Magnetic relaxation in DyVO4

Physica 11413 (1982) 77-81 North-Holland Publishing Company

M A G N E T I C R E L A X A T I O N IN

77

DyVO4

A. K A S T E N , P.H. M f d L L E R and M. S C H I E N L E Physikalisches Institut der Universitiit, D-7500 Karlsruhe, F.R. Germany

Received 3 February 1982 Measurements of the a.c. susceptibility of DyVO4 in the frequency range from 5 Hz to 3 MHz indicate that the magnetic relaxation is dominated by a spin-lattice Orbach process involving the first excited electronic crystal field level at about 40 K. Zero field experiments show significant deviations around the antiferromagnetic ordering temperature Tr~= 3.06 K. Only at temperatures well inside the antiferromagnetically ordered state is spin-spin relaxation faster than the Orbach process and the relaxation time becomes temperature independent. In an external magnetic field Bext= 0.2 T (spherical sample) along the crystallographic a-direction (ordering direction) the Orbach process remains dominant over the entire temperature range (2 K to 7 K).

1. Introduction DyVO4 has tetragonal zircon structure (I41/amd) at r o o m t e m p e r a t u r e [1]. At To = 14 K it undergoes a crystallographic phase transition to orthorhombic symmetry (Imma) caused by a cooperative J a h n - T e l l e r effect [2--4]. This transition splits the two lowest Kramers doublets of Dy 3+ by about 40 K, the ground state becoming an almost pure ___15/2 state along the crystallographic a-axis (first excited doublet: -+15/2 along b). At low temperatures ( T < 7 K) DyVO4 is an almost ideal Ising system. Below Tr~ = 3.06 K DyVO4 becomes antiferromagnetic [2, 5]. Spectroscopic m e a s u r e m e n t s between TN and To observe a quintet structure of the absorption lines [6, 7] due to magnetic short-range order arising from five different local magnetic fields at a given Dy 3÷ ion. The overall splitting from this short-range order is about 12 K. M e a s u r e m e n t s of the M6ssbauer effect [8] in the t e m p e r a t u r e range from 7.7 K to 12.5 K show that in this region in DyVO4 there is spin-lattice relaxation by an Orbach process involving the crystal field level at about 40 K. The aim of this work is to determine the dominant relaxation process at lower tem0378-4363/82/0000-0000/$02.75 O 1982 North-Holland

peratures (and frequencies) including the antiferromagnetically ordered phase.

2. Experimental The DyVO4 single crystals used in the experiments were grown either by the Czochralski m e t h o d [9] or by a flux method [10]. Additional experiments were p e r f o r m e d on powder samples made from the components Dy203 and VzO5 by a solid-state reaction (firing for several hours at 1500 K). Within the experimental accuracy the three different types of DyVO4 samples yielded identical results. The m e a s u r e m e n t s presented in this p a p e r were performed using a DyVO4 sphere with a diameter of (3.15 - 0.05) m m (Czochralski). The samples were m o u n t e d at the end of a sample rod inside a 4He cryostat. The sample space was filled with 4ne exchange gas ( - 0 . 1 m b a r ) surrounded by a 4He chamber p u m p e d down to 1.3 K. The t e m p e r a t u r e could be varied by a heater (manganin solenoid, 300 f~) and was measured by a calibrated carbon resistor (Allen-Bradley, 100 fl). The temperature resolution was better than 1 m K below 5 K, the stability better than 2 inK. The absolute accuracy

78

A. Kasten et al. / Magnetic relaxation in DyV04

of the calibration was about ___0.03 K. Magnetic fields could be applied by a 5 T superconducting solenoid (Cryogenic Consultants Ltd.; homogeneity 0.03% over 10 m m DSV) situated in the helium reservoir surrounding the inner part of the cryostat. The field was measured by the magnet current. The a.c. susceptibility of DyVO4 was detected by means of a mutual inductance bridge. Three different coil designs were used for the frequency ranges of 5 Hz to 10 kHz, 100 Hz to 1 MHz, and 100 kHz to 3 M H z . The amplitude of the a.c. magnetic field was always less than 0.1 mT. The signal was detected with a two-phase lock-in amplifier (Ithaco 393). Thus the real and imaginary part of the susceptibility could be measured simultaneously up to frequencies of 230 kHz. At higher frequencies the lock-in amplifier was replaced by an a.c. voltmeter (Philips). An online computer (PDP 11/03) controlled t e m p e r a t u r e and magnetic field and recorded the measuring results. A temperature, field or frequency dependent run consisted of three separate m e a s u r e m e n t s of: (i) the (complex) offset of the set-up without sample; (ii) phase and gain with a "laboratory standard crystal" (GdVO4); (iii) the (complex) susceptibility of the DyVO~ sample. Because of the crystallographic phase transition in DyVO4 at To = 14 K, there are crystallographic domains in the sample at low temperatures. This would be noticed in an experiment since for about 50% of the volume the aand b-axes are interchanged, thus reducing the susceptibility (gb ~--0), These domains can, however, be removed almost completely by premagnetising the sample along a, which was done prior to all experiments.

