- Email: [email protected]
Critical broadening of the EPR line width in MnF2
Solid State Communications,
Vol.8, pp. 787—790, 1970.
Pergarnon Press.
Printed in Great Britain
CRITICAL BROADENING OF THE EPR LINE WIDTH IN MnF2* Mohindar S. Seehra Department of Physics and Astronomy, University of Rochester and Department of Physics, West Virginia University, Morgantown, West Virginia 26506t U.S.A. and T.G. Castner, Jr. Department of Physics and Astronomy, University of Rochester, Rochester, New York 14627 U.S.A.
The EPR line width in MnF2 was investigated in the range 68°Kto 380°K. The results are fit by the empirical relation All A(T T~)-Y + AH(cx~),where AH(cr) equals the constant high temperature line width. For H!~C y11= 1.17 ±0.03 vJith T~~ TN and for.HiC y~= 1.20 ±0.03 with T, = T~= 66.2 ±0.2°K. —
THE PHENOMENON of EPR line broadening near the Néel temperature of an antiferromagnet is interestfluctuations since it provides information theofcritical of spins. Theories on of the temperature dependence of this critical broadening of the EPR lin~ewidth in a uniaxial antiferromagnet have been developed by several authors.1 5A number of experimental measure-
differs substantially from the critical broadening of the F~nmrline width where ‘y 1ofwas 7 (The critical broadening the F’9 nmr observed. line width is also caused by the critical fluctuations of the Mn~*spins). Furthermore, the data of Burgiel and Strandberg indicates a reversal of the anisotropy of the line width between 77°K and room temperature. Thus although all the
•ments of the temperature dependence of the EPR line broadening in MnF(TN = 67.4°K), the classical example of an uniaxial antiferromagnet, have been made, however the results are not in
above experimental results qualitatively indicate critical broadening it seemed desirable to accurately obtain the temperature dependence of the MnF 2 EPR critical broadening in order to reexamine the validity of the theories.
good agreement with one another. The unpublished data of Geschwind and Jaccarino, and Hutchinson and Stout (as reported by Mon 2) are in disagreement with each other between 85°Kand TN. More 6 reported EPR recently and Strandberg line width~ürgiel measurements between room temperature and TN. They characterized the temperaturedependent portion of the line width by a dependence (T TN) ~ and reported a y 3/8 which is in poor agreement with the theories and —
*
Work supported in part by ONR/•CNA.
tPresent address: West Virginia University, Morgantown, West Virginia 26506 U.S.A.
787
In this paper we report EPR line width measurements on MnF2 for H C-axismeasurements and Hi. Caxis between 68°Kand 380°K.The were made at 9 GHz using bolometer detection and 10Hz field modulation. A resonant cavity was not employed in order to avoid broadening the EPR line width due to magnetic losses. Instead a shorted waveguide was used. Several sample sizes were tried to be certain the size effect8 was negligible. The MnF 2 single crystal was obtained from Ventron Electronics Corporation. Temperatures between 77°Kand dry ice temperature were obtained by a heater. The temperature
788
CRITICAL BROADENING OF THE EPR LINE WIDTH IN MnF
2
Vol.8, No. 10
50~
(a)
(b)
~Ioo
I00<•
,-t- ~o I
bc
...“~I
I
(T—~)
K
6
I
10
(T—1~) ‘K
~I
0
(T—T~ K
5
~
LH
II
of the line width is plotted against (T — T~,)on FIG. 2. (a) (AH)~, the temperatur~dependent part a log—log plot. The data is for H I C where (All) ~,= (All — 290)oe. The solid line is the best fit. (b) A similar plot for H i. C where (AH) ~ = (AH — 275)oe is plotted against (T— Ti). For the best fit Tk = (66.2 ±O.2)°K. The vertical
C
.,
•
.
.
.
.
.
scale is the same as in (a). 2
3
4
5
6
T/ TN
FIG. 1. (a) The experimental peak to peak line width All plotted against (T — TN) for H C and Hi. C. For comparison the data of other investigators for H C is also shown: _.. Geschwind and Jaccarino2 ., Hutchinson and Stout 2~, --x- - Burgiel and Strandberg ~., Solid lines through points correspond to this work. (b) Comparison between experimental results and theory for H C. Solid line: Tanaka’s Theory4 for b.c.c. lattice., dotted line: Mon’s Theory~., open circles are data points of this work.
