at temperatures between 20 a n d 85 K using constant-k i, constant-Q, scans of energy transfer at values of q in the [~'~'0] direction corresponding to ~"= (0, 0, 2.9). We here define Q = k i - k f , where k i ( k f ) are the incident (final) n e u t r o n wavevector and q = Q - ~'. We define the energy transfer as h~0 = E i - E f , where E i ( E f ) is the initial (final) n e u t r o n energy. T~ was determined to be (52.231 _+ 0.010) K from the t e m p e r a t u r e dependence of the (002) Bragg reflection. Since the nuclear incoherent cross section of C1 gives rise to an elastic peak in the scattering, this was carefully measured and together with a constant b a c k g r o u n d subtracted from the measured intensity. A typical scan is shown in fig. 1. As Q was nearly parallel to [001], the observed scattering was due to spin fluctuations within the (001) planes. However, fluctuations parallel and perpendicular to the easy direction in
30C
±
r
F
Rb2Cr[l~
°1oo
§ z
-, • ,
e-0"2
.
-
o'•
o o°
. •
-0.I
0 ENERGY TRANSFER (meV)
Fig. 1. Scattering at Q = ( - O . O ] ,
-0.01,
•
•",.
01 2.9), T = 5 1 . 0 8
.
02 K,
× observed counts, • - c o u n t s after background and incoherent elastic contribution subtracted. Solid line is best fit to data of central Lorentzian (long dash) and sharp spin wave (short dash) functions convolved with resolution function (see text).
© E l s e v i e r S c i e n c e P u b l i s h e r s B.V.
M.T. Hutchings et al. / Critical spin dvnanlics in Rb_,CrCI4
674
-~
T
T
T--~w
(~
q=0.0262~-'
q=0 0349A ~,.~
040-
,
o.o0
t\
40
-
\
-
-
60 TEMPERATURE (K) Fig. 2. Renormalisation of spin wave energy with temperature at q values in [~'~'0] direction measured relative to (0, 0, 2.9). The inset shows the measured low q spin wave energy dispersion in [f~'0] at 6 K. 45
these planes c a n n o t be distinguished. At temperatures well below T sharp spin waves are observed at all q, with a gap at q = 0 of 0.1 meV at 5 K. As the t e m p e r a t u r e increases the low wavevector spin waves renormalise anomalously falling more rapidly t h a n H a r t r e e - F o c k theory predicts [2]. Near T~ there is clear evidence of the presence of a central c o m p o n e n t to the scattering, unusual for a ferromagnet. The data were analysed using the F I T S Q W routine, which convolves parametrised forms of the scattering function S ( Q , w) with the resolution function, and fits the resulting expression to the data. The best fits were o b t a i n e d by taking two c o n t r i b u t i o n s to S ( Q , ,0): the first from ' s h a r p ' spin waves which had no measureable b r o a d e n i n g (i.e. < 0.002 meV) at all q and T, as calculated by the R E S F L D routine [6], and the second from a central Lorentzian c o m p o n e n t of the form S(Q,,~)-If(Q)
x
12
(1
h,~B e h'4~) k u T
F (1"2+,02 ) ( K Z + q 2)
Here f ( Q ) is the form factor, h~o the energy transfer, - 1 / k B T , I" is the Lorentzian half width, and ~ the correlation length within the plane given empirically by ~ 2 = ~0 + at2~ above Tc a n d ~ = ~0 below To. t = ( T T~), K o = 7 . 3 × 1 0 3~ i a=2.2×10 s,~ ~. and v = 0.83 [3]. The non-zero K0 is due to [3d] effects. A typical fit to the d a t a is s h o w n in fig. 1, where the two convolved c o n t r i b u t i o n s are plotted The different lineshape of the spinwave c o n t r i b u t i o n on energy loss a n d gain is due to 'focussing' effects of the resolution ellipsoid, The spin wave energy renormalisation for low wavevectors, q < 4% of the zone b o u n d a r y , is shown in fig. 2 where it
is seen that there is a rapid drop in energy, at progressively higher temperatures as q increases. The central peak width F increases with q at each t e m p e r a t u r e where data were taken, varying approximately linearly with q at T < T~ a n d quadratically at T > T~. F increases only slightly with t e m p e r a t u r e increase, a n d is non-zero (0.014 meV) at T~ at q = 0, most p r o b a b l y due to [3d] effects. Full details of the data analysis and results will be presented in a future publication. The observation of a central peak c o m p o n e n t to the scattering a n d the a b r u p t spin wave renormalisation near T~, are two interesting features of the critical scattering from Rb2CrCI 4. The m e a s u r e m e n t s were m a d e relative to the [2d] rod, away from the [3d] Bragg reflection, a n d it should be noted that [3d] effects are observed in the quasistatic scattering in the temperature region of the rapid renormalisation. However somewhat similar renormalisation effects observed in K 2CuF 4 have been tentatively attributed to [2d] X - Y behaviour [7]. It is not yet clear what is the cause of this a n o m a l o u s renormalisation in Rb2CrC14. This work was supported in part by the SERC and a Harwell E M R grant. We t h a n k W.G. Stirling for helpful discussions. [1] E. Janke, M.T. Hutchings, P. Day and P.J. Walker, J. Phys. C 16 (1983) 5959. [2] M.T. Hutchings, J. Als-Nielsen, P.A. Lindgard and P.J. Walker, J. Phys. C 14 (1981) 5327. [3] J. Als-Neilsen and M.T. Hutchings, in preparation. [4] C. Cornelius, P. Day, P.J. Fyne, M.T. Hutchings and P.J. Walker, J. Phys. C (1985) to be published. [5] B. Dorner, Acta Cryst. A28 (1972) 319. [6] E.J. Samuelsen, Structural Phase Transitions and Soft Modes eds. E.J. Samuelsen, E. Andersen and J. Fedder (Oslo Universitetsforlaget, 1971)p. 189. [7] K. Hirakawa, H. Yoshizawa, J.D. Axe and G. Shirane, J. Phys. Soc. Japan 52 (1983) 4220.