3. Results 3.1. Temperature sweeps

Fig. 1 shows the t e m p e r a t u r e dependence of the zero field susceptibility (X' and X") along the

X I

g ==

c

i

i

¢

3

4

5

X ~

2

T[K]

Fig. 1. Temperature dependence of the real 0(') and imaginary part (X") of the magnetic a.c. susceptibility of a spherical DyVO4 sample (Bext= 0; a.c. field along the crystallographic a-direction) for different frequencies: (a) v = 10 Hz, (b) v=109Hz, (c) v= 1.10kHz, (d) v=3.03kHz, (e) v= 10.98kHz, (f) v=30.36kHz, (g) v=102.16kHz, (h) v= 227.80 kHz. (The scaling factors of X' and X" are identical.) crystallographic a-axis of a spherical DyVO4 sample for eight different frequencies. The transition from the antiferromagnetic to the paramagnetic state leads to an increase of X'. The inflection point of X' vs. T is at TN = 3.06 K independent of frequency. No absorption (X") related to the phase transition in zero external field could be observed. There is, however, some absorption due to magnetic relaxation. The height and location of the m a x i m u m of X" is frequency dependent. The absorption is strongest at the highest frequencies and its maximum shifts to lower temperatures with decreasing frequencies. Even at the lowest frequency used (5 Hz), some absorption can still be detected. As a function of frequency the m a x i m u m crosses smoothly the antiferromagnetic-toparamagnetic phase boundary. In the paramagnetic range the m a x i m u m of X" gives the relax-

A. Kasten et al. / Magnetic relaxation in D y V 0 4

ation time ~" (~-= 1/27rv) at the corresponding temperature. Just below TN, however, because of the antiferromagnetic ordering, the modulus of X (and thus g' and X") decreases sharply with falling temperature and this temperature asymmetry makes it increasingly difficult to determine the relaxation time correctly from this type of measurement. Temperature sweeps in constant external magnetic fields up to about 0.5 T yield qualitatively identical results, apart from the fact that the phase transition shifts to lower temperatures and there is some additional absorption related to the phase transition.

3.2. Frequency sweeps Frequency sweeps of the a.c. susceptibility in constant temperature and external field were performed to get more qualitative information about the magnetic relaxation, in particular to arb. units 1.0

I

I

I

a

79

exclude the influence of the temperature dependence of the static susceptibility. Fig. 2a shows the frequency dependence and fig. 2b the corresponding Cole-Cole plot of a typical measurement at T = 3.0 K and n e x t = 0.2 T. The maximum of X" and the inflection point of X' in fig. 2a yield the relaxation time at this temperature and field. The Cole-Cole plot (fig. 2b) is a somewhat flattened semi-circle starting at the origin, suggesting that the relaxation process may approximately be described by a single relaxation time. Qualitatively this remains true for the entire temperature and field range covered by our experiments (1.8 K < T < 5 K; next< 0.7 T), although below about 2.3 K there are significant deviations from simple Debye behaviour and the assumption of a single relaxation time becomes less justified with decreasing temperature (fig. 3). The ratio of maximum X" to the static value of the susceptibility varies from 0.45 (T = 4 K) to less than 0.3 below 2 K.

3.3. The relaxation process

X' ~OOoo o

The temperature dependence of the reciprocal relaxation time in DyVO4 as derived from temperature sweeps in next = 0.2T and next = 0 T (paramagnetic range alone) and frequency sweeps (paramagnetic and antiferromagnetic

o o o o o o

0.5

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3.0

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3.3 kHz O

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1.0 X'

Fig. 2. (a) F r e q u e n c y d e p e n d e n c e of X' (O) and X" ( 0 ) of DyVO4 (sphere) at T = 3.0 K and Be,t = 0.2 T parallel to a. (b) C o l e ~ 2 o l e plot (X" vs. X') of (a). T h e scaling factor is different f r o m figs. 1 and 3.

