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Magnetic susceptibility of RbMnF3
Volume 39A, number 1
PHYSICS LETTERS
MAGNETIC
10April 1972
SUSCEPTIBILITY
OF RbMnF 3
E.E. BRAGG* and M.S. S E E H R A t
Department of Physics, West Virginia University Morgantown, West Virginia 26506, U.S.A. Received 15 February 1972 Magnetic susceptibility measurements in the Heisenberg antiferromagnet RbMnF 3 are reported between 55 and 300 °. Comparison with the high-temperature series calculations of Rushbrooke and Wood gives J = 3.37 _+0.05°K.
Magnetic properties of RbMnF 3 have attracted considerable attention since this system is considered to be the ideal example of Heisenberg antiferromagnet [1]. In this paper we report the first measurements of the static magnetic susceptibility × in this material. The data above the N6el temperature T N are analysed using the high-temperature series calculations of Rushbrooke and Wood [2, 3]. Magnetic susceptibility measurements were made by a home-designed, modified form of Foner-type vibrating sample magnetometer [4]. The details of this magnetometer will be published elsewhere [5]. The magnetometer was calibrated using a single crystal disc of nickel and the calibration was verified by measuring the temperature dependence o f X in MnF 2 between 52°K and 300°K and comparing this with the published data on MnF 2 [6]. The single crystal of RbMnF 3 weighing 0.502 g was obtained from Semi Elements Inc. Measurements were made in a field of 3 kOe. Since × in RbMnF 3 is isotropic above T N, the crystal was oriented in an arbitrary direction. The absolute and the relative accuracy o f X is estimated to be + 3% and -+ 1% respectively. Magnetic susceptibility of RbMnF 3, between 80°K and 300°K is shown in fig. 1. The susceptibility between 80°K and 55°K remained temperature independent and is not shown in the figure. The maximum in X occurs at a temperature about 6% higher than the known T N ~ 83.0°K [1]. This is to be compared with the theoretical value of 9.8% for the S.C. [sing lattice [7]. * NDEA Fellow I Supported in part by a summer grant from the West Virginia University.
,g2
44
-
.'.,........
:
60 . v..,4t
2C0
.
TN
.
I
IL~O
,
.
,
I
,
,
,
160
l
,
200
,
,
I
240
,
~
,
.
44
I
280
Temperature (*K)
Fig. 1. Magnetic susceptibility x (right hand scale) and (x)-I =
NgZtaO2/×J (left hand scale) plotted as a function of temperature. The solid curve is drawn using eq. (1). The experimental points are normalized using J = 3.37°K and g = 1.975. The diamagnetic contribution to x has been neglected since it is negligible [81. The temperature-dependent paramagnetic susceptibility × for a Heisenberg antiferromagnet (with nearest neighbor exchange o f the form Hex = - 2 , / S I • S/) has been calculated by Rushbrooke and Wood [2, 3] for a general lattice and general spin using the hightemperature series expansion method. Their expression for the simple cubic lattice (z=6) and spin S = 5/2 antiferromagnet reduces to 6
Ng2IjoZs(s+ l)[×J = 30 ~,, (-l)"b,,/O"
(1)
I1---0
with b 0 = !, b I = - 3 5 . 0 , b 2 = 221.7, b 3 = - 6 0 8 . 2 , b 4 = 26 049.6, b 5 = - 2 1 0 986.3 and b 6 = - 1 2 788 436.0. Here 0 = kT/J, N = number of spins/g, 29
Volume 39A, number 1
PIIYSICS LETTERS
/x~ = Bohr magneton and X is measured in emu/g. The calculated inverse reduced susceptibility 1 / ~ = Ng21a#2/XJ using eq. ( I ) is p l o t t e d against temperature in fig. 1. For c o m p a r i s o n with the data, the value o f g and J was varied. Variation o f J affects the slope whereas variation o f g moves the curve up or down. For best agreement we find J = 3.37 -+ 0 . 0 5 K and g ; 1,975. Within our e x p e m n e n t error of X this value o f g agrees with the experimental value of 1.997 as measured by ESR. Our value o f J is in excellent agreement with thal obtained from the analysis o f the spin wave spectrum o f R b M n F 3 at 4.2°K which gave J = 3.4 -+ 0 . 3 ' K [81. We note that the fit to the high-temperature series has been made for 0 > 25. This and the fact that we are using the series for X-1 rather than X itself makes our m e t h o d equivalent to that o f Danielien and Stevens
30
10April 1972
J9]. This has also been pointed out by R u s h b r o o k e and Wood [3].
R~:ferences [l] D.T. Teaney, M.J. Ereiser and R.W.tt. Stevenson, Phys, Rev. Lett. 9 (1962) 212. 121 G,S. Rushbrooke and P.J. Wood, Mol. Phys. 1 (1958) 257. [31 G.S. Rushbrooke and P.J. Wood, Mol. Phys. 6 I1963~ 409. 14J S. l:oner, Rev. Sci, Instr. 30 (19591 548. 151 M,N. Seehra and E.E. Bragg, to be published. J6] S. boner, J. Phys. Radium 20 (1959) 336. [7l M,E. l'isher and M.I:. Sykes, Physica 28 (1962) 939, 181 C.(,. Windsor and R.W.tl. Stevenson, Proc. Phys. Soc. (London) 87 (1966) 501. 19l A. Danielian and K.W.II. Stevens, Proc. Phys. Soc, (London) 77 (1961) 124.
