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Anomalous spin glass behavior in the geometrically frustrated magnet Ni0.75 : Fluormica
0022~3697(95)004&9
Pergamon
1. Phys. Chem Solids Vol57, Nos 6-8, pp. 1085-1089. 1996 Copyright 0 1996 Elwier Science Ltd Printed in Great Britain. All rights reserved W22-3697/96 Sl5.00 + 0.00
ANOMALOUS SPIN GLASS BEHAVIOR IN THE GEOMETRICALLY FRUSTRATED MAGNET Ni0,75: FLUORMICA G. T. SEIDLER,
S. A. SOLINt
and D. R. HINES
NEC Research Institute, 4 Independence Way, Princeton, NJ 08540, U.S.A (Received 28 May 1995; accepted in revisedform 31 May 1995) report the magnetic properties of a fluormica clay intercalated with magnetic Ni*+ ions. The composition of the fluormica host is carefully selected to result in three-quarters Ni’+ filling of a triangular lattice of possible cation gallery sites. Although three-quarters filling is consistent with formation of a (2 x 2)RO” superlattice (e.g the kagome lattice), X-ray diffraction studies of the Nir,75: fluormica material show no evidence for superlattice ordering of the Ni*+ Ions. The nearest-neighbor magnetic interaction is Abstract-We
antiferromagnetic with a Weiss temperature 8 w = -8 K. As a consequence of the triangular coordination of the magnetic ions, N&.75: fluormica has geometric magnetic frustration. A spin-glass-like transition occurs at To = 4.5 K. We observe anomalous dynamical properties in this glass, including a region of temperatureindependent magnetization relaxation reminiscent of systems in which quantum fluctuations drive the dynamics. We compare and contrast these results with prior experimental and theoretical work on the analogous compositionally ordered system, the 2D kagomk antiferromagnet. Keywordr: A. oxides, B. crystal growth, C. X-ray diffraction, D. magnetic structure.
1. INTRODUCTION
Both the experimental and the theoretical study of compositionally-ordered but geometrically frustrated magnets (OGFMs) have advanced dramatically in recent years [l, 21. Experimental systems with geometric frustration and a high degree of compositional order include helium-3 on graphite [3-S], several pyrochlores and jarosites [6-91, Gd3Ga5012 [lo], and SrCr,Galz_,019 [l l-161. Theoretical work has centered almost exclusively on the properties of the low-temperature ground state of an ideal OGFM, with special emphasis on the often novel role played by fluctuations [l7-211. We report the magnetic properties of a carefully chosen synthetic clay which is intercalated with magnetic ions to form a 2D geometrically frustrated magnet which is compositionally disordered. Magnetic clays have been extensively studied, with occasional reports of possible spin glass behavior [22, 231. Our results show that this family of layered materials are ideal for studying the theoretically important regime between the OGFM and the conventional spin glasses. We depict in Fig. l(a) the general case of three spins subject to pairwise interactions labeled by the exchange constants Jo0 in the Heisenberg Hamiltonian H = -CJ,,S,
-So.
In metallic spin glasses the functional form of the RKKY [24-261 interaction together with the positional randomness (i.e. topological disorder) of the dilute magnetic impurities lead to randomness in the sign and magnitude of the Jo0 [27, 281. A significant fraction of possible sets of three neighboring spins will have all three J,, < 0. The three pairwise interactions cannot then be simultaneously satisfied; such a situation is called random frustration [27, 281. The higher-symmetry case where Jti = Jbc = J,, < 0 is instead called geometric frustration [l]. As a consequence of the degeneracy of the exchange constants, OGFMs often show a macroscopic degeneracy of their thermodynamic ground states with zero point entropies as large as of order 0.1-l ka per spin site and spin-wave contributions to the internal energy of order kaT [2, 17-211. The most heavily studied OGFM is the 2D kagomk Heisenberg antiferromagnet, the spins of which occupy a kagomk lattice such as that shown as bold black lines in Fig. l(a). This OGFM has at least two distinct classes of lowest energy states with each consisting of a highdimensional manifold of possible spin configurations, one with q = (0,O) and the other with q = (a, &) [2]. The subtle role played by fluctuations in selecting particular lowest energy configurations at finite but low temperatures (i.e. T/ 1J 1=O.Ol) has led to an extensive theoretical literature [l7-21, 29, 301. The magnetoplumbite SrCrsGa4019
t Author to whom correspondence should be addressed.
approximates 1085
a 2D kagomt
(SCGO) closely
antiferromagnet
[ 1 1- 161.
G. T. SEIDLER et al.
(a 1
of geometric frustration in the strongly disordered system. We now describe the synthesis, structure, and magnetic properties of a synthetic fluormica clay with magnetic ions intercalated into the gallery. This layered material has been specially tailored so that Ni2+ ions randomly occupy three-quarters of the sites of a 2D triangular lattice, a density appropriate for the formation of a (2 x 2)RO” kagome superlattice. We find that the nearest-neighbor magnetic interaction is antiferromagnetic. Thus this material has strong compositional disorder, but still has geometric frustration. We consider it to be the compositionally disordered analog of the 2D kagome antiferromagnet.
