Elasticity and Antiferromagnetism of Metallic Antiferromagnetics R

Elasticity and antiferromagnetism of metallic antiferromagnetics R. Street, J.H. Smith

To cite this version:

R. Street, J.H. Smith. Elasticity and antiferromagnetism of metallic antiferromagnetics. J. Phys. Radium, 1959, 20 (2-3), pp.82-87. 10.1051/jphysrad:01959002002-308200. jpa-00236072

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ELASTICITY AND ANTIFERROMAGNETISM OF METALLIC ANTIFERROMAGNETICS By R. STREET and J. H. SMITH, Department of Physics, The University, Sheffield, England.

Résumé. 2014 On peut prévoir une variation du module d’Young avec la température au point de Néel sur les substances antiferromagnétiques. Nous donnons ici les résultats des mesures rela- tives aux alliages CuMn(03B3) et aux alliages CuMn à plusieurs phases (03B1 + y) On trouve sur ces derniers la variation prévue due à Mn 03B1 et également une anomalie, vers 130 °K, attribuée à la présence de MnCu y précipité. Cette dernière phase est ferromagnétique au-dessous de 130 °K. Une variation régulière avec la température du module d’Young de Pd confirme le fait qu’aux basses températures Pd ne serait pas antiferromagnétique.

Abstract. 2014 If an antiferromagnetic is spontaneously deformed on cooling through the Néel temperature, then the application of an external stress results in a redistribution of domain vectors, e.g. they may rotate or antiferromagnetic domain walls may move. This causes an additional strain component which will be apparent as an anomalous variation of the Young’s modulus with the temperature. The results of measurements of the temperature dependence of Young’s modulus for antiferromagnetic 03B3-CuMn alloys and mixed phase (03B1 + 03B3) CuMn alloys are reported. The (03B1 + y) alloys show (a) a Young’s modulus variation of the expected form which is due to the contained 03B1-Mn, (b) a Young’s modulus anomaly at about 130 °K associated with the precipitated 03B3-CuMn (containing 40 atomic percent Mn). It is shown that the latter phase below 130 °K exhibits ferromagnetic characteristics. A smooth temperature variation of Young’s modulus has been obtained for Pd which is consistent with the assumption that Pd is not antiferromagnetic at low temperatures.

Introduction. - The dependence of Young’s 1950) and thus exhibit antiferromagnetostriction. modulus on the state of magnetization of ferro- Neutron diffraction studies show that the direc- magnetic materials has been known for many tions of antiferromagnetism generally coincide with years, the phenomenon is known as the AE-effect. crystallographic directions of low order. It is For a ferromagnetic of non-zero magnetostriction therefore possible for boundary walls separating an external stress Z in general affects the distri- domains having different directions of antiferro- bution of the magnetization vectors, by rotating magnetism to move and the directions of antiferro- them away from preferred axes or by domain magnetism to rotate away from preferred direc- boundary movement, and the resultant rate of tions under the influence of an external stress. change of intensity of magnetization with stress Measurements of the temperature variation of (è)l/è)Z)H is equal to the rate of change of magneto- Young’s môdulus of pressed bars of cobalt and strictive deformation with field (è)À/H)z. When nickel oxides show a very pronounced decrease in an external stress is applied, in addition to the modulus near the Néel temperatures of the two normal elastic strain of the lattice, e, there is materials (Street and Lewis, 1951 ;g Fine, 1953). another component of strain, cm, produced by the The object of this communication is to report some magnetostrictive deformation accompanying the observations made recently on the temperature redistribution of the magnetization vectors. At variations of Young’s modulus of metallic antifer- magnetic saturation, the magnetization vectors are romagnetic materials. all aligned along the field direction, hence è)À/è)H = )7/t)Z = 0 and E is the only component Expérimental. - The method of measurement of strain produced by the stress Z. Thus in the was similar to that described by Zacharias (1933). unsaturated state the value of Young’s modulus The specimens, of rectangular cross section ZI(F- + Sjn) is less than its value at magnetic satu- 2.00 mm X 3.00 mm, were cemented to quartz ration. crystals, of identical cross section, which were cut It follows that in zero applied field the Young’s so that longitudinal vibrations along the length of modulus of a ferromagnetic should decrease when the composite oscillator were excited by an alter- cooled through the Curie temperature. Above the nating p.d. applied to electrodes deposited on Curie temperature no spontaneous ferromagnetic opposite side faces of the crystal. The resonant order exists and e;m = 0 ; below the Curie tempe- frequencies of oscillation of the composite oscil- rature e;m =1= 0. lator, f o, are given by the relation X-ray techniques have been employed to show that antiferromagnetic materials are spontaneously deformed when they are heated or cooled through their Néel temperatures (Tombs and Rooksby, where fa, fq are respectively the fundamental fre-

