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Magneto-elastic coupling in CuGeO3
Synthetic Metals 86 (1997) 2243-2244
ELSEVIER
Magneto-Elastic
Coupling in CuGeOj
B. Dumoulin’, P. Fronzes’, M. Pokier’, A. Revcolevschib, G. Dhalenneb a Centre de Recherche en Physique du Wide et DPprtement de Physique, Universitk de sherbrooke , Sherbrooke, Qutbec, Canada JIK 2R1 b Laboratoire de Chimie des Solides, Universik! de Paris&d, 91405 Orsay Ceder, France
Abstract Ultrasonic investigations of the spin-Peierls compound are reported and analyzed on the basis of magneto-eleastic coupling. Sound velocity anomalies reported recently fix pure or doped CuGe0~ compounds can be interpreted using a simple theoretical model. We conclude that such anomalies are completely independent of the existence of the spin-Peierls transition reported for the pure compounds Keywo&r: Magnetic measurement.&ucutml
phase tmnsitions, Magnetic phase tmnsitions
-
l.Introduction The orthorhombic structure of CuGeOr is composed of linear chains of Cur+ (S=l/2) magnetic ions running along the c axis, well separated from each other by Cl60 chains [l]. The magnetic ions Cuz+ are strongly coupled by antiferrOmagnetic (AF) intrachain interactions. CuCIeOs is also characterized by its ability to accept substitution on the cationic sites. Two types of substitutions have mainly been studied, Si substitnted for Ge on the Ge-0 chains and Ztr substituted for Cu on the magnetic chains. At low dopant concentrations the addition of impurities atkts drastically the spin-Peierls (SP) instability and induces a 3D AF phase at low temperature for higher concentrations. Both the SP and AF Neel states disappear for concentrations higher than 5%. However, an anomalous variation of the velocity of sound as a function of temperature seems to be observed for all crystals at high temperatures (between 20 and 200 K). This can be seen from Fig 1. where we are. presenting velocity data obtained on pure and doped CuGeG single crystals.
0.004
-
$
pureCuGe0
3
-
Zndoped
0.002
a 0.000 .-00024
*
0.0
100.0 T em perature
200.0 (K )
Fig. 1 Relative variation of sound velocity M a lbc4ion of tanperature for pureanddopedcuGcoaystaklllc~uetim~rcf[q
2. Experimental
Results
In an ultrasonic experiment the elastic constant (which is directly proportional to the velocity of sound) is obtained by measuring the velocity of longitudinal waves propagating along the c axis. It has been shown in a previous paper [2] that the elastic constant CD is the only one to exhibit an anomalous behaviour over the temperature range 2-200 K in pure CuGe4,The relative variation of the velocity for 100 Mhz longitudinal waves propagating along the c axis is presented in Fig. 1 for pure and doped CUG~OJ crystals. 0379-6779/97/$17.00 Q 1997 Elsevier Science S.A AU rights reserved PII 503794779(96)04820-5
The curves have been shifted relative to one another for a better appreciation of the variations. For the three crystals studied, when the temperature is decreased below 200 K or so, the velocity increases first by a small amount, saturates around 100 K and increases further more rapidly below 60 K. The velocity tends to saturation below 20 K but a softening is produced as different magnetic transitions are approached. In the pure crystal the soflening proceeds down to 14.5 K where the SP transition occurs: a stitTening whose temperature dependence can be associated with the order parameter is observed down to the lowest temperatures. In the 0.7% Sidoped crystal, the softening
2244
B. Dumoulin et al. /SyntheticMetals
isstoppedat9KwhentheSPstatesetsin,thenasaturationof the velocity is observed over a narrow temperature range before a turther softening is produced at the 3D AF transition around 4 K. In the 3.2% Zndoped crystal, no SP state is observed: the softening indicates only the outcome of the 3D AF state at 4 K. These velocity data indicate clearly that the elastic anomaly observed at high temnperatures between 50 and 100 K is not a precursor of the SP transition since it is observed in ctystals for which the SP transition is absent. We believe that the ultrasonic anomaly has a magneto-elastic origin. This is suggested by the previous observation of a similar anomalous elastic behavior of CU in another quasi-1D magnetic material [4]. In CsNiCls a S = 1 AF system with smaller intrachain exchange interaction (J = 33 K), the rapid sUBming of the velocity observed below 40 K is indeed depressed by a magnetic field and it has been satisfactorily explained by magnetic fluctuations coupled to the lattice. We claim here that an analog picture can be applied to the Cuw compound.
86 (1997) 2243-2244
Among others, at one loop order, we obtain a cormction for the elastic constant that has the form (3)
This is the theoretical result that has been portrayed in Fig. 2. (The relative variation of the elastic constant C33 is equal to twice the relative variation of the sound velocity). As one can see, the agreement between the theoretical prediction and the experimental result is more then qualitative although the above relation results from a one loop calculation. We can then reasonably think that the anomalies seen for the velocity of sound in CuGe@ are resulting t+om a magnemelastic coupling which is not directly involve in the spin-Peierls transition.