025

050 a r b units

075

×'

Fig. 3. C o l e - C o l e plots (X" vs. X') derived f r o m frequency sweeps in next = 0.2 T parallel to a for various t e m p e r a t u r e s . (a) T = 4.00 K, 0a) T = 3.40 K, (c) T = 2.80 K, (d) T = 2.50 K, (e) T = 2.32 K, (f) T = 2.22 K, (g) T = 2.13 K, (h) T = 1.96 K. N o t e that the m a x i m u m static susceptibility is at T = 3.40 K

Co).

A. Kasten et al. / Magnetic relaxation in DyV04

80

r a n g e ) is shown in figs. 4 a n d 5 in l o g a r i t h m i c plots of t h e a.c. f r e q u e n c y v vs. 1/T. In Bext = 0.2 T (fig. 4) t h e t e m p e r a t u r e d e p e n d e n c e is desc r i b e d b y an O r b a c h p r o c e s s d o w n to a b o u t 2.5 K. A fit in t h e r a n g e 2.5 K to 6.5 K (50 H z t o 3 M H z ) yields

'~ N

10

5

4

3

I

[

I

I

k

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"~

F

2.5

2 T(K)

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v = v~oe x p ( - A / T ) , with v® = 1.3 x 109 H z (r~o= 1.2 × 10 -1° see) a n d A = 39 K. T h e r e is no s y s t e m a t i c d e v i a t i o n f r o m t h e O r b a c h d e p e n d e n c e at t h e p a r a m a g n e t i c - t o a n t i f e r r o m a g n e t i c p h a s e b o u n d a r y at TN(0.2 T ) = 2.90 K. From IR spectroscopy and Raman experim e n t s [2, 11] t h e e n e r g e t i c p o s i t i o n of t h e first e x c i t e d e l e c t r o n i c s t a t e of D y 3+ is k n o w n to b e at I

\, A N

-r" \

•

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2 TIK

0

7 00T

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02T

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Fig. 4. Reciprocal relaxation time (~"= 1/2~rv) of DyVO4 as function of temperature in a plot of log v vs. lIT. Bext = 0.2 T parallel to a. • derived from temperature sweeps; C) derived from frequency sweeps; [] M6ssbauer effect [8]; - Orbach process v = 1.3 x 109 Hz exp(-39K/T). Insert: energy diagram of the lowest single ion states of Dy3+ in DyVO4 at T--< 7 K. The five components of the ground state splitting belong to different Dy3+ ions with five different arrangements of the four nearest neighbour moments. In Bex, > 0 there is an additional "pseudo-splitting" from two possible orientations relative to the external field.

0

011

I

I

I

02

03

0t~

~

L

05

06

I/T(K-~)

Fig. 5. Reciprocal relaxation time of DyVO4 as function of temperature in a plot of log v vs. 1/T. B e x t = 0.0 T. • derived from temperature sweeps; O derived from frequency sweeps; [] M6ssbauer effect [8]; - - Orbach process v= 1.3 x 109 Hz exp(-39K/T). Insert: as in fig. 4.

a b o u t A = 4 0 K . D u e to m a g n e t i c s h o r t - r a n g e o r d e r t h e r e a r e five p o s s i b l e e n e r g i e s of t h e g r o u n d s t a t e c o r r e s p o n d i n g to five a r r a n g e m e n t s of t h e f o u r n e a r e s t D y 3+ n e i g h b o u r m o m e n t s (total splitting 12 K). W i t h t h e n e a r e s t n e i g h b o u r s in t h e g r o u n d state ( m o m e n t s a l o n g ---a) t h e e x c i t e d level is p r a c t i c a l l y unsplit. T h e s e e n e r g y levels a n d t h e i r shifts in an a p p l i e d m a g n e t i c field a l o n g a a r e given in t h e inserts of figs. 4 a n d 5. This level d i a g r a m is o n l y valid u p to a b o u t 7 K since at h i g h e r t e m p e r a t u r e s A is r e d u c e d c o n s i d e r a b l y by t h e g r a d u a l d i s a p p e a r a n c e of t h e J a h n - T e l l e r d i s t o r t i o n a n d t h e Ising c h a r a c t e r of t h e e l e c t r o n i c states is r e m o v e d . A t T < 7 K, h o w e v e r , A is p r a c t i c a l l y c o n s t a n t a n d large c o m p a r e d to t h e m a g n e t i c splitting of t h e g r o u n d state. This r e m a i n s t r u e e v e n in a p p l i e d fields up to a b o u t 1 T. B e c a u s e of the Ising g r o u n d s t a t e the p r o b ability for s p i n - s p i n r e l a x a t i o n is c o n s i d e r a b l y