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphysrad:01959002002-308200 83

quencies of resonant longitudinal oscillation of the temperature for two typical alloys of this series are spécimen and the quartz crystal alone ; ms, mq are shown in Figure 1. As expected, these curves the masses of the specimen and the crystal. Experi- show pronounced minima which occur at the tran- mentally f o and f q are measured as functions of sition temperature of the alloys. temperature from which ’ /8 may be calculated. The interpretation of the results obtained is Hence Young’s modulus is determined by the rela- uncertain in view of the fact that Tt TN. tion ’ However, investigations of the stress dependence of the intensity of the (110) (magnetic) neutron diffraction et loc. that and were to be peak (Bacon al., cit.) suggests ts f, always arranged very strain nearly equal adjusting the length of the the additional component Em in the antiferro- by speci- state arises from wall move- men and various magnetic boundary by using quartz crystals having from of values of In this the effect of ment rather than rotation domain magne- f q. way, perturbing tization vectors. walls the adhesive at the of the and Only boundary separating junction crystal domains directions of antiferro- specimen was minimized: having digerent will move on the of an The oscillator was mounted in an magnetism application composite external stress. Other domain exist -enclosure which could be evacuated or filled with types may e.g. if a line within a domain the direc- low helium as a heat exchanger and means along spin pressure tions are a wall occur of or was t 1 t 1 t t, boundary may heating cooling were It pos- " provided. domains such that on sible to determine relative values of between " changed-step Young’s wall modulus to within 1 in 104. moving through the the spin directions are part formally represented by t t t t t t t t t. The Results and discussion two domains separated by a boundary of this type have the same antiferromagnetostrictive strain the of stress will Cu-Mn Alloys. - The antiferromagnetic pro- along any direction, application not result directly in wall movement and the perties of single y CuMn alloys containing phase contribution to will be zero. From the more than about 70 atomic of z. expres- percent manganese sions for the modulus summarized have been investigated by Bacon et al. (1957). Young’s change in the it will be seen that when domain Below a transition temperature, Tt, which depends Appendix movements are involved of on the are boundary comparison composition, alloys antiferromagnetic results with theoretical is and have a face-centred tetragonal structure. At experimental predictions difficult as of the area of domain walls the transition temperature the alloys undergo a knowledge and the forces impeding wall movement are required.

