Using coherent x-ray speckle metrology, we have measured the influence of
disorder on major loop return point memory (RPM) and complementary point memory
(CPM) for a series of perpendicular anisotropy Co/Pt multilayer films. In the
low disorder limit, the domain structures show no memory with field cycling--no
RPM and no CPM. With increasing disorder, we observe the onset and the
saturation of both the RPM and the CPM. These results provide the first direct
ensemble-sensitive experimental study of the effects of varying disorder on
microscopic magnetic memory and are compared against the predictions of
existing theories.Comment: 4 pages, 4 figures. Accepted for publication in Physical Review
  Letters in Nov. 200

B. Hu

C. R. Buechler

E. A. Jagla

E. E. Fullerton.

J. B. Kortright

J. E. Davies

J. Hunter Dunn

J. J. Turner

J. M. Deutsch

K. Liu

K. M. Chesnel

L. B. Sorensen

M. S. Pierce

O. Hellwig

O. Narayan

S. D. Kevan

T. Mai

English

arXiv

Using coherent x-ray speckle metrology, we have measured the influence of disorder on major loop return point memory (RPM) and complementary point memory (CPM) for a series of perpendicular anisotropy Co/Pt multilayer films. In the low disorder limit, the domain structures show no memory with field cycling-no RPM and no CPM. With increasing disorder, we observe the onset and the saturation of both the RPM and the CPM. These results provide the first direct ensemble-sensitive experimental study of the effects of varying disorder on microscopic magnetic memory and are compared against the predictions of existing theories

Pierce, MS

Buechler, CR

Sorensen, LB

Turner, JJ

Kevan, SD

Jagla, EA

Deutsch, JM

Mai, T

Narayan, O

Davies, JE

Liu, K

Hunter Dunn, Jonathan,

Chesnel, KM

Kortright, JB

Hellwig, O

Fullerton, EE

Lund University.

Swepub

Disorder-induced microscopic magnetic memory

Using coherent x-ray speckle metrology, we have measured the influence of disorder on major loop return point memory (RPM) and complementary point memory (CPM) for a series of perpendicular anisotropy Co/Pt multilayer films. In the low disorder limit, the domain structures show no memory with field cycling--no RPM and no CPM. With increasing disorder, we observe the onset and the saturation of both the RPM and the CPM. These results provide the first direct ensemble-sensitive experimental study of the effects of varying disorder on microscopic magnetic memory and are compared against the predictions of existing theories

