- Email: [email protected]
Magnetic properties of dilute MgCe alloys
3. Phys. Chm
S&i.%
1975,
Vol. 36 pp. 1223-1224.PergamonPress. hinted in &eat B&in
MAGNETIC PROPERTIES OF DILUTE MgCe ALLOYS C. R. Bumt and R. G. PJRJCH Department of Physics, State University of New York at Binghamton,Binghamton,NY 13901,U.S.A. (Received 22 January
(1975)
Abstract-The magnetic susceptibility of mono~rystalline dilute MgCe alloys has been investigated. An anisotropic susceutibilitv was found and exblained as the consequence of a crystalline field spiitti~ of the ground state of about 3.2K: .
1.~ROD~ON Recent experiments on dilute alloys of Eu and Yb in Mg indicate that valence changes occur as the temperature is varied at atmospheric pressure[l]. It is also thought that certain alloys of Ce undergo valence alternations as a function of temperature[2] and we were interested in learning if dilute alloys of Ce in Mg might do this also. The results we describe below indicate that Ce is trivalent in Mg and that it undergoes no configurational change. The crystalline electric field in a metal has a large influence on the magnetic character of a rare earth ion at low tem~rat~e, often producing anisotropy and signiticant deviations from Curie-Weiss behavior. The magnetic measurements we have performed on a monocrystalline dilute alloy of Ce in Mg enable a determination of the crystal field in hfg. Although it should be much too oversimplified for a metal, simple crystal field calculations have proved remarkably effective in predicting the effect of the crystalline field in many alloys, and’this proves to be the case in MgCe alloys also. Interestingly, deviations of the experimental data from these crystal field predictions at the lowest temperatures, similar to those in known Kondo alloys YCe and Lace [3,41 suggest the possibility that Ce may be in a Kondo state at su~ciently low temperatures. In fact, several years ago Hedgcock and Petrie [S] thought the possibility of a Kondo state in MgCe alloys sufficient to investigate the electrical resistivity of a series of these alloys. Their results indicated that there was no Kondo anomaly in the resistivity. We shall show later that our magnetic studies indicate that they may not have carried their investigation to sufficiently low temperatures.
method. The anisotropy was measured by measuring the torque exerted on the crystal in a magnetic field. The results xl shown in Fig. I indicate that a Curie-Weiss law is obeyed above 20 K. The curvature in xL below 20 K is explained by the influence of the crystalline field. The anisotropy in magnetic susceptibility is large only at the lowest temperatures. At 1.5K xL = 8.40 X 10V6 while xl = 4.10 x 10” emu/gram. As the temperature is increased the anisotropy becomes smaller unuf at T = 3.6 K the anisotropy becomes zero then reverses sign. At T = 4.2 K xI = 4.83 x 10” while xn= 506 x lo-’ emu/~m. As the tempe~~e is increased this small anisotropy increases slightly in magnitude until about 20 K, then decreases, The anisotropy becomes too small to measure around 60 K. 3.CRYSTAL.FlRLDCALCULATION
The crystal field of the hcp Mg lattice can be represented by the Hamiltonian[6]
and its influence on the sixfoid degenerate 2F‘~,~ groundstate of the Ce’3 ion is to spht it into three doublets. Only the first two terms of the Hamiftoni~ are operative for the Ce ion, and these produce an energy splitting of A, and AZbetween the ground doublet and the higher two. We
2.EXPRRMEUTALREtZ%TS
Using high purity Mg and 993% pure Ce, several alloys of MgCe were grown in a graphite crucible by lowering the crucible throu~ a temperature gradient. The monocrystalline alloy for which magnetic susceptibility results are reported below had a Ce concentration of 0.36 atomic percent. The work of Hedgcock and Petrie[5] indicates that alloys of Ce in Mg form good solid solutions at low concentrations. The magnetic susceptibility xl, with the magnetic field perpendicular to the hexagonal crystalline axis of the Mg host, was measured by the usual Faraday Supported in part by a State University of New York Research Foundation Award.
Fig. 1. Inverse magnetic susceptibility x1-’ versus temperature for an 0.36 atomic percent monocrystalline M&e alloy with the magnetic field perpendicular to the hexagonal c-axis, The solid line is the calculated crystal field fit to the experimental points.