2. EXPERIMENT 2.1. Sample synthesis and structure
0 oxygen
0 Fluorine
.
l’etrahcdfalSilicon & Aliminum
0
OctahedralMagnesium
Fig. 1. (a) The three triangularly coordinated spins in the upper left demonstrate frustration-for Jap < 0 the three pairwise interactions cannot he simultaneously satisfied.The lattice shown is the kagome lattice, a (2 x 2)RO”superlattice of the triangular lattice. (b) Schematic illustration of the tetrahedral and octahedral sites in a 2 : 1 layered fluortnica. This idealized structure with no c axis rotation of the tetrahedra (see text) has the oxygen atoms on the basal surfaces organized in a kagome lattice (heavy solid lines). d is the basal-spacing. However, SCGO has 10% non-magnetic dilution in its quasi-2D kagome planes. Numerical results find that the macroscopic ground state degeneracy of the 2D kagome antiferromagnet is largely insensitive to dilution [30], although a proposed chiral-nematic ordering is destroyed by the compositional disorder [29]. Measurements of SCGO find an unusual spinglass-like state with a large value of the mean field suppression factor lew/ro] = 130 [13, 141. Strong evidence exists for incomplete spin freezing on a unitcell length scale even at T = 50mK; the remaining ground state degeneracy is being accessed locally via quantum fluctuations [15, 161. Similar evidence for weak ‘spin liquid’ behavior exists in another OGFM with more complete compositional order [3 11. Given that the data on SCGO establish the continuing importance of the geometric nature of the frustration in the weakly compositionally disordered 2D kagome antiferromagnet, we inquire as to the role
The high temperature (1400°C) growth of SrttYs Mg2,,s(A1Si3)0t0F2 (Sr0,7s: fluormica) has been described elsewhere [32], and is similar to the original work of Beall [33, 341. We use Sr2+ as the precursor cation because it is large enough to be excluded from the intralayer sites during high temperature synthesis. As Sr2+ is a non-magnetic ion Sr,-,,s : fluormica cannot be used to study the properties of geometrically frustrated magnets. The intercalative substitution for Sr2+ by Ni2+ is achieved in two steps: swelling of the clay by immersion in an n-butyl ammonium/HCl solution (pH 7), then ion exchange in a NiCl solution in a 125C hydrothermal environment for 24 h [32]. Hexagonal platelets of Nis,,s : fluormica as large as 100 microns result. We present in Fig. l(b) a perspective drawing of the idealized structure of this clay. Its layers are composed of a sheet of edge-shared MgOs octahedra coupled above and below to sheets of (AlSi)04 tetrahedra. The hexagonal pockets in the kagome lattice of basal oxygen atoms form a triangular lattice. In the real structure, all of the tetrahedra undergo correlated rotations about the c axis which result in a distortion of and expansion of the hexagonal pockets to allow them to accommodate cations such as S? [33, 341. However, the triangular lattice structure of the gallery cation sites is preserved in this distortion. In Sro.,s : fluormica three-quarters of the triangular lattice sites are occupied. The lowest energy arrangement of these ions is a (2 x 2)RO’ kagomi superlattice. Indeed, X-ray precession photographs of the (hk0) basal plane show weak kagome superlattice reflections (f3/2, f3/2, 0); therefore local kagome ordering of the St-‘+ gallery cations exists for the as-prepared Sr0.7s: fluormica. However, X-ray precession photographs of the NiO.,s : fluormica do not show evidence
Anomalous spin glass behavior in the geometrically frustrated magnet
Do -
4omo
? -
20,ooo
0
200
300
‘I- WI
Fig. 2. The temperature dependence of the inverse susceptibility of N&,r5: fluormica. The solid line is a fit to Curie-Weiss behavior for T > 150K. for kagome superlattice ordering of the Ni2+ ions. The Ni2+ ions randomly occupy three-quarters of the triangular lattice of cation sites in the gallery of the fluormica host.
2.2. Magnetic measurements All DC magnetization measurements are performed in a commercial SQUID magnetometer (Quantum Design, U.S.A.). The randomly oriented powder samples are sealed in suprasil quartz at room temperature with approximately 0.3 atm of He as exchange gas. For all measurements we find only dipolar response and consequently we ignore higher multipole corrections to the sample magnetization. We use a shortened scan length (4 cm) of the sample through the radiometer coils so as to keep the sample in a region of high magneticfield homogeneity at all times. The data are verified to be independent of scan length. Magnetic field changes are unidirectional, i.e. the field does not overshoot the desired target field. In the relaxation measurements, by zero-field cooled (zfc) we mean the sample was zero-field cooled, the magnet ramped to 100 Oe, and the subsequent relaxation measured. Similarly, by thermoremanent (trm) we mean the sample is field cooled in lOOOe, the magnet ramped to OOe, and again the subsequent relaxation measured. As data collection time is limited when T < 4.5 K in our magnetometer, we evaluate dM/d(ln(r)) in the time window 240 < t < 2400 s at all temperatures.
