We have determined the magnetic phase diagram of Dy as a function of epitaxial strain , applied field H, and temperature T. $roman Y sub x roman Lu sub 1-x- alloys were employed as templates to clamp the films at selected strains. The separate roles of epitaxial clamping and strain are identified for the first time. There is a clearly defined transition as the strain is changed at low temperature from the clamped helical phase to the ferromagnetic phase. The transition is modeled by a linear coupling treatment of the magnetoelastic strains

Flynn, C.P.

Tsui, F.

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VOLUME 71, NUMBER 9 PHYSICAL REVIEW LETTERSMagnetic Phase Diagram of Epitaxial Dysprosium30 AUGUST 1993F. Tsui* and C. P. FlynnDepartment of Physics, University of Illinois at Urbana Ch-ampaign, I IIO West Green Street, Urbana, Illinois 6I80I(Received 27 May 1993)We have determined the magnetic phase diagram of Dy as a function of expitaxial strain s, appliedfield 0, and temperature T. Y„Lu]— alloys were employed as templates to clamp the films at selectedstrains. The separate roles of epitaxial clamping and strain are identified for the first time. There is aclearly defined transition as the strain is changed at low temperature from the clamped helical phase tothe ferromagnetic phase. The transition is modeled by a linear coupling treatment of the magnetoelasticstrains.PACS numbers: 75.70.Ak, 75.30.Kz, 75.80.+qRecent publications emphasize that magnetic phase di-agrams may be tuned by epitaxy [1]. The effects are ex-pected to be the largest when a phase transition is accom-panied by a large magnetoelastic strain. The strain ener-gy alters the energy balance among alternative phaseswhen the magnetic material is prevented from changingshape by its epitaxial clamping to a substrate. A separateeffect is the epitaxial strain e caused by interfacial atomicregistry between the substrate and the magnetic film(pseudomorphic strain). All the energies change smooth-ly with the strain and this modifies the phase diagramfurther. The effects of clamping and strain have not beenseparated in previous research. Here we explore the mag-netic phase diagram of epitaxial dysprosium, which un-dergoes large magnetostrictive strains —0.5% at T, =85K in the bulk material, where the antiferromagnetic (H:helical) to ferromagnetic (F) phase transition occurs [2].hcp Dy is of particular interest because basal plane epi-taxy on Y, which causes a 1.6% expansion of the Dy basalplane, completely suppresses the F phase, owing toclamping and/or strain [3]. However, a metastable mag-netized phase in Dy/Y superlattices can be induced by a 5kOe field applied below 15 K [3]. In contrast, epitaxy onLu, which compresses the a and b axes by 2.4%, doublesthe Dy T, [1,4]. A related observation for Dy/Lu super-lattices is that the spontaneous orthorhombic distortion ofthe Dy basal plane in the F phase, present in pure Dy, issuSciently strong to distort the surrounding Lu lattice aswell [1]. These striking epitaxial effects add special in-terest to the study of clamped Dy epilayers.To examine the effects of magnetostrictive clampingand strain separately we have grown c axis Dy singlecrystals 50 A thick on selected substrates. The methodsof molecular beam epitaxy employed here start from1000 A each of Mo(110), then Y(0001), freshly grownon sapphire (1120), and are described elsewhere [3]. Thehigh quality of the resulting crystals is documented there(see also below). It is known that Dy films thicker than100 A undergo some inelastic strain relief so that theproperties depend on the film thickness. In the presentcase the thickness was limited to 50 A. An initial 1500 Aof template material was prepared before the Dy growth,(110) Mo(0002) Y LuSapphire——(0002) Y31 32 37 38 4028 (deg)I41FIG. 1. X-ray Bragg scan of (Yo.6sLuo. ss) lsoox/Dysox/(Yo6sLuo, ss)loop sandwich film grown along the [0001] direc-tion. The coherence length of the alloy is —500 A. Braggpeaks for the sapphire