(oc + y) CuMn Alloys. - It is of interest to inves- tigate the temperature dependence of Young’s modulus of iI..-Mn as a useful preliminary to the consideration of the antiferromagnetic domain structure of the element. The investigation cannot be undertaken directly using pure oc-Mn samples since the material is extremely brittle and cannot be machined into the required regular shape. The difficulty has been overcome in the following way. Starting materials containing various proportions of copper were prepared by melting in an argon arc furnace and then after heating for extended periods of time at temperatures near the melting point they were rapidly quenched, thus retaining the Fie. 1. - Temperature variation qf Young’s modulus for y solid solution. Materials prepared in this way y-CuMn alloys containing 80 and 85 atomic percentage containing as much as 95 atomic percent of manga- Mn., nese were relatively easy to machine and it was possible to produce specimens of the required form martensitic transformation, above Tt they are no from them. The specimens were then trans- longer antiferromagnetic and have a face-centred formed to the mixed (oc + y) phase by heating for cubic structure. The extrapolated Néel tempe- many hours at 600 °C. Thus the specimens con- rature, TN, determined from the temperature taining high proportions of manganese consisted of dependence of the intensity of the (110) (magnetic) a matrix of oc-Mn with a precipitated y-phase neutron diffraction peak is always greater than Tt. containing approximately 40 atomic percent man- The values of Young’s modulus as functions of ganese. From the phase diagram of this system 84 determined by Dean et al. (1945) a transformed specimens (fig. 2) have the form characteristic of specimen having a total of 95 atomic percent ce-Mn (White and Woods, 1957). manganese contains over 90 % oc-Mn. The elec- In figures 3(a) and (b), values of Young’s trical resistivity vs. temperature curves of the modulus expressed as ratios of the 0 OC value are plotted as a function of temperature for (oc + y) CuMn alloys containing various proportions of manganese. All the curves taken with specimens containing more than 70 atomic percent Mn show a stepwise variation in Young’s modulus at about 104 OK which is rather higher than the Néel temperature of oc-IVIn - i.e. 100 OK deduced from neutron diffraction measurements by Shull and Wilkinson (1953) and 95 oR. deduced from spécifie heat measurements by Tauer and Weiss (1957). The decrease in Young’s modulus on the Néel cooling through temperature implies" that ce-Mn must undergo antiferromagnetostrictive deformations when antiferromagnetic ordering sets in. It is difficult to estimate the magnitude of the antiferromagnetostriction since there is no information on the crystalline anisotropy energy or the number of domain boundary walls and the impe- dance to their motion.

FIG. 2. - Temperature variation of resistivity of (oc + y) CuMn alloys containing 80, 85 and 92.5 at. % Mn. Ordinates- pl Po where P = resistivity at temperature T, po = resistivity at 0 OC,

FIG. 3(b). - Variation of Youngs modulus of (a + y) CuMn alloys containing 50, 69, 80 and 90 at. % Mn. E == Youngs modulus at temperature T, Eo = Young’s modulus at 0 °C. The origin of the ordinate axis is arbitrary.

FIG. 3 (a) - Temperature variation of Young’s modulus of (a + y) CuMn alloys containing 95 at. % Mn (upper An obvious feature of the results shown curve) and 90 at % Mn (lower curve). Ordinates EJE, parti- = in occurrence of maxima where F = Young’s modulus at temperature T, .Eo cularly figure 3(b) is the Youngs modulus at 0 °C. at about 130 OK, due to magnetic ordering in the 85

y-CuMn contained in the specimens. Measu- temperature slowly increased : - the results rements have been made of the magnetic suscep- plotted on the curves marked p were obtained tibility of the mixed phase (oc + y) materials pre- with the various measuring fields acting parallel to pared as described above and also on specimens of the field applied during cooling ; the curves a show single phase y-CuMn alloys containing 40 and the results obtained with the measuring fields 50 atomic percent Mn. Typical results of measu- acting antiparallel to the field applied during rements of the temperature dependence of the cooling. These results shows that cooling in a force acting on the specimens placed in a non- magnetic field results in a " frozen-in " magnetic uniform magnetic field are shown in figure 4. moment, parallel to the field, which is magne- When the specimens are cooled through 130 OK in tically hard, reverse fields of 11 kOe are not suffi- zero field the susceptibility reaches a broad maxi- cient to reverse its direction ; fields up to 7 kOe mum at 130 °K which suggests antiferromagnetic have little effect on the moment as may be seen ordering. However, preliminary investigations of from figure 5. At the higher reverse fields the the neutron diffraction patterns of the 50 atomic percent y-CuMn alloy at 80 OK do not indicate long-range antiferromagnetic ordering of the type observed with Mn-rich y-CuMn alloys. In addition the specimens exhibit an unusual ferromagnetic behaviour which appears by allowing them to cool through 130 OK in an applied field. This ferromagnetic behaviour is also exhibited by copper rich y-MnCu alloys (Owen et al., 1957). The results shown in figure 4 were obtained by