I087
frustration that is geometric rather than random. The unusual downward-curvature deviation from Curie-Weiss behavior at 150K will be discussed elsewhere [35]. We show in Fig. 3 the field cooled and zero-field cooled DC susceptibilities, xrc and xZrc, respectively, for an applied field of H = 100Oe in the narrowed temperature range 1.6 < T < 20 K. There is an onset of some magnetic irreversibility at approximately 10 K, and a spin-glass-like transition at TG = 4.5 K. At this temperature xZf,(T) has a broad peak and the temperature dependencies of the two susceptibilities noticeably diverge. Note that 10w/T~ 1 = 2. Ramirez [l] has proposed that both compositional order and geometric frustration are necessary to obtain large values of the mean field suppression factor. Our data on N&s : fluormica obviously support this hypothesis. Returning to the data in Fig. 3, the rapid increase in magnetic irreversibility starting at 4.5 K indicates that the characteristic time for spin reorientation exceeds the experimental measurement time of -200s per measurement temperature. We note that xr,( T) for Ni0.75: fluormica is noticeably temperature dependent below our nominal glass temperature of T, = 4.5 K. In canonical spin glasses xrc is expected to be temperature independent below TG because deep metastable states at T = TG are generally close in spin configuration to deep metastable states at T<
TG.
In the 2D kagome antiferromagnetic, the geometric frustration and particular lattice symmetry lead to a contribution to the free energy by the entropy and spin-wave energy of order unity times kBT per spin [19-21,301. Recall that OGFMs
typically exhibit large
values of 1Ow/T~ 1[ 11.As a consequence the order of
1J 1per spin energetic contribution from the Heisenberg Hamiltonian still dominates the free energy, and temperature independent xfc is observed [13, 141,just as in usual spin glasses [27,28].
3. RESULTS AND DISCUSSION We show in Fig. 2 the reciprocal
susceptibility
of
dehydrated Nis.,s : fluormica in an applied field H = 1OOOe. The Curie-Weiss behavior has ew =
-8 K, indicating antiferromagnetic nearest-neighbor interactions. We conclude that Nis,,s : fluormica is a compositionally disordered system with magnetic
TW Fig. 3. The temperature dependence of the field cooled (fc) and zero-field cooled (zfc) magnetic susceptibilities of Nit,75 : Ruormica. Note the rapid divergence in the magnetic irreversibility at To = 4.5 K (see text).
1088
G. T. SEIDLER et al.
However, in our disordered system we have 1ew/TGI = 2. If geometric frustration alone is sufficient to still cause a high degeneracy of the ground state and low-lying excited states, then over a wide temperature range below T, the energetic and the combined entropic and spin-wave contributions to the free energy will be comparable in magnitude in N&
: jluormica. In such a case, even the coarse features of the free energy as a function of spin configuration undergo restructuring as temperature is varied and consequently xfC may no longer be temperature-independent below T,. Also, one naturally expects that the low temperature ground state and low temperature spin dynamics may be novel. The magnetization relaxation measurements which we now report are a direct characterization of the spin dynamics in the glassy state of our compositionally disordered geometrically frustrated magnet. We show in Fig. 4 the measured magnetization relaxation rates dM/d(ln(t)) in both zfc and trm modesforH= lOOOeand1.7
‘B ‘,‘.9m=nmc=.
6’
8
IO
T(K) Fig. 4. The temperature dependence of the zero-field cooled (zfc, open boxes) and thermoremanent (trm, filled circles) magnetization relaxation rates of N&s : fluormica. We define To = 3.OK to indicate the onset of temperatureindependent zfc relaxation (see text). Inset-zfc magnetization relaxation at T = 4.75 K. The major divisions on the vertical axis are spaced by 1.Ox lOa emu. fact the temperature
independent
relaxation
persists
to T K T,, we believe it would be the first example of
bulk, rather than microscopic, spin liquid behavior. We also present the trm relaxation rate (filled circles) in Fig. 4. Once again, the data are not similar to that observed in canonical spin glass. Although encouraged by the agreement of the two experimental methods at our lowest experimental temperatures, we cannot fully explain the complicated temperature dependence of this relaxation rate. We do note that in a system supporting a spin liquid state the difference in preparation conditions for the two relaxation measurements might yield different relaxation rates. Thermoremanent relaxation begins from a state which is a perturbation of a field cooled state-a state where the ground state degeneracy of the Hamiltonian is partially lifted by the applied field. On the other hand, isothermal relaxation begins from a state where any consequences of the high ground state degeneracy will be optimized.
4. CONCLUSION
We report measurements of the magnetic properties of NiO,rS: fluormica. This compositionally disordered geometrically frustrated magnet exhibits a rapid increase in magnetic irreversibility below TG = 4.5 K with both similarities to and differences from data for canonical spin glasses. Unlike the compositionally ordered geometrically frustrated magnets which show large deviations from mean-field behavior, NiO,rS: fluormica has ( Qw/TGI x 2. However, despite the absence of large mean field suppression, the presence of geometric rather than random frustration appears to play a key role in the anomalous dynamical properties of the glassy state.
Anomalous spin glass behavior in the geometrically frustrated magnet Acknowledgement-We thank P. Chandra for useful discussions during the preparation of this manuscript.
1089
18. Shender E. F., Sov. Phys. JETP 56, 178 (1982). 19. Harris A. B., Kallin C. and Berlinsky A. J., Phys. Rev. E 45,2899 (1992).