A . Kasten et al. / Magnetic relaxation in DyV04

reduced (gb, gc =0). Our experiments (fig. 4) show that the dominant relaxation process in Bext = 0.2 T is Orbach spin-lattice involving the first excited electronic level. Only at the lowest temperatures ( T < 2 . 5 K ) is there a slight systematic deviation towards higher frequencies suggesting the gradual onset of additional relaxation channels. Within the experimental accuracy the crystal field splitting derived from the fit to the Orbach process agrees with the spectroscopic value of A and the M6ssbauer data by Gorobchenko et al. [8] in the temperature range between 7.7K and 12.5K (4MHz to 50MHz; squares in figs. 4 and 5). The relaxation times obtained in zero field experiments (fig. 5) are somewhat shorter than those in 0.2T. The overall temperature dependence is quite similar. Two details, however, are different: (i) In the plot of log v vs. 1/T there is a pronounced kink at TN = 3.06K. At this temperature we get maximum deviation from the Orbach behaviour (straight line in fig. 5). Towards higher and lower frequencies (temperatures) the experimental points seem to approach the straight line asymptotically. (ii) At low temperatures the relaxation time reaches a saturation value of about 0.8msec (v = 200 Hz; see fig. 5). As in the frequency sweeps at 0.2 T the absorption becomes rather broad at low temperatures and the Cole circles are considerably flattened. We assume that in zero external field at about 2.2 K spin-spin relaxation becomes comparable to the spin-lattice Orbach process. There are, however, considerable deviations from a simple Debye behaviour in this temperature range and the concept of a single relaxation time must not be taken too seriously.

4. Summary Our experiments have shown that the Orbach spin-lattice process, found by Gorobchenko et al. [8] in M6ssbauer experiments, remains the dominant relaxation mechanism in DyVO4 down

81

to temperatures well inside the antiferromagnetically ordered state, although in zero external field there are deviations around the magnetic ordering temperature. Below about 2.2K the Orbach process gets too slow compared to spinspin relaxation and the relaxation tends to become temperature independent. Experiments at lower frequencies (temperatures) and a more detailed study of the magnetic field dependence of the relaxation are in progress.

Acknowledgements The authors are indebted to Prof. H.G. Kahle for helpful suggestions and comments and to Dr. G. Miiller-Vogt, Dr. W. Wendl and W. Braun for growing and preparing crystals. We are particularly grateful to Profs. E. Fick, G. Sauermann and G. Weber for stimulating discussions on the subject of magnetic relaxation.

References [1] H. Schwarz, Z. anorg allg. Chem. 323 (1963) 44. [2] A.H. Cooke, C.J. Ellis, K.A. Gehring, M.J.M. Leask, D.M. Martin, B.M. Wanklyn, M.R. Wells and R.L. White, Solid State Commun. 8 (1970) 689. [3] G.A. Gehring and K.A. Gehring, Rep. Prog. Phys. 38 (1975) 1 and references therein. [4] A. Kasten, Z. Physik B38 (1980) 65 and references therein. [5] P.J. Becker, G. Dummer, H.G. Kahle, L. Klein, (3. Miiller-Vogt and H.C. Schopper, Phys. Lett. 31A (1970) 499. [6] J.C. Wright and H.W. Moos, Phys. Rev. B4 (1971) 163. [7] A. Kasten and P.J. Becker, J. Phys. C: Solid St. Phys. 7 (1974) 3120. [8] V.D. Gorobchenko, I.I. Lukashevich, V.G. Stankevich, E.V. Mel'nikov and N.I. Filippov, Soy. Phys.-Solid State 14 (1973) 2140. [9] R.C. Ropp, Mat. Res. Bull. 10 (1975) 271. [10] W. Hintzmann and G. Miiller-Vogt, J. Crystal Growth 5 (1969) 274. [11] R.J. Elliott, R.T. Harley, W. Hayes and S.R.P. Smith, Proc. Roy. Soe. A328 (1972) 217.