I
I
1
I
0 .o
3. Theoretical Results In order to extract the magnetwlastic coupling contribution to the sound velocity variation, we have to use, atIer corrections for thermal expansion [5], the best extrapolation for the temperature dependence of the normal elastic behavior. This can be done most easily for the pure crystal for which we have data up to 300 K. The softening of the velocity due to the sole magneto elastic coupling is presented in Fig. 2 (dashed curve) with the theoretical prediction (full curve). The theoretical curve has been obtained by the introduction of an additional term to the usual spin-Peierls Hamiltonian. This term couples elastic deformation (long wavelength phonons) with spins. Schematically, the full Hamiltonian will read:
-1 .o
-2 .o
-3 .o
-4.0
1
forms:
1
100.0 T em
(1) The new terms that are usually neglected in theoretical models for the spin-Peierls transition are Hi and H_ and take the
I
I
0.0
2001)
peramre (K )
Fig. 2 caredal data for the dative variationOfSOUlldvclocay(daShCd curve) and the result fbm theodcal calallations (ml auvcd)
Acknowledgments The authors
(2) (ii)
48
Jn the following we will limit ourselves to the 1D part of the model. This means that we should only keep the terms involving lattice displacements along the chains, namely the terms with a=p=3. We then write the spin degrees of freedom as spinless fennion using the Wigner-Jordan transformation. This gives us the combine functional-integral and possibility to use renormalization group (RG) methods for fermions. The RG will naturally generate corrections to the terms of Hz and &_.
thank C. Bourbormais for stimulating discussions. B.D. and UP.. would like to thank the Natural Sciences and Engineering Research Council (NSERC), le Fonds pour la formation de Chercheurs et 1’Aide B la Recherche (FUR), and the Canadian Institute for Advanced Research (CIAR) for financial support. 5. References [l] H. Vollenke et al., Monatsh. Chem. 98, 1352 (j%7). 121M. Poirier erul, Phys.Rev B52,16058 (1995). [3] S. Jandl et al., to appear in Phys.Rev.B(19%). [4] Y. Trudeau et& Phys.Rev. B46, 169 (1992). [5] H. Winkehnann et uf., Phys.Rev. B51,12884 (11995).
ELSEVIER
Magneto-Elastic
Coupling in CuGeOj
B. Dumoulin’, P. Fronzes’, M. Pokier’, A. Revcolevschib, G. Dhalenneb a Centre de Recherche en Physique du Wide et DPprtement de Physique, Universitk de sherbrooke , Sherbrooke, Qutbec, Canada JIK 2R1 b Laboratoire de Chimie des Solides, Universik! de Paris&d, 91405 Orsay Ceder, France
Abstract Ultrasonic investigations of the spin-Peierls compound are reported and analyzed on the basis of magneto-eleastic coupling. Sound velocity anomalies reported recently fix pure or doped CuGe0~ compounds can be interpreted using a simple theoretical model. We conclude that such anomalies are completely independent of the existence of the spin-Peierls transition reported for the pure compounds Keywo&r: Magnetic measurement.&ucutml
phase tmnsitions, Magnetic phase tmnsitions
-
l.Introduction The orthorhombic structure of CuGeOr is composed of linear chains of Cur+ (S=l/2) magnetic ions running along the c axis, well separated from each other by Cl60 chains [l]. The magnetic ions Cuz+ are strongly coupled by antiferrOmagnetic (AF) intrachain interactions. CuCIeOs is also characterized by its ability to accept substitution on the cationic sites. Two types of substitutions have mainly been studied, Si substitnted for Ge on the Ge-0 chains and Ztr substituted for Cu on the magnetic chains. At low dopant concentrations the addition of impurities atkts drastically the spin-Peierls (SP) instability and induces a 3D AF phase at low temperature for higher concentrations. Both the SP and AF Neel states disappear for concentrations higher than 5%. However, an anomalous variation of the velocity of sound as a function of temperature seems to be observed for all crystals at high temperatures (between 20 and 200 K). This can be seen from Fig 1. where we are. presenting velocity data obtained on pure and doped CuGeG single crystals.