20. Ritchey I., Chandra P. and Coleman P., Phys. Rev. 847, 15342 (1993).
REFERENCES 1. Ramirez A. P., Annual Review of Materials Science
(Edited by Merton C. Flemings, John B. Wachtman, Jr, Elton K. Kaufmann and Joseph A. Giordmaine), Vol. 24, p. 453. Annual Reviews Inc, Palo Alto (1994). 2. Shender E. F. and Holdsworth P. C. W., Fluctuations and Order: The New Synthesis (Edited by M. M. Millonas). MIT Press, Boston (1994). 3. Greywall D. S. and Busch P. A., Phys. Rev. Lett. 62,1868 (1989). 4. Greywall D. S. and Busch P.A., Phys. Rev. Lett. 65,2788 (1990). 5. Greywall D. S., Phys. Rev. B 41, 1842 (1990). 6. Reimers J. N., Greedan J. E., Kremer R. K., Gmelin E. and Subramanian M. A., Phys. Rev. B 43,3387 (1991). I. Gaulin B. D., Reimers J. N., Mason T. E., Greedan J. E. and Tun Z., Phys. Rev. Lett. 69,3244 (1992). 8. Raju N. P., Gmelin E. and Kremer R. K., Phys. Rev. B 46,5405 (1992). 9. Townsend M. G., Longworth G. and Roudaut E., Phys. Rev. B33,4919 (1986). 10. Schiffer P., Ramirez A. P., Huse D. A. and Valentino A. J., Phys. Rev. Len. 73,250O (1994).
11. Obradors X., Labarta A., Isalgue’, Tejada J., Rodriguez J. and Pernet M., Solid State Commun. 65, 189 (1988). 12. Ramirez A. P., Espinosa G. P. and Cooper A. S., Phys. Rev. B 45,2505 (1992). 13. Ramirez A. P., Espinosa G. P. and Cooper A. S., Phys. Rev. Lett. 64,207O (1990).
14. Martinez B., Sandiumenge F., Rouco A., Labarta A., Rodriguez-Carvajal J., Tovar M., Causa M. T., Gali S. and Obradors X., Phys. Rev. B 46,10786 (1992). 15. Broholm C., Aeppli G., Espinosa G. P. and Cooper A. S., Phys. Rev. Lett. 65,3173 (1990). 16. Uemura Y. J.. Keren A.. Le L. P.. Luke G. M.. Sternlieb B. J. and Wu W. D. Hyber$ne Interact 85, 181 (1994). 17. Villain J., Bidaux R., Carton J.-P. and Conte R., J. Physique 41, 1262 (1980).
21. Reimers Jan N., Berlinsky A. J., Phys. Rev. B. 48,9539 (1993).
22. Suzuki Masatsuga, Yeh Mildred, Burr C. R., Whittingham M. S., Koga K. and Nishihara H., Phys. Rev. B &I1229 (1989). 23. Zhou Ping, Amarasekera J., Solin S. A., Mahanti S. D. and Pinnavaia T. J., Phys. Rev. I? 47,16486 (1993). 24. Ruderman M. A. and Kittel C., Phys. Rev. %, 99 (1954). 25. Kasuya T., Prog. Theor. Phys. 16,45 (1956). 26. Yosida K., Phys. Rev. 106,893 (1957). 27. Binder K. and Youne A. P.. Rev. Mod. Phvs. 58. 801 (1986). 28. Fischer K. H., and Hertz J. A., Spin Glasses. Cambridge University Press, Cambridge (1991). 29. Chandra P. and Coleman P., Phys. Rev. Lrtt. 66, 100 (1991). 30. Shender E. F., Cherepanov V. B., Holdsworth P. C. H. and Berlinsky A. J., Phys. Rev. Lett. 70, 3812 (1993). 31. Harris M. J., Zinkin M. P., Tun Z., Wanklyn B. M. and Swainson I. P., Phys. Rev. Lett. 73, 189 (1994). 32. Solin S. A., Hines D. and Haushalter R., Mol. Cryst. Liq. Cryst. 244, 143 (1994). 33. Beall G. H., Advances in Nucleation and Crystaffization in Glasses (Edited by L. L. Hench and S. W. Freiman), p. 251. Am. Ceramic Sot., Columbus (1971). 34. Hoda S. N. and Beall G. H., Adv. Ceram. 4,287 (1982). 35. Solin S. A., Thorpe M. F. and Hines D. R.. to be published. 36. Fruchter L. and Malozemoff A., Phys. Rev. B 43,8709 (1991).
31. Seidler G. T., Rosenbaum T. F., Beauchamp K. M., Jaeger H. M., Crabtree G. W., Welp U. and-Vinokur V. M.. Phvs. Rev. Lett. 74. 1442 (1995). 38. Ibrahim M. M., Darwish S: and Sdehra’M. S., Phys. Rev. B 51,295s (1995). 39. Ramirez A. P., Jager-Waldau R. and Siegrist T., Pitys. Rev. B43, 10461 (1991). 40. Blatter Gianni, Geshkenbein Vadim B. and Vinokur Valeri M., Phys. Rev. Lett. 66, 3297 (1991).