FIG. 5. - Temperature variation of permanent moment for 40 at. percent Mn y-CuMn alloy cooled in field of 10 kOe. The values of a are averages calculated from the separations of the a and p sections of curves typified in figure 4. Fields applied were 3 kOe, X 5 kOe, + 7 kOe, 0 10 kOe, Ll11 kOe.

ferromagnetic moment is time dependent but this phenomenon has not been investigated in detail at the present time.

Palladium and chromium. - The temperature variation of Young’s modulus for a specimen of palladium shows no anomaly at 80 OK at which temperature there is a broad peak in the susceptibility vs. temperature curve (Hoare and FiG. 4. - Temperature variation of force acting on spe- Matthew, 1952). The elasticity measurements thus cimen of 40 at. percent Mn y-CuMn alloys. The three support the view that the susceptibility maximum curves were obtained with fields of and measuring 7,10 is due to electronic band structure and 11 kOe. (For explanation of sections a and p see text.) changes not due to the occurrence of antiferromagnetism. There is some doubt as to whether chromium is allowing the specimens to cool to 80 OK in an antiferromagnetic (Shull and Wollan, 1956). The applied field of 10 kOe. Measurements were then original investigations (Shull and Wilkinson, 1953) made of the forces acting on the specimens as their indicated a Néel temperature 470’DK, but there is 86

no anoinaly in the Young’s rnodulus at this tempe- Considering reversible changes only, the equi- which would be if antiferro- value of lVl for a stress will ,’ rature expected librium given be given magnetism were to occur. However, the absence by f’(M) + f’A(M) = 0 or of an anomaly in Young’s modulus is not absolutely conclusive as this could arise in an antiferromagnetic having very high uniaxial crystalline anisotropy. This is an implicit relation between M and Z This situation probably occurs in rhombo- from which dM/dZ may be derived : hedral Cr203 (Street and Lewis, 1956) but it would seem to be unlikely in cubic materials. hence Appendix. - Let À be the component, resolved along the direction of applied measuring stress, of the magnetostrictive strain of an antiferromagnetic at zero applied stress. domain system. À may be expressed in terms of Thus an coefficient Àc and a antiferromagnetostriction (dÀ/dZ)z=0 = (dM/dZ) (dX/dM) = lÀc ’Y’(O)]2/f(O) function, T(M) of aparameter .NI which is characteristic of t he domain process considered, e. g. if rota- d À/dZ has the dimensions of compliance (inverse tion of domain magnetization vectors occurs, M is elasticity) and is the contribution to the total com- the angle of rotation away from a preferred direc- pliance produced by the strain component em men- tion, if domain boundary movement occurs M is the tioned in the text. positional co-ordinate of the boundary. Thus we Below the Néel temperature the measured com- write À = Àc T(M). pliance 1 jEb = ( s + Em) /Z and the value deter- For an applied stress Z the component of strain mined by extrapolation from measurements above energy density due to domain changes is the Néel temperature 1 jEa = C JZ. Hence

1 where the prime denotes differentiation with res- 1 pect to M. Thus values of A Ê appropriate.to any domain Hence f’(M) = - z Àc ’Y/(M). process may be evaluated by appropriate substi- The energy density of the domain system will tution in this general equation (Street and Lewis, have other contributions arising from crystalline 1958). Values of A ( 1 JE)for various’domain proces- and internal strain anisotropy, boundary wall ses in randomly oriented polycrystalline materials energy etc. These contributions do not involve M assuming uniform stress distribution are summar- explicitly and in sum are represented by fA(M). ized below :

Rotations :

Against high internal strain anisotropy. Zi = internal stress. X = (3 /2) Xc[cos2 0- (1/3)]. Where 0 = angle between direction of antiferromagnetism and measuring direction.