Pierce, M S

Buechler, C R

Sorensen, L B

Turner, J J

Kevan, S D

Jagla, E A

Deutsch, J M

Davies, J E

Dunn, J Hunter

Chesnel, K M

Kortright, J B

Fullerton, E E

eScholarship - University of California

UC Santa CruzUC Santa Cruz Previously Published WorksTitleDisorder-induced microscopic magnetic memory.Permalinkhttps://escholarship.org/uc/item/972873ctJournalPhysical review letters, 94(1)ISSN0031-9007AuthorsPierce, M SBuechler, C RSorensen, L Bet al.Publication Date2005-01-14DOI10.1103/PhysRevLett.94.017202 Peer reviewedeScholarship.org Powered by the California Digital LibraryUniversity of CaliforniaPRL 94, 017202 (2005) P H Y S I C A L R E V I E W L E T T E R Sweek ending14 JANUARY 2005Disorder-Induced Microscopic Magnetic MemoryM. S. Pierce,1 C. R. Buechler,1 L. B. Sorensen,1 J. J. Turner,2 S. D. Kevan,2 E. A. Jagla,3 J. M. Deutsch,4 T. Mai,4O. Narayan,4 J. E. Davies,5 K. Liu,5 J. Hunter Dunn,6 K. M. Chesnel,7 J. B. Kortright,7 O. Hellwig,8,* and E. E. Fullerton.81Department of Physics, University of Washington, Seattle, Washington 98195, USA2Department of Physics, University of Oregon, Eugene, Oregon 97403, USA3The Abdus Salam International Centre for Theoretical Physics, Trieste, Italy4Department of Physics, University of California, Santa Cruz, California 95064, USA5Department of Physics, University of California, Davis, California 95616, USA6MAX Laboratory, Box 118, SE-221 00 Lund, Sweden7Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA8Hitachi Global Storage Technologies, San Jose, California 95120, USA(Received 10 November 2003; published 6 January 2005)0031-9007=Using coherent x-ray speckle metrology, we have measured the influence of disorder on major loopreturn point memory (RPM) and complementary point memory (CPM) for a series of perpendicularanisotropy Co=Pt multilayer films. In the low disorder limit, the domain structures show no memory withfield cycling—no RPM and no CPM. With increasing disorder, we observe the onset and the saturation ofboth the RPM and the CPM. These results provide the first direct ensemble-sensitive experimental studyof the effects of varying disorder on microscopic magnetic memory and are compared against thepredictions of existing theories.DOI: 10.1103/PhysRevLett.94.017202 PACS numbers: 75.60.Ej, 07.85.Qe, 61.10.–i, 78.70.DmThe magnetic recording industry deliberately introducescarefully controlled disorder into its materials to obtain thedesired hysteretic behavior. Over the past 40 years, suchmagnetic hardening has developed into a high art form [1].Although we do not yet have a satisfactory fundamentalmicroscopic description of magnetic hysteresis, beautifultheories of magnetic memory based on random micro-scopic disorder have been developed over the past ten years[2]. How well do these theories compare with experimentalresults? To address this question, we have deliberatelyintroduced increasing degrees of disorder into a series ofthin multilayer perpendicular magnetic materials andstudied how the configuration of the magnetic domainsevolve as these systems are cycled around their majorhysteresis loops.Until very recently [3], our best information about therepeatability of the domain configurations was deducedfrom the associated magnetic avalanches via theBarkhausen noise [4]. Our best current microscopic theo-ries [2] were built on the microscopic information providedby Barkhausen measurements and on the macroscopicinformation provided by classical magnetometry measure-ments. If the Barkhausen noise repeats perfectly for everycycle of the major loop, then the avalanches occur inprecisely the same time order and it is plausible to inferthat the microscopic spatial evolution of the domains isalso the same. However, very recently it became possibleto directly probe the precise spatial distribution of themagnetic domains using coherent x-ray speckle metrology(CXSM) instead of indirectly inferring the domain con-figurations from the time sequence of the avalanches [3].Here we have applied this powerful new CXSM tech-nique to investigate the effects of disorder on the domain05=94(1)=017202(4)$23.00 01720evolution in a series of Co=Pt multilayer samples withperpendicular magnetic anisotropy. In addition to theirpossibly profound implications for the existing theoriesabout the disorder and avalanches in 2D systems [2],such perpendicular magnetic films are of intense currentinterest because they promise significant increases in mag-netic storage density [1].We address two long-standing questions in this Letter:(1) The existence of quasistatic major hysteresis loopsnaturally raises the first question: how is the microscopicmagnetic domain configuration at one point on the majorloop related to the configurations at the same point on themajor loop during subsequent cycles? We will call thiseffect major loop microscopic return point memory(RPM). There are two limiting possibilities for this evo-lution: (a) the domains evolve in precisely