Pergamon
1. Phys. Chem Solids Vol57, Nos 6-8, pp. 1085-1089. 1996 Copyright 0 1996 Elwier Science Ltd Printed in Great Britain. All rights reserved W22-3697/96 Sl5.00 + 0.00
ANOMALOUS SPIN GLASS BEHAVIOR IN THE GEOMETRICALLY FRUSTRATED MAGNET Ni0,75: FLUORMICA G. T. SEIDLER,
S. A. SOLINt
and D. R. HINES
NEC Research Institute, 4 Independence Way, Princeton, NJ 08540, U.S.A (Received 28 May 1995; accepted in revisedform 31 May 1995) report the magnetic properties of a fluormica clay intercalated with magnetic Ni*+ ions. The composition of the fluormica host is carefully selected to result in three-quarters Ni’+ filling of a triangular lattice of possible cation gallery sites. Although three-quarters filling is consistent with formation of a (2 x 2)RO” superlattice (e.g the kagome lattice), X-ray diffraction studies of the Nir,75: fluormica material show no evidence for superlattice ordering of the Ni*+ Ions. The nearest-neighbor magnetic interaction is Abstract-We
antiferromagnetic with a Weiss temperature 8 w = -8 K. As a consequence of the triangular coordination of the magnetic ions, N&.75: fluormica has geometric magnetic frustration. A spin-glass-like transition occurs at To = 4.5 K. We observe anomalous dynamical properties in this glass, including a region of temperatureindependent magnetization relaxation reminiscent of systems in which quantum fluctuations drive the dynamics. We compare and contrast these results with prior experimental and theoretical work on the analogous compositionally ordered system, the 2D kagomk antiferromagnet. Keywordr: A. oxides, B. crystal growth, C. X-ray diffraction, D. magnetic structure.
1. INTRODUCTION
Both the experimental and the theoretical study of compositionally-ordered but geometrically frustrated magnets (OGFMs) have advanced dramatically in recent years [l, 21. Experimental systems with geometric frustration and a high degree of compositional order include helium-3 on graphite [3-S], several pyrochlores and jarosites [6-91, Gd3Ga5012 [lo], and SrCr,Galz_,019 [l l-161. Theoretical work has centered almost exclusively on the properties of the low-temperature ground state of an ideal OGFM, with special emphasis on the often novel role played by fluctuations [l7-211. We report the magnetic properties of a carefully chosen synthetic clay which is intercalated with magnetic ions to form a 2D geometrically frustrated magnet which is compositionally disordered. Magnetic clays have been extensively studied, with occasional reports of possible spin glass behavior [22, 231. Our results show that this family of layered materials are ideal for studying the theoretically important regime between the OGFM and the conventional spin glasses. We depict in Fig. l(a) the general case of three spins subject to pairwise interactions labeled by the exchange constants Jo0 in the Heisenberg Hamiltonian H = -CJ,,S,
-So.
In metallic spin glasses the functional form of the RKKY [24-261 interaction together with the positional randomness (i.e. topological disorder) of the dilute magnetic impurities lead to randomness in the sign and magnitude of the Jo0 [27, 281. A significant fraction of possible sets of three neighboring spins will have all three J,, < 0. The three pairwise interactions cannot then be simultaneously satisfied; such a situation is called random frustration [27, 281. The higher-symmetry case where Jti = Jbc = J,, < 0 is instead called geometric frustration [l]. As a consequence of the degeneracy of the exchange constants, OGFMs often show a macroscopic degeneracy of their thermodynamic ground states with zero point entropies as large as of order 0.1-l ka per spin site and spin-wave contributions to the internal energy of order kaT [2, 17-211. The most heavily studied OGFM is the 2D kagomk Heisenberg antiferromagnet, the spins of which occupy a kagomk lattice such as that shown as bold black lines in Fig. l(a). This OGFM has at least two distinct classes of lowest energy states with each consisting of a highdimensional manifold of possible spin configurations, one with q = (0,O) and the other with q = (a, &) [2]. The subtle role played by fluctuations in selecting particular lowest energy configurations at finite but low temperatures (i.e. T/ 1J 1=O.Ol) has led to an extensive theoretical literature [l7-21, 29, 301. The magnetoplumbite SrCrsGa4019
t Author to whom correspondence should be addressed.
approximates 1085
a 2D kagomt
(SCGO) closely
antiferromagnet
[ 1 1- 161.
G. T. SEIDLER et al.
(a 1
of geometric frustration in the strongly disordered system. We now describe the synthesis, structure, and magnetic properties of a synthetic fluormica clay with magnetic ions intercalated into the gallery. This layered material has been specially tailored so that Ni2+ ions randomly occupy three-quarters of the sites of a 2D triangular lattice, a density appropriate for the formation of a (2 x 2)RO” kagome superlattice. We find that the nearest-neighbor magnetic interaction is antiferromagnetic. Thus this material has strong compositional disorder, but still has geometric frustration. We consider it to be the compositionally disordered analog of the 2D kagome antiferromagnet.