2,6 Above room temperature the line width for H isC.essentially independent of temperature
and is 290 ±5oe for H C and 275 ±5oe for Hk C. The H C value is slightly smaller than that reported by Gulley, el a!. 10 As the temperature is lowered the line broadens in both directions, however the line width for H C remains greater than that for Hi. C at all temperatures contrary to earlier observations.6 Below (T — 7~) 20~K the anisotropy in the line width between the two directions increases, as in the behavior of the F ‘~ nmr line width,7 with AH(H 1 C) -‘~ 1.7
was measured with a calibrated copper—constantan thermocouple. The line widths reported in this paper are the peak-to-peak magnetic field separation in the absorption derivative. The Lorentzian line shape was not observed to change between 380°K and 67.9°K, however for H C the line shape becomes asymmetrical for (T — TN) < 2°Kand the correct value of the line width becomes less certain. The line shape for H i. C was reasonably symmetrical at the lowest temperature theasured, suggesting the width diverges at a temperature T < TN, as predicted
AH(H
by Moriya.9
shows the comparison between the theories24 for the H It C case and our data by plotting AH/AH(cx~)vs. T:/TN. The theoretical expressions
Figure la shows our EPR line width
.L C) for (T — TN) 1°K. The temperature dependence of our data is noticeably stronger than that of Burgiel and Strandberg and that of Hutchinson and Stout, and slightly stronger than than the data of Geschwind and Jaccarino, however the earlier data is not extensive enough to determine an explicit temperature dependence. For small (T — TN) the lower values of Burgiel and Strandberg (measurements at 35 GHz) might result from the higher ratio of Zeeman energy to anisotropy energy, the magnetic field possibly inhibiting the critical broadening. Figure lb
AH~,(AH,, 1, = (1/3) 1~’2 times the total halfintensity width of the Lorentzian absorption curve) as a function of (T — TN) for H It C and Hi C, along with the data reported previously
are varying more rapidly with temperature than the experimental results for large T/TN, while they are varying slightly more slowly for small T/T~, indicating the lack of agreement of the theoretical and experimental temperature dependences.
Vol.8, No. 10
CRITICAL BROADENING OF THE EPR LINE WIDTH IN MnF2
Our line width measurements can be fit to within ±5% by the relation 7+empirical AH(cn), where AH(m) is the AK = A(ThighT0) constant temperature line width given above, Figure 2 shows the temperature-dependent portion of All, namely (AH) ~= AH AH(tx), for both field directions plotted against (T T~)where T 0 = T11 ~ TN for H I C and T~= T~< TN for H .i. C. of The uncertainty in (AK) is theT~) same100°K. order magnitude as (AH)T forr (T For (T T~)< 100°Kthe data fits a straight line for Hi. C and also for H C except for —
—
—
—
—
789
for spin fluctuations with slightly smaller values of y. and y,~.From ofa theoretical standpoint the critical broadening the EPR line width represents an average over all wave number spin fluctuations and the result might be expected to differ from the staggered susceptibilities, yet
these results indicate the differences are small. For a simple cubic lattice ygas= Fisher and is 2 have calculated 1.23, which
Burford’ close to the y’s inferred from the EPR line width, however the model of a cubic system is not strictly applicable to MnF 3.
(T TN) < 2°Kwhere the line is highly asymmetrical. The fit yields y,,,= 1.17 ±0.03 and = 1.20 ±0.03 with T~= 66.2 ±0.2°K.This simple power law dependence for (AH) ~ is to be compared with the temperature dependence of the staggered susceptibilities found by Schulhof et al,” who measured the critical
In conclusion the temperature dependence of the critical broadening of the EPR line width of MnF2 has shown to closely follow a power law (T T~)~’ similar to the critical broadening similar to the critical broadening of the nmr line width for small (T TN) and also analogous to
magnetic scattering of neutrons between 77°K and TN in MnF2. They found the staggered mode susceptibilities for spin fluctuations follow the laws ~ (T — TN )-7~i with y,, = 1.24 ±0.02
the criUcal spin fluctuations of the staggered mode susceptibilities, but with slightly smaller exponents. The present results disagree quantitatively with previous experimental EPR line
and X~ (T — T~)~‘~with yj = 1.47 ±0.1 and T~= 66°K. The temperature-dependent portion of All is surprising similar to the temperature dependence of the staggered mode susceptibilities
width measurements. The present theories of the EPR line broadening due to critical fluctuations cannot explain the data quantitatively.
—
—
—
REFERENCES 1.
