The antiferromagnetism of manganese copper alloys By G. E. Bacon, A H, arwell and I. W. Dunmur, J. H. Smith and R. Street, The University, Sheffield (i Communicated by W. Sucksmith, F.R—Received 31 January 1957— Revised 10 April 1957) Manganese-rich y phase alloys of manganese + copper have been investigated by neutron and X-ray diffraction techniques, and the temperature variations of magnetic susceptibility and electrical resistivity have been measured. The disappearance of long-range antiferromagnetic ordering has been correlated with the face-centred-tetragonal -> face-centred-cubic marten sitic transformation of these alloys. The Neel temperatures and the magnetic moments of the manganese ions, for alloys of various compositions, have been determined. The Neel tem perature increases approximately linearly with increasing manganese content and extrapo lates to 660° K at 100 % Mn; the value of 2-4 + 0*1/% has been obtained for the ionic moment of the manganese ions in pure }'-Mn. Experiments on plastically strained specimens show that compressive stress results in alinement of the c axes of the crystallites along the -type direction most nearly parallel to the stress axis. The ionic moments are alined along the c axis and the susceptibility of plastically strained specimens is anisotropic. An analysis is given of the results of measurements of the anisotropy of susceptibility from which may be calculated Xw and X the susceptibilities of a single antiferromagnetic domain measured ±9 respectively parallel and perpendicular to the direction of antiferromagnetism.
224 G. E. Bacon, I. W. Dunmur, J. H. Smith and R. Street (1941) has calculated the values of Xw and x± for a antiferromagnetic model, using a molecular field approximation and assuming interaction between nearest- neighbour ions only, with the following results: increases monotonically from zero at the absolute zero of temperature, to its maximum value at = is a constant independent of temperature for < and y„ = x± at = Thus (XL— Xu), which is a measure of the anisotropy of susceptibility, decreases mono tonically from a maximum at T = 0° K to zero at T = Anderson (1950), Smart (1952) and others have extended Van Vleck’s molecular field calculations in attempts to predict the temperature variation of the susceptibility of real anti ferromagnetics of the MnO type. It has been shown that although the theory accounts qualitatively for the experimental observations, the quantitative predic tions differ by a large factor from the experimental values of susceptibility.
The antiferromagnetism of manganese copper alloys 225 several days at temperatures about 100° C below the upper limit of the y field and then quenching in water. The exact compositions were determined by chemical analysis, and spectrographic examination revealed that no detectable amounts of impurity were introduced by the methods of preparation.
G. E. Bacon, I. W. Dunmur, J. H. Smith and R. Street 4. Results (a) Measurements on isotropic alloys Meneghetti & Sidhu (1957) have investigated solid solutions of manganese in copper up to 85 at. % of manganese, by neutron diffraction techniques. At com positions greater than 69% manganese, they deduced an antiferromagnetic structure in which the ionic moments are alined along the c axis. The ions at 000 and ||0 positions have moments parallel to the c axis, while the ions in ^0| and 0^| positions have moments antiparallel to the c axis. The neutron diffraction pattern of this structure contains a fairly intense (110) magnetic reflexion and a (201) magnetic reflexion of intensity about 14 % of the (110). We have confirmed this postulated structure for manganese-rich alloys up to 95 at. % Mn. In this structure, antiferromagnetic coupling between ions which are nearest neighbours is operative.
The antiferromagnetism of manganese copper alloys 227 decrease far too rapidly to be in agreement with the expected function. How ever, it is possible to fit the experimental results obtained at temperatures below 390° K to B2S functions, treating the Neel temperature TN as an arbitrary para meter. Bl functions with spin quantum numbers S = % and 1 are also plotted on figure 2. It will be seen that the value of S cannot be deduced precisely by this method of curve fitting. Within the limits of experimental error, the temperature Tt at which the intensity of the (110) reflexion becomes zero (420° K) coincides with the f.c.t. -> f.c.c. transition temperature for this alloy (cf. figure 1). The onset of the tetragonal to cubic transformation thus leads to rapid disordering of the antiferromagnetic arrangement of the structure.