the same de-terministic way during each cycle; this is the predictionof all of the best current (zero-temperature) microscopictheories [2]. (b) The domains evolve completely differ-ently during each cycle; their evolution is completelynondeterministic; this is the expectation for thermallydominated systems. There has been surprisingly little theo-retical work on nonzero-temperature models. We showbelow that our samples exhibit behavior intermediate be-tween these two limits—their memories improve withincreasing disorder, yet never become perfect. (2) Theinversion symmetry of the quasistatic major hysteresisloops through the origin naturally raises the second ques-tion: how are the magnetic domains at one point on themajor loop related to the domains at the complementarypoint during the same and during subsequent cycles? Wewill call this effect major loop complementary point mem-ory (CPM) [5].2-1  2005 The American Physical SocietyPRL 94, 017202 (2005) P H Y S I C A L R E V I E W L E T T E R Sweek ending14 JANUARY 2005Our samples were grown by magnetron sputtering onsilicon-nitride-coated, smooth, low-stress 1 cm by 1 cmsilicon wafers. Each wafer had a 2 mm by 2 mm square160-nm-thick freestanding SiNx membrane at its center.We used this thin SiNx window for our transmissionCXSM measurements. Our samples all had Co0:4 nm=Pt0:7 nm50 with Pt buffer layers (20 nm) and Pt caps(2.3 nm). Our sample numbers correspond to the pressure(in milliTorr) of the argon gas that we used to sputter them.For low argon pressures, the sputtered metal atoms arrive atthe substrate with considerable kinetic energy which lo-cally heats and anneals the growing film, leading to smoothCo=Pt interfaces [6]. For higher argon sputtering pressures,the sputtered atoms arrive at the growth substrate withminimal kinetic energy, resulting in rougher Co=Pt inter-faces [6].We measured the major hysteresis loops for all of oursamples using both Kerr and SQUID magnetometry. Theproperties of the major loops show clear changes that arerelated to the increasing roughness. Figure 1 shows that theshape of the major loops change from being nucleation-dominated to being disorder-dominated. Table I shows thatthe saturation magnetization decreases as the microscopicdisorder increases. Our smoother samples (3 and 7) exhibitsoft loops with low remanence and distinct domain nuclea-tion. Between 7 and 8.5, there is a transition to loops whichdo not show a distinct domain nucleation region. Between8.5 and 20, the ascending and descending slopes of eachloop remain the same, but the loops gradually widen untilthe full magnetic moment is left at remanence. We showbelow that this change in character of the loops coincideswith the change in their measured RPM and CPM.In addition, we also found via magnetometry that all ofour films exhibit perfect macroscopic major and minorloop RPM and CPM [3]. This shows that the ensemble-average magnetization is the same for any given point on aloop, but it does not prove that the individual magneticFIG. 1 (color online). Measured magnetic hysteresis loops.Starting at the origin, and moving to increasing applied fieldjHj, the loops shown are for samples 3, 7, 8.5, 10, 12, and 20.The inversion symmetry through the origin is shown.01720domains are precisely the same. We show below, in fact,that even for our hard magnetic films with essentiallycomplete remanence, that less than 60% of the domainsare identical after reversal.Our experiments were performed at the Advanced LightSource at Lawrence Berkeley National Laboratory. Weused linearly polarized x rays from the third and higherharmonics of the beam line 9 undulator. The photon energywas set to the cobalt L3 resonance at 778 eV. To achievetransverse coherence, the raw undulator beam was passedthrough a 35-micron-diameter pinhole before being scat-tered in transmission by the sample. The resonant magneticscattering was collected by a soft x-ray charge-coupleddevice camera. The magnetization of the film was variedby an electromagnet, which applied fields perpendicular tothe film.The effects of our controlled disorder on the magneticdomains in real space and reciprocal space are shown inFig. 2. The magnetic force microscopy (MFM) images onthe top show that the domains form characteristic wormlikelabyrinths at low disorder but that these labyrinths becomeincreasingly indistinct as the structural disorder is in-creased. The magnetically scattered intensities versus theradial wave vector transfer are shown on the bottom. Theyshow (1) that the magnetic correlation length decreaseswith increasing disorder, (2) that the magnetic domain sizedistribution is well defined even though it is not visible inthe MFM images, and (3) that increasing the disorderdecreases the characteristic domain size.We have previously shown that changes in the magneticdomain structure can be measured via their magneticspeckle patterns [3]. To quantify the correlation betweentwo speckle