MORI H. and KA’VASAKI K., Prog. theor. Phys. 28, 971 (1962).
2.
MORI H., Prog. theor. Phys. 30, 578 (1963).
3.
TOMITA K. and TANAKA M., Prog. theor. Phys. 33, 1(1965). TOMITA K., Proc.
4.
Magnetism, Nottingham, 103 (1964). TANAKA M., J. Phys. Soc. Japan 27, 781 (1969).
5.
KAV1IASAKI K., Prog. theor. Phys. 39, 285 (1968).
6.
BURGIEL J.C. and STRAND3ERG M.W.P., J. Phys. Chem. Solids 26, 865 (1965).
7.
HELLER P. and BENEDEK G.B., Phys. Rev. Leti. 8, 428 (1962).
8.
10.
SEEHRA M.S., Rev. scient lnstr. 39, 1044 (1968). See also SEEHRA M.S. and CASTNER T.G., Jr., Phys. kondens. Materie 7, 185 (1968). MORIYA T., Prog. theor. Phys. 28, 371 (1962). See also SHULMAN R.G. and JACCARINO V., Phys. Rev. 108, 1219 (1957). GULLEY J.E., SILBERNAGEL B.G. and JACCARINO V., J. appi. Phys. 40, 1318 (1969).
11.
SCHULHOF M.P., HELLER P., NATHANS R. and LINZ A., (to be published). A preliminary report
12.
was given by SCI-HJLHOF M.P., HELLER P. and NATHANS R., Bull. Am. Phys. Soc. 14, 738 (1969). FISHER M.E. and BURFORD R., Phys. Rev. 156, 583 (1967).
9.
mt.
Conf.
790
CRITICAL BROADENING OF THE EPR LINE WIDTH IN MnF2 Die Linienbreite der paramagnetischen Resonanz von MnF2 wurde in 7+ AH(co), wobei Temperaturbereich von 68°Kbis 380°K untersucht. Die Ergebnisse erfillien die empirische Beziehung AK = A[T — TC)~ AH(cx) gleich der konstanten Hochtempatur-Linienbreite ist. Für HI! C isty 1,= 1.17 ±0.03 mit T~~ TN und für HiC ist = 1.20 ±0.03 mit T~ = T1 = 66.2 ±0.2°K.
Vol.8, No. 10
Vol.8, pp. 787—790, 1970.
Pergarnon Press.
Printed in Great Britain
CRITICAL BROADENING OF THE EPR LINE WIDTH IN MnF2* Mohindar S. Seehra Department of Physics and Astronomy, University of Rochester and Department of Physics, West Virginia University, Morgantown, West Virginia 26506t U.S.A. and T.G. Castner, Jr. Department of Physics and Astronomy, University of Rochester, Rochester, New York 14627 U.S.A.
The EPR line width in MnF2 was investigated in the range 68°Kto 380°K. The results are fit by the empirical relation All A(T T~)-Y + AH(cx~),where AH(cr) equals the constant high temperature line width. For H!~C y11= 1.17 ±0.03 vJith T~~ TN and for.HiC y~= 1.20 ±0.03 with T, = T~= 66.2 ±0.2°K. —
THE PHENOMENON of EPR line broadening near the Néel temperature of an antiferromagnet is interestfluctuations since it provides information theofcritical of spins. Theories on of the temperature dependence of this critical broadening of the EPR lin~ewidth in a uniaxial antiferromagnet have been developed by several authors.1 5A number of experimental measure-
differs substantially from the critical broadening of the F~nmrline width where ‘y 1ofwas 7 (The critical broadening the F’9 nmr observed. line width is also caused by the critical fluctuations of the Mn~*spins). Furthermore, the data of Burgiel and Strandberg indicates a reversal of the anisotropy of the line width between 77°K and room temperature. Thus although all the
•ments of the temperature dependence of the EPR line broadening in MnF(TN = 67.4°K), the classical example of an uniaxial antiferromagnet, have been made, however the results are not in
above experimental results qualitatively indicate critical broadening it seemed desirable to accurately obtain the temperature dependence of the MnF 2 EPR critical broadening in order to reexamine the validity of the theories.
good agreement with one another. The unpublished data of Geschwind and Jaccarino, and Hutchinson and Stout (as reported by Mon 2) are in disagreement with each other between 85°Kand TN. More 6 reported EPR recently and Strandberg line width~ürgiel measurements between room temperature and TN. They characterized the temperaturedependent portion of the line width by a dependence (T TN) ~ and reported a y 3/8 which is in poor agreement with the theories and —
*
Work supported in part by ONR/•CNA.
tPresent address: West Virginia University, Morgantown, West Virginia 26506 U.S.A.