1223
C. R. BURRand R. G. PIRICH
1224
find that this crystal field splitting produces a magnetic susceptibility which can be written: N/3*g; (eeAdrT+ 9 + 25 eVAJkT) xi,= m
where 2 = 2(l+ e-AP+ e-4’“‘) By varying the constants &and But we were able to obtain the curve for xI shown in Fig. 1. We found it necessary to use a paramagnetic Curie temperature B = 1.42 K with both ~11 and xI to achieve the fits. The fit to XIabove 4.2 K was about as good above 4.2 K as for xI. The constants BZUand Ba used in this fit were 9.0 x 1O-3 and 10.8 x IO-‘K respectively. These produced an overall crystal field splitting of 3.2 K which is much smaller than usuafy obtained in metals. However, it is of the order of rna~~de of the tern~e~t~e 3.6 K at which the ~so~py changes sign and becomes small. Interestingly the reversed anisotropy is obtained above 4.2 K, it shows a slight peak around 15 K and does not become negligible until above 60 K in agreement with experiment. Although the general features are correct, the predicted anisotropy is too small in magnitude. However, below 4,2K the predicted magnetic susceptibility ~11deviates strongly from the experimental results. No evidence of magnetic orderiug is observed. We feel, therefore that the deviation of xi from the crystal field prediction may indicate a Kondo state for the Ce ion at very low temperature. 4.
INFLUENCE OF TIiEKONDO STATEON MAGNETICSUkKEFTIBILlTY
Dilute alloys of Lace and YCe have been shown to exhibit the Kondo effect[3,4]. There is a similarity between these alloys and the M&e system, p~icul~iy for YCe. Y~~urn is hexagonal as is Mg. The pe~endicuIar magnetic susceptibility ,Q of YCe shows little deviation from Curie-Weiss behavior [7j, neither does the xl of MgCe. The parallel susceptibility ~11of YCe is smaller than xl and deviates strongly from the crystal field prediction. Similar behavior occurs for xi of MgCe as can be seen in Fig. 2. Borchi and DeGennaro[3] have shown that a calculation of the crystal field effects on the magnetic susceptibility of a Kondo system enables a theoretical fit to x,, of YCe. The similarities with YCe led us to apply the c~c~ation of Borchi and DeGennaro to
Fig. 2. Magneticsusceptibilityxr of the same0.36atomic percent M&e alloy versus temperature. The experimental points deviate strongly from the crystal field prediction (solid curve) at the lowest temperatures. The dashed curve is the crystat field fit modified by the Borchi-DeGennaro cakxlation[3].
MgCe using the same Qe width D = 800 K. We used the crystal field splitting A = 3-2 K found from the fit to x1. and obtained a value for the parameter n(&)T = 0.14. As can be seen in Fig. 2 a surprisingly good fit to XI is obtained when our crystal field prediotiob is modified by the Borchi and DeGennaro calculation. 5.CONCLUSIONS
We have investigated the maipietic properties of dilute MgCe alloys and have determined that Ce is trivalent in, Mg and undergoes no co~~tion~ change as the temperature is varied. There is a crystalline field splitting of the 2F3,2ground state of the Ce+l ion which is about 3.2 K. There is a deviation of the exgerimental points from the crystal field prediction at the lowesi temperatures. It must be remembered that the magnetic susceptibility results alone are insufficient to indicate the presence of a Kondo state, but our results suggest that the search of Hedgcock and Petrie for a Rondo state in M&e alloys may not have been extended to su~cien~y low tem~ra~es. REFERENCE!3
1. 2. 3. 4. 5. 6.
Burr C. R., (To be published). Tsuchida T. and Wallace W. E., J. Chem. Phys. 43,381l (l%J). Borchi E. and De Gennaro S., Phys. Rev. B9, 209 (1974). De Gennaro S. and Borchi E., Phw. Rev. B9.4985W43. He&cock F. T. andPetrie B., &id J. F&y&48,1283(1970). Hut&& M. T., Solid State Physics Vol. 16 (Edited by F. Seitz and D. T~buR) p. 227. Academic Press, New York 0%4). 7. Sugawara T. and Yoshida S., 1. Low T. P!rys. 7, 657 (1971).
