Phase boundaries near the bicritical point of MnF2

Volume 57A, number 5

PHYSICS LETTERS

12 July 1976

PHASE BOUNDARIES NEAR THE BICRITICAL POINT OF MnF2

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Y. SHAPIRA and C.C. BECERRA * Francis Bitter National Magnet Laboratory, ** Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA Received 17 May 1976 Phase boundaries near the bicritical point (Tb = 64.74 ±0.01 K, Hb = 118.45 + 0.4 kOe) of the uniaxial antiferroinagnet MnF2 ~ ere redetermined with higher precision from ultrasonic attenuation measurements. The results are compared with recent theories of Fisher et at.

For a simple antiferromagnet the phase diagram in the temperature-field (T-H) plane consists of three phases: paramagnetic (P), antiferromagnetic (AF), and spin-flop (SF). Recently the boundaries near the bicritical point (Tb, Hb), where the three phases coexist, have attracted considerable attention [1,2] According to [1] ,at (Tb,Hb) both the P-AF boundary, T~’~(H), and the P-SF boundary, Tc’(H), are the tangent to the AF-SF boundary T(HSf). The predicted equations Tc’(H) and Ta” (H) near= (Tb, Hb) 2 H~forpt]/[t +q~H2 J-I~)]~ ~ ~ are (1) .

~H

respectively, where t = (Tc”° Tb)/Tb and p = Tb (dHsfZ/dflb. The theoretical values for a iiniaxial antiferromagnet with cylindrical symmetry (n = 3) are = 1.25, w 9Tb) 2.51, and q =symmetr~’ (S/ (dTc’7dH )H 0.1/w~1 For=orthohombic (n = 2), Ø 1.18,Q 1,andq (2/3Tb)(dTC°/d.H )H=o. The parameter w 11 is not universal. In this letter new data for the phase boundaries of the uniaxial antiferromagnet MnF2 are compared with eq. (1). These data are more accurate than those reported earlier by our groups [3,4] allowing a comparison with the detailed predictions in [1]. Accurate data for MnF2 were presented recently by King and Rohrer [5] but for a more limited field range. Phase transitions were determined ultrasonically, as in [3]. Two improvements introduced in the pre-

sent work were: 1) higher precision in T~(H),varying between 10 and 25 mK from run to run; 2) a rotating sample holder which allowed Hto be aligned parallel to the [001] axis to within 0.5°by maximizing the sharp attenuation spike at HSf [6] With this alignment, the pike at HSf was observed up to temperatures T/Tb 0.997. Most measurements were made on sample No. 1 with TN Tc”(O) = (67.30 ±0.015) K, but some were made on sample No. 2 (used also in [4]) with TN =absolute (67.31 calibration ±0.015) K.ofAn 0.02 K in the theuncertainty platinum of resistance thermometer is not included. Fig. 1. shows the data for all the runs, corrected for the demagnetizing field. These give p 1.0 X 1010 0e2, (dTc°IdH2)H_o= (1.60 ±0.05) X 10 10 K/0e2 for sample 1 and (1.53 ±0.04) X 10 10 K/0e2 for sample 2. The 10% uncertainty in p has a negligible .

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supported in part by a joint grant from the National Science Foundation (USA) and the Conseiho Nacional de Pesquisas (Brasil). On leave from the University of S~’oPaulo. Supported by Fundac~ode Amparo a Pesquisa do Estado de STo Paulo, Brasil. Supported by the National Science Foundation.

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T (K) Fig. 1. Overall view of the phase boundaries for MnF2, with H I [001]. Data points near (Tb, Hb) were deleted for clarity.

483

Volume 57A, numberS

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PHYSICS LETTERS

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Fig. 2. Results of all runs for the phase boundaries near the bicritical point. The curves are type 2 fits for n = 2 and n = 3 (see text).

effect on the fits below. Fig. 2 shows all the data near (Tb, Hb). The results of the best run, in which Ta” (H) and Tc’(H)were determined with a precision of ±10 mK, are presented in fig. 3. Inspection of all data gives, Hb (118.45 + 0.4) kOe, and Tb (64.74 + 0.0]) K. The uncertainty in Hb reflects a scatter from run to run and an uncertainty in the field calibration, The results of each run and of all runs combined, for H~’ 105 kOe, were fitted to eq. (1). Three types of fits were used. In type 1, 0 and Q were taken from theory, p and Hb from experiment, and q, w11 and Tb were allowed to vary. All such fits gave 64.73
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12 July l9~76

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64.8 64.9 1(K) 1’ig. 3. Results of the best run for th phase boundaries neat (Tb, Hb). The curve isa type 1 fit for n 3; For this fit, 0.72 X l0_i2 Oe q=

0.68
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References

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[1] M. Fisher, ALP Conf. Proc. 24 (1975) 273; Phys. Rev. Lett. 34(1975)1634. [2] H. Rohrer, Phys. Rev. Lett. 34 (1975) 1638; N.F. Oliveira Jr., A. Paduan Filho and SR. Salinas, Phys. Lett. 55A (1975) 293. [3] Y. Shapira and S. Foner, Phys. Rev. B 1(1970) 3083.

[41 Y. Shapira and R.D. Yacovitch, AlP Conf. Proc. 1976, to be published.

[5] A.R. King and H. Rohrer, AlP Conf. Proc. 1976 (to be published). [61Y. Shapira and J. Zak, Phys. Rev. 170 (1968) 503.