787
In this paper we report EPR line width measurements on MnF2 for H C-axismeasurements and Hi. Caxis between 68°Kand 380°K.The were made at 9 GHz using bolometer detection and 10Hz field modulation. A resonant cavity was not employed in order to avoid broadening the EPR line width due to magnetic losses. Instead a shorted waveguide was used. Several sample sizes were tried to be certain the size effect8 was negligible. The MnF 2 single crystal was obtained from Ventron Electronics Corporation. Temperatures between 77°Kand dry ice temperature were obtained by a heater. The temperature
788
CRITICAL BROADENING OF THE EPR LINE WIDTH IN MnF
2
Vol.8, No. 10
50~
(a)
(b)
~Ioo
I00<•
,-t- ~o I
bc
...“~I
I
(T—~)
K
6
I
10
(T—1~) ‘K
~I
0
(T—T~ K
5
~
LH
II
of the line width is plotted against (T — T~,)on FIG. 2. (a) (AH)~, the temperatur~dependent part a log—log plot. The data is for H I C where (All) ~,= (All — 290)oe. The solid line is the best fit. (b) A similar plot for H i. C where (AH) ~ = (AH — 275)oe is plotted against (T— Ti). For the best fit Tk = (66.2 ±O.2)°K. The vertical
C
.,
•
.
.
.
.
.
scale is the same as in (a). 2
3
4
5
6
T/ TN
FIG. 1. (a) The experimental peak to peak line width All plotted against (T — TN) for H C and Hi. C. For comparison the data of other investigators for H C is also shown: _.. Geschwind and Jaccarino2 ., Hutchinson and Stout 2~, --x- - Burgiel and Strandberg ~., Solid lines through points correspond to this work. (b) Comparison between experimental results and theory for H C. Solid line: Tanaka’s Theory4 for b.c.c. lattice., dotted line: Mon’s Theory~., open circles are data points of this work.
2,6 Above room temperature the line width for H isC.essentially independent of temperature
and is 290 ±5oe for H C and 275 ±5oe for Hk C. The H C value is slightly smaller than that reported by Gulley, el a!. 10 As the temperature is lowered the line broadens in both directions, however the line width for H C remains greater than that for Hi. C at all temperatures contrary to earlier observations.6 Below (T — 7~) 20~K the anisotropy in the line width between the two directions increases, as in the behavior of the F ‘~ nmr line width,7 with AH(H 1 C) -‘~ 1.7
was measured with a calibrated copper—constantan thermocouple. The line widths reported in this paper are the peak-to-peak magnetic field separation in the absorption derivative. The Lorentzian line shape was not observed to change between 380°K and 67.9°K, however for H C the line shape becomes asymmetrical for (T — TN) < 2°Kand the correct value of the line width becomes less certain. The line shape for H i. C was reasonably symmetrical at the lowest temperature theasured, suggesting the width diverges at a temperature T < TN, as predicted
AH(H
by Moriya.9
shows the comparison between the theories24 for the H It C case and our data by plotting AH/AH(cx~)vs. T:/TN. The theoretical expressions
Figure la shows our EPR line width
.L C) for (T — TN) 1°K. The temperature dependence of our data is noticeably stronger than that of Burgiel and Strandberg and that of Hutchinson and Stout, and slightly stronger than than the data of Geschwind and Jaccarino, however the earlier data is not extensive enough to determine an explicit temperature dependence. For small (T — TN) the lower values of Burgiel and Strandberg (measurements at 35 GHz) might result from the higher ratio of Zeeman energy to anisotropy energy, the magnetic field possibly inhibiting the critical broadening. Figure lb
AH~,(AH,, 1, = (1/3) 1~’2 times the total halfintensity width of the Lorentzian absorption curve) as a function of (T — TN) for H It C and Hi C, along with the data reported previously
are varying more rapidly with temperature than the experimental results for large T/TN, while they are varying slightly more slowly for small T/T~, indicating the lack of agreement of the theoretical and experimental temperature dependences.