PHYSICS LETTERS
MAGNETIC
10April 1972
SUSCEPTIBILITY
OF RbMnF 3
E.E. BRAGG* and M.S. S E E H R A t
Department of Physics, West Virginia University Morgantown, West Virginia 26506, U.S.A. Received 15 February 1972 Magnetic susceptibility measurements in the Heisenberg antiferromagnet RbMnF 3 are reported between 55 and 300 °. Comparison with the high-temperature series calculations of Rushbrooke and Wood gives J = 3.37 _+0.05°K.
Magnetic properties of RbMnF 3 have attracted considerable attention since this system is considered to be the ideal example of Heisenberg antiferromagnet [1]. In this paper we report the first measurements of the static magnetic susceptibility × in this material. The data above the N6el temperature T N are analysed using the high-temperature series calculations of Rushbrooke and Wood [2, 3]. Magnetic susceptibility measurements were made by a home-designed, modified form of Foner-type vibrating sample magnetometer [4]. The details of this magnetometer will be published elsewhere [5]. The magnetometer was calibrated using a single crystal disc of nickel and the calibration was verified by measuring the temperature dependence o f X in MnF 2 between 52°K and 300°K and comparing this with the published data on MnF 2 [6]. The single crystal of RbMnF 3 weighing 0.502 g was obtained from Semi Elements Inc. Measurements were made in a field of 3 kOe. Since × in RbMnF 3 is isotropic above T N, the crystal was oriented in an arbitrary direction. The absolute and the relative accuracy o f X is estimated to be + 3% and -+ 1% respectively. Magnetic susceptibility of RbMnF 3, between 80°K and 300°K is shown in fig. 1. The susceptibility between 80°K and 55°K remained temperature independent and is not shown in the figure. The maximum in X occurs at a temperature about 6% higher than the known T N ~ 83.0°K [1]. This is to be compared with the theoretical value of 9.8% for the S.C. [sing lattice [7]. * NDEA Fellow I Supported in part by a summer grant from the West Virginia University.
,g2
44
-
.'.,........
:
60 . v..,4t
2C0
.
TN
.
I
IL~O
,
.
,
I
,
,
,
160
l
,
200
,
,
I
240
,
~
,
.
44
I
280
Temperature (*K)
Fig. 1. Magnetic susceptibility x (right hand scale) and (x)-I =
NgZtaO2/×J (left hand scale) plotted as a function of temperature. The solid curve is drawn using eq. (1). The experimental points are normalized using J = 3.37°K and g = 1.975. The diamagnetic contribution to x has been neglected since it is negligible [81. The temperature-dependent paramagnetic susceptibility × for a Heisenberg antiferromagnet (with nearest neighbor exchange o f the form Hex = - 2 , / S I • S/) has been calculated by Rushbrooke and Wood [2, 3] for a general lattice and general spin using the hightemperature series expansion method. Their expression for the simple cubic lattice (z=6) and spin S = 5/2 antiferromagnet reduces to 6
Ng2IjoZs(s+ l)[×J = 30 ~,, (-l)"b,,/O"
(1)
I1---0
with b 0 = !, b I = - 3 5 . 0 , b 2 = 221.7, b 3 = - 6 0 8 . 2 , b 4 = 26 049.6, b 5 = - 2 1 0 986.3 and b 6 = - 1 2 788 436.0. Here 0 = kT/J, N = number of spins/g, 29
Volume 39A, number 1
PIIYSICS LETTERS
/x~ = Bohr magneton and X is measured in emu/g. The calculated inverse reduced susceptibility 1 / ~ = Ng21a#2/XJ using eq. ( I ) is p l o t t e d against temperature in fig. 1. For c o m p a r i s o n with the data, the value o f g and J was varied. Variation o f J affects the slope whereas variation o f g moves the curve up or down. For best agreement we find J = 3.37 -+ 0 . 0 5 K and g ; 1,975. Within our e x p e m n e n t error of X this value o f g agrees with the experimental value of 1.997 as measured by ESR. Our value o f J is in excellent agreement with thal obtained from the analysis o f the spin wave spectrum o f R b M n F 3 at 4.2°K which gave J = 3.4 -+ 0 . 3 ' K [81. We note that the fit to the high-temperature series has been made for 0 > 25. This and the fact that we are using the series for X-1 rather than X itself makes our m e t h o d equivalent to that o f Danielien and Stevens
30
10April 1972
J9]. This has also been pointed out by R u s h b r o o k e and Wood [3].
R~:ferences [l] D.T. Teaney, M.J. Ereiser and R.W.tt. Stevenson, Phys, Rev. Lett. 9 (1962) 212. 121 G,S. Rushbrooke and P.J. Wood, Mol. Phys. 1 (1958) 257. [31 G.S. Rushbrooke and P.J. Wood, Mol. Phys. 6 I1963~ 409. 14J S. l:oner, Rev. Sci, Instr. 30 (19591 548. 151 M,N. Seehra and E.E. Bragg, to be published. J6] S. boner, J. Phys. Radium 20 (1959) 336. [7l M,E. l'isher and M.I:. Sykes, Physica 28 (1962) 939, 181 C.(,. Windsor and R.W.tl. Stevenson, Proc. Phys. Soc. (London) 87 (1966) 501. 19l A. Danielian and K.W.II. Stevens, Proc. Phys. Soc, (London) 77 (1961) 124.