substrate, the Y buAer, and the MobuA'er are also shown.and the same template material was regrown as a 100 Athick cap directly on the Dy, in order to double theclamping strength and best establish the chosen pseu-domorphic strain. For this purpose Y Lu] — alloys wereselected. These tune the Dy basal plane from an expan-sion of a=1.6% for x =1 to a compression of c= —2.4%for x =O. In practice alloys with 0.2 (x & 0.8 were usedtogether with results for the pure metal templates [3,4].Earlier results for Dy on Er [5] and pure bulk Dy [2,6]provide further relevant information.Figure 1 presents an x-ray Bragg scan for the case ofthe sample with x =0.65, which is typical for the materi-als employed here. The Bragg scan width shows that thecoherence length is 500 A along the growth direction; theobserved mosaic spread is —0.2'. The observations pointto crystals of su%ciently high structural quality that themagnetic behavior is expected to be insensitive to anyremaining structural defects.Magnetization measurements on these materials werecarried out using a commercial SQUID magnetometer.1462 003 1-9007/9 3/7 1 (9)/1462 (4)$06.001993 The American Physical SocietyVOLUME 71, NUMBER 9 PHYSICAL REVIEW LETTERS 30 AUGUST 1993The experiments were designed to determine the field andtemperature dependent magnetic behavior of Dy clampedat diA'erent basal plane strains. Helimagnetic orderingoccurs near the bulk Neel temperature T~ =175 K in allthe present materials, and is thus very insensitive to theepitaxial strain e. Strong but diAering magnetizationswere observed in field-cooled and zero-field-cooled mea-surements, much as in earlier studies of Sc [7], Y [3], andLu [4] templates. These nonequilibrium characteristicsarise from thin film constraints on the accessible magnet-ic domain structures. The ferromagnetic transition wasprobed using the field-cooled magnetization with resultsshown for the template alloy with x=0.4 in Fig. 2. Attemperatures above the zero field critical temperature T„the field dependent magnetization curves thus deducedexhibit discernible slope changes. These determine thevariation of H, with T for H & 0 at that particular valueof the basal plane strain a The slope change that occursat lower fields, before the rapid rise, pertains to the col-lapse of the spiral phase. Its midpoint is defined for thepresent purpose as H, .At still higher fields a second slope change occurs atHf, before the magnetization saturates. Magnetic andneutron scattering measurements have not yet been ableto establish for pure Y and pure Lu templates whetherthis is a regime of mixed F and H phases or a fanconfiguration derived from a distorted helix similar tothat observed at high fields above —130 K in pure Dy[2].Open circles in Fig. 3 show the locus of H, as a surfacedepending on the temperature T and on the basal planestrain s, defined by the alloy template. The smoothed be-havior is indicated by solid lines. In completing thefigure, use has been made of published results for Dygrown on Y and Lu templates [3,4], indicated by soliddata points. Results for Dy on Er above the T, of Er arealso shown by solid points near a=1 /p [5]. The figuremakes clear that the magnetism is insensitive to c neara=1.6% (pure Y template) and g= —2.4% (Lu). A rap-id transition from H, large to zero near e=O marks thehelical to ferromagnetic phase transition induced here bychanging s. Accordingly, T, (for 0, =0) rises rapidly to—85 K near a=0 and, for 0 & e& —2%, it changes al-most linearly with e.It is an important observation that H, (T) for the H toF transition of pure Dy is quite similar to that for Dy onY Lu~ — . The behavior of pure Dy is shown by a thickline near e=O in Fig. 3. Without question it lies close tothe surface in Fig. 3 derived from the use of alloy tem-plates. In the first place, the combined observations sug-gest that the process mapped by the surface in Fig. 3must be similar to the well-studied magnetization ob-served for pure Dy, in part through fan