patterns, we use image auto and cross corre-lation to extract the generalized correlation coefficient ,which is unity when the speckle patterns are identical andis zero when the speckle patterns are completely uncorre-lated [3].The first question that we addressed was whether oursamples exhibited major loop microscopic RPM. To do so,we compared two speckle patterns collected at the samepoint on the major loop, but separated by one or more fullexcursions around the major loop. For our smooth samplesTABLE I. Co=Pt Sample Characteristics.Samplea rmsb Msc Hcd3 0.48 1:36 0:06 0:08 0:018.5 0.62 1:14 0:05 1:3 0:210 0.69 1:07 0:05 1:6 0:212 0.90 1:10 0:05 2:5 0:320 1.44 0:92 0:04 5:9 0:2aGrowth pressure, milliTorr.brms interfacial roughness, nm.cSaturation magnetization of Co, 103 emu=cm3.dCoercive field, kOe.2-2FIG. 3 (color online). Measured RPM and CPM values versusthe applied field for the 8.5 milliTorr sample.FIG. 4 (color online). RPM and CPM values at the coercivepoint versus disorder. Top: our measured RPM and CPM valuesversus the measured rms roughness. Bottom: the RPM and CPMvalues obtained from our nonzero-temperature numerical simu-lations that combine the RCIM and the RFIM.FIG. 2 (color online). Measured effects of the argon sputteringpressure on the magnetic domains. Top: real space. Three squaremicron MFM images of the magnetic domain structure atremanence are shown. Note the apparent disappearance of thelabyrinthine structure as the disorder grows. Bottom: reciprocalspace. The radial profiles measured by coherent x-ray magneticscattering at the coercive point. The labels (3, 8.5, 10, 12, and 20)indicate the argon sputtering pressure in milliTorr during thegrowth of that film (see Table I).PRL 94, 017202 (2005) P H Y S I C A L R E V I E W L E T T E R Sweek ending14 JANUARY 2005with soft loops, we found little correlation between thesespeckle patterns. In sharp contrast, we always found strongcorrelations peaking near  0:6, for our rougher, hard-loop samples.The second question that we addressed was if oursamples exhibited major loop microscopic CPM. To doso, we compared the speckle pattern collected at one pointon the major loop with speckle patterns collected at theinversion-symmetric complementary point on subsequentcycles. Again, for our lowest disorder samples, we foundno correlation between these speckle patterns—zero CPMvalues. However, for the more disordered samples, wefound significant, nonzero CPM values that were consis-tently smaller than the corresponding RPM values.Our measured RPM and CPM values for sample 8.5 areshown in Fig. 3. The data for three sequential completeexcursions around the major loop are shown. For eachvalue of the applied field H, Fig. 3 shows the measuredRPM and CPM values for that field. There are severalinteresting trends: (1) Neither the RPM value nor theCPM value depends on the number of intermediate loopsor on the choice of the starting half loop. This indicates thatthe deterministic components of the RPM and CPM areessentially stationary. This implies that the memory in oursystem is largely reset by bringing the sample to saturation.It also strongly suggests that the same disorder is produc-ing both the RPM and the CPM. (2) Our RPM values areconsistently larger than our CPM values. (3) Both the RPMand the CPM values are largest near the initial domain01720nucleation region, which occurs at about 1 kOe for thissample. This suggests that the subsequent decorrelation isproduced by the domain growth; this is confirmed by ourmagnetic x-ray imaging studies. (4) Both the RPM and theCPM values decrease monotonically to their minimumvalues near complete reversal which occurs at about4 kOe for this sample. This again suggests that the decor-relation is produced by the domain growth.Figure 4 shows our major loop microscopic RPM andCPM correlation coefficients, measured at the coercivepoint for each sample, plotted versus our measured rmsroughness. We measured the interfacial roughness for eachsample by taking multiple atomic force microscope (AFM)images and calculating the rms variation of the measuredheights. We also verified that the roughness in our sampleswas conformal and increased monotonically with the argonsputtering pressure by measuring their specular x-ray re-flectivities using 0.154 nm x rays. As noted above, our twosmooth samples have essentially zero RPM and CPMvalues. In contrast, all of our rough samples exhibit non-zero RPM and CPM values that increase as the roughness2-3PRL 94, 017202 (2005) P H Y S I C A L R E V I E W L E T T E R Sweek ending14 JANUARY 2005increases. This increase starts precisely where the majorloops change from being nucleation-dominated to beingdisorder-dominated.Our results are the first direct measurements of theeffects of controlled microscopic disorder on microscopicreturn point memory and complementary point memory formajor loops. How can we understand our experimentalresults in the light of the current microscopic