228 G. E. Bacon, I. W. Dunmur, J. H. Smith and R. Street The results of the measurements on the temperature dependence of resistivity are shown in figure 4 (a). For alloys of manganese content greater than about 75 at. %, the curves of resistivity against temperature are similar in that the temperature coefficient of resistivity is greater at lower temperatures than at higher temperatures. At the f.c.t. f.c.c. transition temperatures of 80 to 95 at. % Mn compositions, the resistivity increases rapidly with temperature. The three curves (i), (ii) and (iii) of figure 4(6) are representative of the effect of heat treatment on the transition temperature. The broken lines shown on some of the curves suggest the form of the resistivity-temperature variation which would be observed if the antiferromagnetic ordering were not destroyed by the structural phase change.
The antiferromagnetism of manganese copper alloys 229 be determined from the average moment by simple proportion. This procedure assumes that long-range antiferromagnetic order is complete at = 0° K, and also that the manganese and copper atoms are distributed at random throughout the atomic sites in the structure. The results are shown in figure 5 in which the magnetic moment of the manganese ion, in Bohr magnetons, is plotted against the alloy composition. It would appear to be justified to extrapolate the curve of figure 5 to 100 % manganese to obtain the magnetic moment of manganese ions in the f.c.t. y manganese structure. The extrapolated value is 2-4 + 0*1 p,B.
230 G. E. Bacon, I. W. Dunmur, J. H. Smith and R. Street The temperature variations of susceptibility of 85 and 90 at. % Mn + Cu alloys are plotted in figure 6. It will be seen that above the transition temperature, the susceptibility increases with increasing temperature and no Curie-Weiss law behaviour is observed; in the region of the transition temperature there is a sharp rise in susceptibility. It is not possible to make any measurements of the y phase at temperatures much in excess of 250° C as transformation from the pure y phase to a mixture of a and y phases begins at about this temperature.
The antiferromagnetism of manganese copper alloys 231 and 3-76 A respectively. Thus, the effects observed are consistent with the assump tion that plastic strain results in a re-orientation of the axes of the crystallites such that the -type direction lying most nearly parallel to the axis of compression becomes the c axis of the tetragonal unit cell and also the direction of antiferro magnetism. Thus, the magnetic interaction vector, q, which is numerically equal to the sine of the angle, <x, between the magnetic moment and the scattering vector, is increased for the (110) reflexion under the conditions shown for curve (6) of n e u t r o n ^ beam scattering 111 200 002 vector 200 002 200 002 Bragg angle, 6 (deg.) Figure 7. Neutron diffraction patterns of 85 at. % alloy, (a) Compressive stress zero, cylinder axis either horizontal or vertical for neutron measurement, (b) After application of a compressive stress of 40 Kg mm-2 along the cylinder axis; the scattering vector is perpendicular to the axis of compression. The increase in the intensities of the (110) and (200) reflexions, compared with those in curve (a) are due to preferential alinement of c axes approximately parallel to stress axis, (c) As for curve (b) but with the scattering vector parallel to the axis of compression. The low intensities of the (110) and (200) reflexions are due to alinement of c axes approximately parallel to the stress axis.
232 G. E. Bacon, I. W. Dunmur, J. H. Smith and R. Street the c axes now tend to be alined along the scattering vector, making a zero and reducing the magnetic scattering to zero. This expectation is confirmed by curve (c) where the (110) reflexion is reduced to a very small intensity. At the same time, we should expect a marked increase in the number of (002) planes which are in a reflecting position and a decrease for (200). This is also confirmed by the diffrac tion pattern where it will be observed that the (200) reflexion has practically disappeared. In the unstrained state, the magnetic moments were shown to be distributed isotropically, by observing the approximate equality of intensity of the (110) reflexion for different orientations of the specimen.