Against uniaxial crystalline anisotropy. Anisotropy energy density is /(7]) z sin2 q + ... Away from preferred directions of antiferroma- Àll1 = conventional single crystal magnetostrictive gnetism which are [100] directions (cubic mate- coefficient. rials. K, = first crystalline anisotropy energy coefficient. Movement of boundaries : Separating change-step domains Separating domains, in cubic materials, with ortho- S = area of boundaries per unit volume. gonal directions of a. f. m. f’:t (0) = second differential w. r. t. position of energy of domain boundary walls per unit volume. This analysis is treated in greater detail and applied particularly to the AE-eflect and magnetic REFERENCES of susceptibility ferromagnetics by Street’ and BACON (G. E.), DUNMUR (I. W.), SMITH (J. H.) and STREE Lewis (1958). (R.), Proc. Roy. Soc., 1957, A 241, 223. DEAN (R. S.), LONG (J. R.), GRAHAM (T. R.), POTTER 87

(E. V.) and HAYES (E. T.), Trans. Amer. Soc. Metals, regions. If true the hystérésis curve will not be 1945, 34, 443. about the M axis as has been found FINE Rev. Mod. symmetrical (M. E.), Physics, 1953, 25, 158. in Cobalt-cobaltous HOARE (F. E.) and MATTHEWS (J. C.), Proc. Roy. Soc., the oxide system. 1952, A 212,137. - 1 OWEN (J.), BROWNE (M. E.), ARP (V.) and KIP (A. F.), Mr. Street. would agree that it is possible J. Phys. Chem. Solids, 1957, 2, 85. that the magnetic hardness in Cu-Mn alloys may SHULL (C. G.) and WOLLAN (E. O.), Solid State Physics, be due to antiferromagnetic-ferromagnetic inter- , vol. 2 York : 1956, (New Academic Press), p. 181. action. However this case is not as SHULL and WILKINSON (M. Rev. Mod. obviously (C. G.) K.), Physics, as that of 1953, 25, 100. clear cut the Co-CoO system referred to STREET (R.) and LEWIS (B.), Nature, London, 1951, 168, by Dr. Meiklejohn. At high Mn content, Cu-Mn 1036 ; Phil. Mag., 1956, 1, 663 ; Proc. Phys. Soc., alloys have well developed long-range antiferro- 1958. 72, 604. structures but this of structure is TAUER (K. J.) and WEISS (R. J.), J. Phys. Chem. Solids, magnetic type 1957, 2, 237. not observed with alloys containing less than about TOMBS (N. C.) and ROOKSBY (H. P.), Nature, London, 1950, 70 atomic percent Mn. Neutron diffraction studies 165, 442. of Cu-Mn alloys containing less than 70 atomic per WHITE (G. K.) and WOODS (S. B.), Canad. J. Phys., 1957, cent indicate 35, 346. manganese short-range magnetic ZACHARIAS (J.), Phys. Rev., 1933, 44, 116. ordering. If there is antiferromagnetic coupling in the alloys exhibiting ferromagnetic behaviour the ordering of spins is certainly différent from that observed at higher manganese contents. As DISCUSSION an alternative to the interaction mechanism it may be suggested that there is short-range ferromagnetic Mr. Meiklejohn.-- I should like to suggest that coupling of spins, characterized by high magneto- the reasôn for the difficulty in reversing the magne- crystalline anisotropy. 1 agree that information tization is due to an interaction between antiferro- on the hysteresis curves of the alloys would be magnetic and ferromagnetic or superparamagnetic very useful in helping to decide the question.