states. Second, asbulk Dy magnetizes it undergoes a tetragonal y distortions~ along the direction of the magnetization M in the basalplane, and a tetragonal a distortion s, along the c axis. Anatural expectation is that epitaxy modifies both e~ and cthrough the eff'ects of clamping and interfacial registry.Figure 3 clearly establishes that the strain e associatedwith misfit does have a profound effect in tuning the filmacross its magnetic phase diagram. However, the clamp-ing caused by epitaxy causes surprisingly little change ofthe phase diagram. The fact that pure Dy behaves verymuch like epitaxial Dy near s=O in Fig. 3 is one demon-stration that clamping alone has no large eAect. Furtherevidence is that the variation of T, with s for c~ 0 coin-cides with the known dependence of T, on uniaxial stressin bulk Dy (broken line in Fig. 3) [6] when converted toan e dependence using the hydrostatic pressure depen-dence. The linear behavior is also consistent with the c400~5K=~40 K60K80K1 00 KI 20 K 10E 200 (40 K160 K550ol ~0 IO 20200 KH (I oe)FIG. 2. Field dependent magnetization curves for the field-cooled (Yp.4&Lup. &5)»ppx/Dy5p+(Yp, 4gLup gg) ~ppx at various tem-peratures. The magnetic field was applied along one of the aaxes in the growth plane. Note that above T, =90 K, the mag-netization exhibits a low field anomaly at H, before its rapidrise to saturation. The critical fields H, and Kf are indicatedby dashed lines.E (ohio)FIG. 3. The magnetic phase diagram for epitaxial Dy thinfilms grown along the c axis. The phase boundary correspondsto the locus of critical field H, . T, is defined where the phaseboundary intersects the T-s plane at zero field. The open cir-cles are data points from this research on (Y„Lu~ —„)~5ppx/Dy5pg(Y Lu~ —„)~ppz sandwich films, and the closed circles areobtained from Refs. [3-5]. The smoothed behavior is indicatedby solid lines. The dashed line through the nearly linear part ofthe T, curve indicates the equivalent bulk uniaxial behavior [6l.1463VOLUME 71, NUMBER 9 PH YSICAL REVI EW LETTERS 30 AUGUST 1993dependence of T, obtained from observations for Dy par-tially relaxed on Lu [4]. The behavior is different fore& 0 where a transition takes place and T, deviates fromthe linear behavior of the strained but unclamped bulkDy and drops rapidly to zero. These first observations ofthe separate eff'ects of clamping and epitaxial strain onthe magnetic phase diagram lead us to the unexpectedconclusion that, while strain causes large changes, theeAect of clamping is quite small particularly for a~0.Any model discussion of H, (T) must include the ob-served transition in the e dependence where the eAect ofclamping seems to change drastically.In what follows we describe mechanisms by whichmagnetostrictive strains may be favored even in thin epi-taxial films that are clamped by the surrounding material.Our purpose is to explain why clamping has an unexpect-edly small effect on the Dy phase transitions and how itcan appear to have an e dependent transition. All the or-dered phases of Dy consist of ferromagnetic basal planesstacked in an ordered sequence. In the helical phase themoment is rotated from one a axis to the next betweensuccessive planes to yield a magnetic spiral with typicalperiod 10 planes and wave vector q —0. 1 A '. The fer-romagnetic phase is the same except that q =0. In thebulk this phase is accompanied by magnetostriction in theform of one tetragonal strain, e„=—,' (st~ —F2), about thea axis of the basal plane along which the moment points,and a second tetragonal strain along c, namely, s,=3 (2s33 8/f 8$$). Here we discuss two alternativeq =0 phases: one with anisotropic magnetostriction andthe other lacking anisotropy. Our discussion of spontane-ous strain treats only c~ because Fig. 3 indicates that theisotropic basal plane strain e = & (s& t +@22) is fullyclamped in the thin film, in order that epitaxial strain cantune Dy through the difI'erent phases. To proceed we as-sume for simplicity that the Dy