2. EXPERIMENT 2.1. Sample synthesis and structure
0 oxygen
0 Fluorine
.
l’etrahcdfalSilicon & Aliminum
0
OctahedralMagnesium
Fig. 1. (a) The three triangularly coordinated spins in the upper left demonstrate frustration-for Jap < 0 the three pairwise interactions cannot he simultaneously satisfied.The lattice shown is the kagome lattice, a (2 x 2)RO”superlattice of the triangular lattice. (b) Schematic illustration of the tetrahedral and octahedral sites in a 2 : 1 layered fluortnica. This idealized structure with no c axis rotation of the tetrahedra (see text) has the oxygen atoms on the basal surfaces organized in a kagome lattice (heavy solid lines). d is the basal-spacing. However, SCGO has 10% non-magnetic dilution in its quasi-2D kagome planes. Numerical results find that the macroscopic ground state degeneracy of the 2D kagome antiferromagnet is largely insensitive to dilution [30], although a proposed chiral-nematic ordering is destroyed by the compositional disorder [29]. Measurements of SCGO find an unusual spinglass-like state with a large value of the mean field suppression factor lew/ro] = 130 [13, 141. Strong evidence exists for incomplete spin freezing on a unitcell length scale even at T = 50mK; the remaining ground state degeneracy is being accessed locally via quantum fluctuations [15, 161. Similar evidence for weak ‘spin liquid’ behavior exists in another OGFM with more complete compositional order [3 11. Given that the data on SCGO establish the continuing importance of the geometric nature of the frustration in the weakly compositionally disordered 2D kagome antiferromagnet, we inquire as to the role
The high temperature (1400°C) growth of SrttYs Mg2,,s(A1Si3)0t0F2 (Sr0,7s: fluormica) has been described elsewhere [32], and is similar to the original work of Beall [33, 341. We use Sr2+ as the precursor cation because it is large enough to be excluded from the intralayer sites during high temperature synthesis. As Sr2+ is a non-magnetic ion Sr,-,,s : fluormica cannot be used to study the properties of geometrically frustrated magnets. The intercalative substitution for Sr2+ by Ni2+ is achieved in two steps: swelling of the clay by immersion in an n-butyl ammonium/HCl solution (pH 7), then ion exchange in a NiCl solution in a 125C hydrothermal environment for 24 h [32]. Hexagonal platelets of Nis,,s : fluormica as large as 100 microns result. We present in Fig. l(b) a perspective drawing of the idealized structure of this clay. Its layers are composed of a sheet of edge-shared MgOs octahedra coupled above and below to sheets of (AlSi)04 tetrahedra. The hexagonal pockets in the kagome lattice of basal oxygen atoms form a triangular lattice. In the real structure, all of the tetrahedra undergo correlated rotations about the c axis which result in a distortion of and expansion of the hexagonal pockets to allow them to accommodate cations such as S? [33, 341. However, the triangular lattice structure of the gallery cation sites is preserved in this distortion. In Sro.,s : fluormica three-quarters of the triangular lattice sites are occupied. The lowest energy arrangement of these ions is a (2 x 2)RO’ kagomi superlattice. Indeed, X-ray precession photographs of the (hk0) basal plane show weak kagome superlattice reflections (f3/2, f3/2, 0); therefore local kagome ordering of the St-‘+ gallery cations exists for the as-prepared Sr0.7s: fluormica. However, X-ray precession photographs of the NiO.,s : fluormica do not show evidence
Anomalous spin glass behavior in the geometrically frustrated magnet
Do -
4omo
? -
20,ooo
0
200
300
‘I- WI
Fig. 2. The temperature dependence of the inverse susceptibility of N&,r5: fluormica. The solid line is a fit to Curie-Weiss behavior for T > 150K. for kagome superlattice ordering of the Ni2+ ions. The Ni2+ ions randomly occupy three-quarters of the triangular lattice of cation sites in the gallery of the fluormica host.
2.2. Magnetic measurements All DC magnetization measurements are performed in a commercial SQUID magnetometer (Quantum Design, U.S.A.). The randomly oriented powder samples are sealed in suprasil quartz at room temperature with approximately 0.3 atm of He as exchange gas. For all measurements we find only dipolar response and consequently we ignore higher multipole corrections to the sample magnetization. We use a shortened scan length (4 cm) of the sample through the radiometer coils so as to keep the sample in a region of high magneticfield homogeneity at all times. The data are verified to be independent of scan length. Magnetic field changes are unidirectional, i.e. the field does not overshoot the desired target field. In the relaxation measurements, by zero-field cooled (zfc) we mean the sample was zero-field cooled, the magnet ramped to 100 Oe, and the subsequent relaxation measured. Similarly, by thermoremanent (trm) we mean the sample is field cooled in lOOOe, the magnet ramped to OOe, and again the subsequent relaxation measured. As data collection time is limited when T < 4.5 K in our magnetometer, we evaluate dM/d(ln(r)) in the time window 240 < t < 2400 s at all temperatures.