S&i.%
1975,
Vol. 36 pp. 1223-1224.PergamonPress. hinted in &eat B&in
MAGNETIC PROPERTIES OF DILUTE MgCe ALLOYS C. R. Bumt and R. G. PJRJCH Department of Physics, State University of New York at Binghamton,Binghamton,NY 13901,U.S.A. (Received 22 January
(1975)
Abstract-The magnetic susceptibility of mono~rystalline dilute MgCe alloys has been investigated. An anisotropic susceutibilitv was found and exblained as the consequence of a crystalline field spiitti~ of the ground state of about 3.2K: .
1.~ROD~ON Recent experiments on dilute alloys of Eu and Yb in Mg indicate that valence changes occur as the temperature is varied at atmospheric pressure[l]. It is also thought that certain alloys of Ce undergo valence alternations as a function of temperature[2] and we were interested in learning if dilute alloys of Ce in Mg might do this also. The results we describe below indicate that Ce is trivalent in Mg and that it undergoes no configurational change. The crystalline electric field in a metal has a large influence on the magnetic character of a rare earth ion at low tem~rat~e, often producing anisotropy and signiticant deviations from Curie-Weiss behavior. The magnetic measurements we have performed on a monocrystalline dilute alloy of Ce in Mg enable a determination of the crystal field in hfg. Although it should be much too oversimplified for a metal, simple crystal field calculations have proved remarkably effective in predicting the effect of the crystalline field in many alloys, and’this proves to be the case in MgCe alloys also. Interestingly, deviations of the experimental data from these crystal field predictions at the lowest temperatures, similar to those in known Kondo alloys YCe and Lace [3,41 suggest the possibility that Ce may be in a Kondo state at su~ciently low temperatures. In fact, several years ago Hedgcock and Petrie [S] thought the possibility of a Kondo state in MgCe alloys sufficient to investigate the electrical resistivity of a series of these alloys. Their results indicated that there was no Kondo anomaly in the resistivity. We shall show later that our magnetic studies indicate that they may not have carried their investigation to sufficiently low temperatures.
method. The anisotropy was measured by measuring the torque exerted on the crystal in a magnetic field. The results xl shown in Fig. I indicate that a Curie-Weiss law is obeyed above 20 K. The curvature in xL below 20 K is explained by the influence of the crystalline field. The anisotropy in magnetic susceptibility is large only at the lowest temperatures. At 1.5K xL = 8.40 X 10V6 while xl = 4.10 x 10” emu/gram. As the temperature is increased the anisotropy becomes smaller unuf at T = 3.6 K the anisotropy becomes zero then reverses sign. At T = 4.2 K xI = 4.83 x 10” while xn= 506 x lo-’ emu/~m. As the tempe~~e is increased this small anisotropy increases slightly in magnitude until about 20 K, then decreases, The anisotropy becomes too small to measure around 60 K. 3.CRYSTAL.FlRLDCALCULATION
The crystal field of the hcp Mg lattice can be represented by the Hamiltonian[6]
and its influence on the sixfoid degenerate 2F‘~,~ groundstate of the Ce’3 ion is to spht it into three doublets. Only the first two terms of the Hamiftoni~ are operative for the Ce ion, and these produce an energy splitting of A, and AZbetween the ground doublet and the higher two. We
2.EXPRRMEUTALREtZ%TS
Using high purity Mg and 993% pure Ce, several alloys of MgCe were grown in a graphite crucible by lowering the crucible throu~ a temperature gradient. The monocrystalline alloy for which magnetic susceptibility results are reported below had a Ce concentration of 0.36 atomic percent. The work of Hedgcock and Petrie[5] indicates that alloys of Ce in Mg form good solid solutions at low concentrations. The magnetic susceptibility xl, with the magnetic field perpendicular to the hexagonal crystalline axis of the Mg host, was measured by the usual Faraday Supported in part by a State University of New York Research Foundation Award.
Fig. 1. Inverse magnetic susceptibility x1-’ versus temperature for an 0.36 atomic percent monocrystalline M&e alloy with the magnetic field perpendicular to the hexagonal c-axis, The solid line is the calculated crystal field fit to the experimental points.