surface planes are fullyclamped to their YLu neighbors, with no interfacial slip,and that Y„Lu& and Dy have similar enough elasticconstants to be treated as identical. In a more completepublication we will show that these simplifications do notalter the character of the conclusion so reached.The two q =0 phases of interest here diAer in that oneundergoes a tetragonal distortion about the direction ofmagnetization and the other does not. We compare thetwo energies by expanding the energy about the symme-trical configuration in powers of the strain c~ and retainthe lowest relevant terms. Figure 4 shows a magneticdomain of the distorted phase occupying the full thick-ness d of the magnetic layer for an in-plane dimension l.We assume that, as observed in Dy/Lu superlattice [1],the epilayer minimizes its y strain energy by breakinginto tetragonal domains so arranged that the mean strainvanishes. In each domain the magnetization lies alongone of the easy orientations. It is reasonable to representthe electronic energy E, of magnetization as linearly cou-pled to the tetragonal magnetostrictive strain coordinateAlloy Dy AlloyFIG. 4. Schematic diagram of a magnetic domain (left) inan epitaxial film. It occupies the full thickness of the magneticlayer, d, for a dimension I in the growth plane. Nonuniformelastic fields due to magnetostriction must extend —l into thenonmagnetic bulk. The resulting energy of the film as mode1edin the text is shown to the right.s~ it produces in the pure bulk. Thus E, = —ac~i d, inwhich l d is the domain volume and a for Dy is a con-stant that depends smoothly on a Any distortion of thefilm over an area 'with typical dimension l must createnonuniform elastic fields extending —I into the bulk.The lattice energy for l»d is therefore EI =be„l, inwhich I is the volume and b is an elastic constant. Whenthe energy W=(E, +EI)/l per unit area is now mini-mized, as shown in Fig. 4, to obtain the equilibrium strains„and energy 8' for a distorted phase relative to theundistorted system, one findsa d ~ a'd2b 1'4bThis relaxation energy 8' must be augmented to includean added domain boundary energy per unit area given byEd =cd/l, with c the surface energy, to yield the total en-ergy diAerence between the distorted and undistortedmagnetized phases asQ d dc— (1)4b lThe conclusions we draw from this model are now sim-ply stated. Equation (1) shows that the distorted phase ispreferred when a & 4bc/d This mean. s that the elec-tronic energy is reduced by more than the combined elas-tic and domain boundary energies. In this case 8', is neg-ative and the energy is least when l is small, with I —dthe lower limit of the model. When, in contrast, a issmall and the coe%cient in brackets is then positive, theunstrained phase is stable. W& is now positive, at least forl very large. Investigation of the film thickness d predict-ed by this model will clearly be of future interest.The very similar behaviors of unconstrained bulk Dyand epitaxial Dy for e~ 0 in Fig. 3 present a challengingpuzzle identified above. How is it possible that clamping-fails to cause substantial changes of the critical field?The problem is largely resolved if, as predicted abovefrom Eq. (1), the epitaxial layer distorts into domains of1464VOLUME 71, NUMBER 9 PHYSICAL REVIEW LETTERS 30 AUGUS~ 1993size comparable with the magnetic layer thickness d.This reduces the distortion of the nonmagnetic clampingmaterial to a minimum, and therefore disturbs the bulkphase relationships least. The e dependence of the con-stants a(e), b(e), and c(s) can cause the "unstrained"phase with large domains to be preferred for e& 0, as dis-cused above, and consequently the observed transitionoccurs near a=0.The domain size of 300 A observed for Dy/Lu superlat-tices remains substantially larger than the magnetic layerthickness typically of d =50 A employed in the earlierwork [I]. This must be reconciled with the present modeldiscussion. In the case of superlattices, however, the lat-tice distortion