I087
frustration that is geometric rather than random. The unusual downward-curvature deviation from Curie-Weiss behavior at 150K will be discussed elsewhere [35]. We show in Fig. 3 the field cooled and zero-field cooled DC susceptibilities, xrc and xZrc, respectively, for an applied field of H = 100Oe in the narrowed temperature range 1.6 < T < 20 K. There is an onset of some magnetic irreversibility at approximately 10 K, and a spin-glass-like transition at TG = 4.5 K. At this temperature xZf,(T) has a broad peak and the temperature dependencies of the two susceptibilities noticeably diverge. Note that 10w/T~ 1 = 2. Ramirez [l] has proposed that both compositional order and geometric frustration are necessary to obtain large values of the mean field suppression factor. Our data on N&s : fluormica obviously support this hypothesis. Returning to the data in Fig. 3, the rapid increase in magnetic irreversibility starting at 4.5 K indicates that the characteristic time for spin reorientation exceeds the experimental measurement time of -200s per measurement temperature. We note that xr,( T) for Ni0.75: fluormica is noticeably temperature dependent below our nominal glass temperature of T, = 4.5 K. In canonical spin glasses xrc is expected to be temperature independent below TG because deep metastable states at T = TG are generally close in spin configuration to deep metastable states at T<
TG.
In the 2D kagome antiferromagnetic, the geometric frustration and particular lattice symmetry lead to a contribution to the free energy by the entropy and spin-wave energy of order unity times kBT per spin [19-21,301. Recall that OGFMs
typically exhibit large
values of 1Ow/T~ 1[ 11.As a consequence the order of
1J 1per spin energetic contribution from the Heisenberg Hamiltonian still dominates the free energy, and temperature independent xfc is observed [13, 141,just as in usual spin glasses [27,28].
3. RESULTS AND DISCUSSION We show in Fig. 2 the reciprocal
susceptibility
of
dehydrated Nis.,s : fluormica in an applied field H = 1OOOe. The Curie-Weiss behavior has ew =
-8 K, indicating antiferromagnetic nearest-neighbor interactions. We conclude that Nis,,s : fluormica is a compositionally disordered system with magnetic
TW Fig. 3. The temperature dependence of the field cooled (fc) and zero-field cooled (zfc) magnetic susceptibilities of Nit,75 : Ruormica. Note the rapid divergence in the magnetic irreversibility at To = 4.5 K (see text).
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G. T. SEIDLER et al.
However, in our disordered system we have 1ew/TGI = 2. If geometric frustration alone is sufficient to still cause a high degeneracy of the ground state and low-lying excited states, then over a wide temperature range below T, the energetic and the combined entropic and spin-wave contributions to the free energy will be comparable in magnitude in N&
: jluormica. In such a case, even the coarse features of the free energy as a function of spin configuration undergo restructuring as temperature is varied and consequently xfC may no longer be temperature-independent below T,. Also, one naturally expects that the low temperature ground state and low temperature spin dynamics may be novel. The magnetization relaxation measurements which we now report are a direct characterization of the spin dynamics in the glassy state of our compositionally disordered geometrically frustrated magnet. We show in Fig. 4 the measured magnetization relaxation rates dM/d(ln(t)) in both zfc and trm modesforH= lOOOeand1.7
‘B ‘,‘.9m=nmc=.
6’
8
IO
T(K) Fig. 4. The temperature dependence of the zero-field cooled (zfc, open boxes) and thermoremanent (trm, filled circles) magnetization relaxation rates of N&s : fluormica. We define To = 3.OK to indicate the onset of temperatureindependent zfc relaxation (see text). Inset-zfc magnetization relaxation at T = 4.75 K. The major divisions on the vertical axis are spaced by 1.Ox lOa emu. fact the temperature
independent
relaxation
persists
to T K T,, we believe it would be the first example of
bulk, rather than microscopic, spin liquid behavior. We also present the trm relaxation rate (filled circles) in Fig. 4. Once again, the data are not similar to that observed in canonical spin glass. Although encouraged by the agreement of the two experimental methods at our lowest experimental temperatures, we cannot fully explain the complicated temperature dependence of this relaxation rate. We do note that in a system supporting a spin liquid state the difference in preparation conditions for the two relaxation measurements might yield different relaxation rates. Thermoremanent relaxation begins from a state which is a perturbation of a field cooled state-a state where the ground state degeneracy of the Hamiltonian is partially lifted by the applied field. On the other hand, isothermal relaxation begins from a state where any consequences of the high ground state degeneracy will be optimized.
4. CONCLUSION
We report measurements of the magnetic properties of NiO,rS: fluormica. This compositionally disordered geometrically frustrated magnet exhibits a rapid increase in magnetic irreversibility below TG = 4.5 K with both similarities to and differences from data for canonical spin glasses. Unlike the compositionally ordered geometrically frustrated magnets which show large deviations from mean-field behavior, NiO,rS: fluormica has ( Qw/TGI x 2. However, despite the absence of large mean field suppression, the presence of geometric rather than random frustration appears to play a key role in the anomalous dynamical properties of the glassy state.
Anomalous spin glass behavior in the geometrically frustrated magnet Acknowledgement-We thank P. Chandra for useful discussions during the preparation of this manuscript.
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18. Shender E. F., Sov. Phys. JETP 56, 178 (1982). 19. Harris A. B., Kallin C. and Berlinsky A. J., Phys. Rev. E 45,2899 (1992).