Vol.8, No. 10
CRITICAL BROADENING OF THE EPR LINE WIDTH IN MnF2
Our line width measurements can be fit to within ±5% by the relation 7+empirical AH(cn), where AH(m) is the AK = A(ThighT0) constant temperature line width given above, Figure 2 shows the temperature-dependent portion of All, namely (AH) ~= AH AH(tx), for both field directions plotted against (T T~)where T 0 = T11 ~ TN for H I C and T~= T~< TN for H .i. C. of The uncertainty in (AK) is theT~) same100°K. order magnitude as (AH)T forr (T For (T T~)< 100°Kthe data fits a straight line for Hi. C and also for H C except for —
—
—
—
—
789
for spin fluctuations with slightly smaller values of y. and y,~.From ofa theoretical standpoint the critical broadening the EPR line width represents an average over all wave number spin fluctuations and the result might be expected to differ from the staggered susceptibilities, yet
these results indicate the differences are small. For a simple cubic lattice ygas= Fisher and is 2 have calculated 1.23, which
Burford’ close to the y’s inferred from the EPR line width, however the model of a cubic system is not strictly applicable to MnF 3.
(T TN) < 2°Kwhere the line is highly asymmetrical. The fit yields y,,,= 1.17 ±0.03 and = 1.20 ±0.03 with T~= 66.2 ±0.2°K.This simple power law dependence for (AH) ~ is to be compared with the temperature dependence of the staggered susceptibilities found by Schulhof et al,” who measured the critical
In conclusion the temperature dependence of the critical broadening of the EPR line width of MnF2 has shown to closely follow a power law (T T~)~’ similar to the critical broadening similar to the critical broadening of the nmr line width for small (T TN) and also analogous to
magnetic scattering of neutrons between 77°K and TN in MnF2. They found the staggered mode susceptibilities for spin fluctuations follow the laws ~ (T — TN )-7~i with y,, = 1.24 ±0.02
the criUcal spin fluctuations of the staggered mode susceptibilities, but with slightly smaller exponents. The present results disagree quantitatively with previous experimental EPR line
and X~ (T — T~)~‘~with yj = 1.47 ±0.1 and T~= 66°K. The temperature-dependent portion of All is surprising similar to the temperature dependence of the staggered mode susceptibilities
width measurements. The present theories of the EPR line broadening due to critical fluctuations cannot explain the data quantitatively.
—
—
—
REFERENCES 1.
MORI H. and KA’VASAKI K., Prog. theor. Phys. 28, 971 (1962).
2.
MORI H., Prog. theor. Phys. 30, 578 (1963).
3.
TOMITA K. and TANAKA M., Prog. theor. Phys. 33, 1(1965). TOMITA K., Proc.
4.
Magnetism, Nottingham, 103 (1964). TANAKA M., J. Phys. Soc. Japan 27, 781 (1969).
5.
KAV1IASAKI K., Prog. theor. Phys. 39, 285 (1968).
6.
BURGIEL J.C. and STRAND3ERG M.W.P., J. Phys. Chem. Solids 26, 865 (1965).
7.
HELLER P. and BENEDEK G.B., Phys. Rev. Leti. 8, 428 (1962).
8.
10.
SEEHRA M.S., Rev. scient lnstr. 39, 1044 (1968). See also SEEHRA M.S. and CASTNER T.G., Jr., Phys. kondens. Materie 7, 185 (1968). MORIYA T., Prog. theor. Phys. 28, 371 (1962). See also SHULMAN R.G. and JACCARINO V., Phys. Rev. 108, 1219 (1957). GULLEY J.E., SILBERNAGEL B.G. and JACCARINO V., J. appi. Phys. 40, 1318 (1969).
11.
SCHULHOF M.P., HELLER P., NATHANS R. and LINZ A., (to be published). A preliminary report
12.
was given by SCI-HJLHOF M.P., HELLER P. and NATHANS R., Bull. Am. Phys. Soc. 14, 738 (1969). FISHER M.E. and BURFORD R., Phys. Rev. 156, 583 (1967).
9.
mt.
Conf.
790
CRITICAL BROADENING OF THE EPR LINE WIDTH IN MnF2 Die Linienbreite der paramagnetischen Resonanz von MnF2 wurde in 7+ AH(co), wobei Temperaturbereich von 68°Kbis 380°K untersucht. Die Ergebnisse erfillien die empirische Beziehung AK = A[T — TC)~ AH(cx) gleich der konstanten Hochtempatur-Linienbreite ist. Für HI! C isty 1,= 1.17 ±0.03 mit T~~ TN und für HiC ist = 1.20 ±0.03 mit T~ = T1 = 66.2 ±0.2°K.
Vol.8, No. 10