0.004
-
$
pureCuGe0
3
-
Zndoped
0.002
a 0.000 .-00024
*
0.0
100.0 T em perature
200.0 (K )
Fig. 1 Relative variation of sound velocity M a lbc4ion of tanperature for pureanddopedcuGcoaystaklllc~uetim~rcf[q
2. Experimental
Results
In an ultrasonic experiment the elastic constant (which is directly proportional to the velocity of sound) is obtained by measuring the velocity of longitudinal waves propagating along the c axis. It has been shown in a previous paper [2] that the elastic constant CD is the only one to exhibit an anomalous behaviour over the temperature range 2-200 K in pure CuGe4,The relative variation of the velocity for 100 Mhz longitudinal waves propagating along the c axis is presented in Fig. 1 for pure and doped CUG~OJ crystals. 0379-6779/97/$17.00 Q 1997 Elsevier Science S.A AU rights reserved PII 503794779(96)04820-5
The curves have been shifted relative to one another for a better appreciation of the variations. For the three crystals studied, when the temperature is decreased below 200 K or so, the velocity increases first by a small amount, saturates around 100 K and increases further more rapidly below 60 K. The velocity tends to saturation below 20 K but a softening is produced as different magnetic transitions are approached. In the pure crystal the soflening proceeds down to 14.5 K where the SP transition occurs: a stitTening whose temperature dependence can be associated with the order parameter is observed down to the lowest temperatures. In the 0.7% Sidoped crystal, the softening
2244
B. Dumoulin et al. /SyntheticMetals
isstoppedat9KwhentheSPstatesetsin,thenasaturationof the velocity is observed over a narrow temperature range before a turther softening is produced at the 3D AF transition around 4 K. In the 3.2% Zndoped crystal, no SP state is observed: the softening indicates only the outcome of the 3D AF state at 4 K. These velocity data indicate clearly that the elastic anomaly observed at high temnperatures between 50 and 100 K is not a precursor of the SP transition since it is observed in ctystals for which the SP transition is absent. We believe that the ultrasonic anomaly has a magneto-elastic origin. This is suggested by the previous observation of a similar anomalous elastic behavior of CU in another quasi-1D magnetic material [4]. In CsNiCls a S = 1 AF system with smaller intrachain exchange interaction (J = 33 K), the rapid sUBming of the velocity observed below 40 K is indeed depressed by a magnetic field and it has been satisfactorily explained by magnetic fluctuations coupled to the lattice. We claim here that an analog picture can be applied to the Cuw compound.
86 (1997) 2243-2244
Among others, at one loop order, we obtain a cormction for the elastic constant that has the form (3)
This is the theoretical result that has been portrayed in Fig. 2. (The relative variation of the elastic constant C33 is equal to twice the relative variation of the sound velocity). As one can see, the agreement between the theoretical prediction and the experimental result is more then qualitative although the above relation results from a one loop calculation. We can then reasonably think that the anomalies seen for the velocity of sound in CuGe@ are resulting t+om a magnemelastic coupling which is not directly involve in the spin-Peierls transition.
I
I
1
I
0 .o
3. Theoretical Results In order to extract the magnetwlastic coupling contribution to the sound velocity variation, we have to use, atIer corrections for thermal expansion [5], the best extrapolation for the temperature dependence of the normal elastic behavior. This can be done most easily for the pure crystal for which we have data up to 300 K. The softening of the velocity due to the sole magneto elastic coupling is presented in Fig. 2 (dashed curve) with the theoretical prediction (full curve). The theoretical curve has been obtained by the introduction of an additional term to the usual spin-Peierls Hamiltonian. This term couples elastic deformation (long wavelength phonons) with spins. Schematically, the full Hamiltonian will read:
-1 .o
-2 .o
-3 .o
-4.0
1
forms:
1
100.0 T em
(1) The new terms that are usually neglected in theoretical models for the spin-Peierls transition are Hi and H_ and take the
I
I
0.0
2001)
peramre (K )
Fig. 2 caredal data for the dative variationOfSOUlldvclocay(daShCd curve) and the result fbm theodcal calallations (ml auvcd)
Acknowledgments The authors
(2) (ii)
48
Jn the following we will limit ourselves to the 1D part of the model. This means that we should only keep the terms involving lattice displacements along the chains, namely the terms with a=p=3. We then write the spin degrees of freedom as spinless fennion using the Wigner-Jordan transformation. This gives us the combine functional-integral and possibility to use renormalization group (RG) methods for fermions. The RG will naturally generate corrections to the terms of Hz and &_.
thank C. Bourbormais for stimulating discussions. B.D. and UP.. would like to thank the Natural Sciences and Engineering Research Council (NSERC), le Fonds pour la formation de Chercheurs et 1’Aide B la Recherche (FUR), and the Canadian Institute for Advanced Research (CIAR) for financial support. 5. References [l] H. Vollenke et al., Monatsh. Chem. 98, 1352 (j%7). 121M. Poirier erul, Phys.Rev B52,16058 (1995). [3] S. Jandl et al., to appear in Phys.Rev.B(19%). [4] Y. Trudeau et& Phys.Rev. B46, 169 (1992). [5] H. Winkehnann et uf., Phys.Rev. B51,12884 (11995).