disordertheories, and, in particular, the discrepancy between theRPM and CPM values?A widespread approach in the literature is to approxi-mate the spins as Ising, to use simple spin-flip dynamics,which is controlled solely by the energy of each spin, andto consider zero temperature. It is easy to see then, that formodels where the energy is unchanged when all the spins(and the external field) are reversed, that the configurationsthat the system goes through on the ascending and de-scending branches of the major hysteresis loop are pre-cisely mirror images of each other, so that (at T 	 0) theRPM and CPM values are both precisely unity. This is thestandard prediction for the T 	 0 random anisotropy,bond, and coercivity Ising models (RAIM, RBIM,RCIM). On the other hand, for the T 	 0 random fieldIsing model (RFIM), only perfect RPM is predicted. Notethat both of these predictions are contrary to our experi-mental results; it is therefore clearly important to includethermal effects in our simulations.Within the Ising approximation with simple spin-flipdynamics at nonzero temperature, our experimental result(that the CPM value is comparable but always smaller thanthe RPM value) implies that the disorder has a smallcomponent that breaks spin-reversal symmetry. This canbe modeled by combining (for example) the RFIM and theRCIM. Then our simulations using a dipolar 4 model [7]show that a random field with an amplitude of only 4% ofthe spin-spin coupling can produce an effect similar towhat we see experimentally. Our simulated results usingthis approximation are shown in Fig. 4. Physically, thenecessary local random fields could come either fromfrozen impurity magnetic moments or from a very widedistribution of domain coercivities and incompletesaturation.However, there is another potential origin for our ob-served RPM-CPM asymmetry. Even if the energy is spin-inversion-symmetric, the dynamics governing the spin re-versal are not required to be. Our simulations of a spin-reversal-symmetric, disordered vector-spin model withstrong Ising-like (locally varying) anisotropy, with thedynamics given by the standard Landau-Lifshitz-Gilbert-Bloch-Bloembergen formalism, show dynamic symmetrybreaking [8]. Note that then the time evolution of any spinis given by a precessional term, which is unchanged underspin (and field) reversal, and by a relaxational term, which01720is reversed. Therefore, the overall time evolution is notinvariant under spin reversal, and the ascending and de-scending microscopic states along the major hysteresisloop are not the same.Our results have very strong implications. Within thewidely used approximation of Ising spins and simple spin-flip dynamics, they rule out all of the commonly usedsimple models—e.g., the RAIM, RBIM, RCIM andRFIM—and they necessitate a nonzero temperature com-bination of these. And if one goes beyond the simple Isingapproximation, we have found that it is possible for thedynamics to break the spin-inversion symmetry even if theHamiltonian is symmetric.Our results show that there are still a variety of newinteresting experimental and theoretical questions in thisclassic mature subject: what breaks the RPM-CPM sym-metry? Can the different random Ising models be distin-guished via the field dependence of the RPM and CPMvalues? It will be extremely interesting to see how the RPMand CPM values vary with the sample disorder and withsample temperature—particularly for technologically im-portant magnetic memory materials.We gratefully acknowledge support by the U.S. DOE viaDE-FG02-04ER46102, DE-FG03-99ER45776, DE-AC03-76SF00098, and DE-FG06-86ER45275 and via LLNL-UCDRD. We also gratefully acknowledge helpful discus-sions with K. A. Dahmen and J. P. Sethna.2-4*Partially supported by the Deutsche Forschungs-gemeinschaft via HE 3286/1-1 and is currently atBESSY GmbH, Berlin, Germany.[1] A. Moser et al., J. Phys. D 35, R157 (2002); K. Ouchi,IEEE Trans. Magn. 37, 1217 (2001).[2] For RAIM, see E. Vives and A. Planes, Phys. Rev. B 63,134431 (2001); for RBIM, see E. Vives and A. Planes,J. Magn. Magn. Mater. 221, 164 (2000); for RCIM, seeO. Hovorka and G. Friedman, cond-mat/0306300; forRFIM, see J. P. Sethna, K. A. Dahmen, and O. Perkovic,cond-mat/0406320.[3] M. S. Pierce et al., Phys. Rev. Lett. 90, 175502 (2003);B. Hu et al., Synchrotron Radiation News 14, 11 (2001).[4] S. Zapperi and G. Durin, Comput. Mater. Sci. 20, 436(2001); J. R. Petta, M. B. Weissman, and G. Durin, Phys.Rev. E 57, 6363 (1998); D. Spasojevic et al., Phys. Rev. E54, 2531 (1996).[5] J. R. Hoinville et al., IEEE Trans. Magn. 28, 3398 (1992);A. Jander et al., IEEE Trans. Magn. 34, 1657 (1998);P. Fischer et al., J. Phys. D 35,2391 (2002).[6] E. E. Fullerton et al., Phys. Rev. B 48, 17432 (1993).[7] E. A. Jagla, Phys. Rev. E 70, 046204 (2004).[8] J. M. Deutsch, T. Mai, and O. Narayan, cond-mat/0408158.

Disorder-induced microscopic magnetic memory

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