20. Ritchey I., Chandra P. and Coleman P., Phys. Rev. 847, 15342 (1993).
REFERENCES 1. Ramirez A. P., Annual Review of Materials Science
(Edited by Merton C. Flemings, John B. Wachtman, Jr, Elton K. Kaufmann and Joseph A. Giordmaine), Vol. 24, p. 453. Annual Reviews Inc, Palo Alto (1994). 2. Shender E. F. and Holdsworth P. C. W., Fluctuations and Order: The New Synthesis (Edited by M. M. Millonas). MIT Press, Boston (1994). 3. Greywall D. S. and Busch P. A., Phys. Rev. Lett. 62,1868 (1989). 4. Greywall D. S. and Busch P.A., Phys. Rev. Lett. 65,2788 (1990). 5. Greywall D. S., Phys. Rev. B 41, 1842 (1990). 6. Reimers J. N., Greedan J. E., Kremer R. K., Gmelin E. and Subramanian M. A., Phys. Rev. B 43,3387 (1991). I. Gaulin B. D., Reimers J. N., Mason T. E., Greedan J. E. and Tun Z., Phys. Rev. Lett. 69,3244 (1992). 8. Raju N. P., Gmelin E. and Kremer R. K., Phys. Rev. B 46,5405 (1992). 9. Townsend M. G., Longworth G. and Roudaut E., Phys. Rev. B33,4919 (1986). 10. Schiffer P., Ramirez A. P., Huse D. A. and Valentino A. J., Phys. Rev. Len. 73,250O (1994).
11. Obradors X., Labarta A., Isalgue’, Tejada J., Rodriguez J. and Pernet M., Solid State Commun. 65, 189 (1988). 12. Ramirez A. P., Espinosa G. P. and Cooper A. S., Phys. Rev. B 45,2505 (1992). 13. Ramirez A. P., Espinosa G. P. and Cooper A. S., Phys. Rev. Lett. 64,207O (1990).
14. Martinez B., Sandiumenge F., Rouco A., Labarta A., Rodriguez-Carvajal J., Tovar M., Causa M. T., Gali S. and Obradors X., Phys. Rev. B 46,10786 (1992). 15. Broholm C., Aeppli G., Espinosa G. P. and Cooper A. S., Phys. Rev. Lett. 65,3173 (1990). 16. Uemura Y. J.. Keren A.. Le L. P.. Luke G. M.. Sternlieb B. J. and Wu W. D. Hyber$ne Interact 85, 181 (1994). 17. Villain J., Bidaux R., Carton J.-P. and Conte R., J. Physique 41, 1262 (1980).
21. Reimers Jan N., Berlinsky A. J., Phys. Rev. B. 48,9539 (1993).
22. Suzuki Masatsuga, Yeh Mildred, Burr C. R., Whittingham M. S., Koga K. and Nishihara H., Phys. Rev. B &I1229 (1989). 23. Zhou Ping, Amarasekera J., Solin S. A., Mahanti S. D. and Pinnavaia T. J., Phys. Rev. I? 47,16486 (1993). 24. Ruderman M. A. and Kittel C., Phys. Rev. %, 99 (1954). 25. Kasuya T., Prog. Theor. Phys. 16,45 (1956). 26. Yosida K., Phys. Rev. 106,893 (1957). 27. Binder K. and Youne A. P.. Rev. Mod. Phvs. 58. 801 (1986). 28. Fischer K. H., and Hertz J. A., Spin Glasses. Cambridge University Press, Cambridge (1991). 29. Chandra P. and Coleman P., Phys. Rev. Lrtt. 66, 100 (1991). 30. Shender E. F., Cherepanov V. B., Holdsworth P. C. H. and Berlinsky A. J., Phys. Rev. Lett. 70, 3812 (1993). 31. Harris M. J., Zinkin M. P., Tun Z., Wanklyn B. M. and Swainson I. P., Phys. Rev. Lett. 73, 189 (1994). 32. Solin S. A., Hines D. and Haushalter R., Mol. Cryst. Liq. Cryst. 244, 143 (1994). 33. Beall G. H., Advances in Nucleation and Crystaffization in Glasses (Edited by L. L. Hench and S. W. Freiman), p. 251. Am. Ceramic Sot., Columbus (1971). 34. Hoda S. N. and Beall G. H., Adv. Ceram. 4,287 (1982). 35. Solin S. A., Thorpe M. F. and Hines D. R.. to be published. 36. Fruchter L. and Malozemoff A., Phys. Rev. B 43,8709 (1991).
31. Seidler G. T., Rosenbaum T. F., Beauchamp K. M., Jaeger H. M., Crabtree G. W., Welp U. and-Vinokur V. M.. Phvs. Rev. Lett. 74. 1442 (1995). 38. Ibrahim M. M., Darwish S: and Sdehra’M. S., Phys. Rev. B 51,295s (1995). 39. Ramirez A. P., Jager-Waldau R. and Siegrist T., Pitys. Rev. B43, 10461 (1991). 40. Blatter Gianni, Geshkenbein Vadim B. and Vinokur Valeri M., Phys. Rev. Lett. 66, 3297 (1991).