1223
C. R. BURRand R. G. PIRICH
1224
find that this crystal field splitting produces a magnetic susceptibility which can be written: N/3*g; (eeAdrT+ 9 + 25 eVAJkT) xi,= m
where 2 = 2(l+ e-AP+ e-4’“‘) By varying the constants &and But we were able to obtain the curve for xI shown in Fig. 1. We found it necessary to use a paramagnetic Curie temperature B = 1.42 K with both ~11 and xI to achieve the fits. The fit to XIabove 4.2 K was about as good above 4.2 K as for xI. The constants BZUand Ba used in this fit were 9.0 x 1O-3 and 10.8 x IO-‘K respectively. These produced an overall crystal field splitting of 3.2 K which is much smaller than usuafy obtained in metals. However, it is of the order of rna~~de of the tern~e~t~e 3.6 K at which the ~so~py changes sign and becomes small. Interestingly the reversed anisotropy is obtained above 4.2 K, it shows a slight peak around 15 K and does not become negligible until above 60 K in agreement with experiment. Although the general features are correct, the predicted anisotropy is too small in magnitude. However, below 4,2K the predicted magnetic susceptibility ~11deviates strongly from the experimental results. No evidence of magnetic orderiug is observed. We feel, therefore that the deviation of xi from the crystal field prediction may indicate a Kondo state for the Ce ion at very low temperature. 4.
INFLUENCE OF TIiEKONDO STATEON MAGNETICSUkKEFTIBILlTY
Dilute alloys of Lace and YCe have been shown to exhibit the Kondo effect[3,4]. There is a similarity between these alloys and the M&e system, p~icul~iy for YCe. Y~~urn is hexagonal as is Mg. The pe~endicuIar magnetic susceptibility ,Q of YCe shows little deviation from Curie-Weiss behavior [7j, neither does the xl of MgCe. The parallel susceptibility ~11of YCe is smaller than xl and deviates strongly from the crystal field prediction. Similar behavior occurs for xi of MgCe as can be seen in Fig. 2. Borchi and DeGennaro[3] have shown that a calculation of the crystal field effects on the magnetic susceptibility of a Kondo system enables a theoretical fit to x,, of YCe. The similarities with YCe led us to apply the c~c~ation of Borchi and DeGennaro to
Fig. 2. Magneticsusceptibilityxr of the same0.36atomic percent M&e alloy versus temperature. The experimental points deviate strongly from the crystal field prediction (solid curve) at the lowest temperatures. The dashed curve is the crystat field fit modified by the Borchi-DeGennaro cakxlation[3].
MgCe using the same Qe width D = 800 K. We used the crystal field splitting A = 3-2 K found from the fit to x1. and obtained a value for the parameter n(&)T = 0.14. As can be seen in Fig. 2 a surprisingly good fit to XI is obtained when our crystal field prediotiob is modified by the Borchi and DeGennaro calculation. 5.CONCLUSIONS
We have investigated the maipietic properties of dilute MgCe alloys and have determined that Ce is trivalent in, Mg and undergoes no co~~tion~ change as the temperature is varied. There is a crystalline field splitting of the 2F3,2ground state of the Ce+l ion which is about 3.2 K. There is a deviation of the exgerimental points from the crystal field prediction at the lowesi temperatures. It must be remembered that the magnetic susceptibility results alone are insufficient to indicate the presence of a Kondo state, but our results suggest that the search of Hedgcock and Petrie for a Rondo state in M&e alloys may not have been extended to su~cien~y low tem~ra~es. REFERENCE!3
1. 2. 3. 4. 5. 6.
Burr C. R., (To be published). Tsuchida T. and Wallace W. E., J. Chem. Phys. 43,381l (l%J). Borchi E. and De Gennaro S., Phys. Rev. B9, 209 (1974). De Gennaro S. and Borchi E., Phw. Rev. B9.4985W43. He&cock F. T. andPetrie B., &id J. F&y&48,1283(1970). Hut&& M. T., Solid State Physics Vol. 16 (Edited by F. Seitz and D. T~buR) p. 227. Academic Press, New York 0%4). 7. Sugawara T. and Yoshida S., 1. Low T. P!rys. 7, 657 (1971).