is favored by the proximity of neighboringmagnetic layers. The penalty in energy for deformingneighboring Lu blocks is, in eAect, shared between twoDy layers. That a cooperative eAect of this type doesindeed take place is detected experimentally by the obser-vation that an interaction between Dy moments in succes-sive layers results from this elastic coupling [I]. It seemsreasonable that smaller domains may be necessary tominimize the energy in the present study of isolated lay-ers. The similarity with bulk Dy indicates that thedomain boundary energy may not be important.In summarizing this research from a broader perspec-tive we note first that by systematically tuning the epitax-ial strain we have been able to explore the magneticphase diagram of epitaxial Dy over a range of 4% in basalplane strain. These methods make it possible to interre-late the behaviors observed previously both in isolatedepitaxial systems and in the pure material. The pro-cedure promises widespread utility for other materials inboth scientific and technical applications. For the specificcase of Dy we have confirmed the very wide range ofmagnetic behavior accessible in the epitaxial system,ranging smoothly from a doubling of T, to the completesuppression of ferromagnetism. Our results are unambi-guous in establishing that the magnetic phase diagram istuned almost entirely by the choice of the basal planestrain e. Lattice clamping of the tetragonal magnetos-triction in the basal plane appears to have a relativelysmall eAect on the magnetic behavior. This is observedeven when the elastic energy is comparable in magnitudeto the electronic and magnetic energy diA'erences in thephase transition. The magnetization measurementspresented here do not afford an unambiguous identi-fication of the mechanism responsible for this unexpectedresult. However, a modeling of the behavior shows that adistorted ferromagnetic phase like that of the bulk canremain favored even for a fully clamped film, providedthat it deforms into small domains that minimize theclamping energy.This work was initiated under support by NSF DMR-91-21888 and completed with the help of added supportfrom ONR Grant No. N00014-92-3-1335. The authorsthank R. Clarke and M. B. Salamon for helpful discus-sions.Present address: Department of Physics, University ofMichigan, 500 East University Street, Ann Arbor, MI58109.[1] C. P. Flynn and F. Tsui, Magnetism and Structure inSystems of Reduced Dimenstons, edited by R. F. C. Far-row, B. Dieny, M. Don ath, A. Fert, and B. D.Hermsmeier (Plenum, New York, 1993); R. S. Beach, J.A. Borchers, A. Matheny, R. W. Erwin, M. B. Salamon,B. Everitt, K. Pettit, J. J. Rhyne, and C. P. Flynn, Phys.Rev. Lett. 70, 3502 (1993).[2] B. Coqblin, The Electronic Structure of Rare Earth-Metals and AOoys: Magnetic Heavy Rare Earths(Academic, London, 1977); R. J. Elliott, Magnetic Properties of Rare Earth Metal-s (Plenum, New York, 1972).[3] J. Kwo, in Thin Film Growth Techniques for Low Dimensional Structures, edited by R. F. C. Farrow, S. S. P.Parkin, P. J. Dobson, J. H. Neave, and A. S. Arrott (Ple-num, New York, 1987), p. 337; R. W. Erwin, J. J. Rhyne,M. B. Salamon, J. Borchers, S. Sinha, R. Du, J. E. Cun-ningham, and C. P. Flynn, Phys. Rev. B 35, 6808 (1987).[4] R. S. Beach, A. Matheny, M. B. Salamon, C. P. Flynn, J.A. Borchers, R. W. Erwin, and J. J. Rhyne, J. Appl. Phys.73, 6901 (1993).[5] R. F. C. Farrow, S. S. P. Parkin, V. S. Speriosu, A. Bez-inge, and A, P. Segmuller, Mater. Res. Soc. Symp. Proc.151, 203 (1989).[6] H. Bartholin, J. Beille, D. Bloch, P. Bourtron, and J. L.Feron, J. Appl. Phys. 42, 1679 (1971); M. Rosen and II.Klimker, Phys. Rev. B 1, 3748 (1970).[7] F. Tsui, C. P. Flynn, R. S. Beach, J. A. Borchers, R. W.Eriwin, and J. J. Rhyne, J. Appl. Phys. 73, 6904 (1993).1465

Magnetic phase diagram of epitaxial dysprosium

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Magnetic phase diagram of epitaxial dysprosium

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