000136058 001__ 136058 000136058 005__ 20250319143308.0 000136058 0247_ $$2doi$$a10.1103/PhysRevB.107.214436 000136058 0248_ $$2sideral$$a135213 000136058 037__ $$aART-2023-135213 000136058 041__ $$aeng 000136058 100__ $$aPaga, I. 000136058 245__ $$aSuperposition principle and nonlinear response in spin glasses 000136058 260__ $$c2023 000136058 5060_ $$aAccess copy available to the general public$$fUnrestricted 000136058 5203_ $$aThe extended principle of superposition has been a touchstone of spin-glass dynamics for almost 30 years. The Uppsala group has demonstrated its validity for the metallic spin glass, CuMn, for magnetic fields H up to 10 Oe at the reduced temperature Tr=T/Tg=0.95, where Tg is the spin-glass condensation temperature. For H>10 Oe, they observe a departure from linear response which they ascribe to the development of nonlinear dynamics. The thrust of this paper is to develop a microscopic origin for this behavior by focusing on the time development of the spin-glass correlation length, ξ(t,tw;H). Here, t is the time after H changes, and tw is the time from the quench for T>Tg to the working temperature T until H changes. We connect the growth of ξ(t,tw;H) to the barrier heights Δ(tw) that set the dynamics. The effect of H on the magnitude of Δ(tw) is responsible for affecting differently the two dynamical protocols associated with turning H off (TRM, or thermoremanent magnetization) or on (ZFC, or zero-field-cooled magnetization). This difference is a consequence of nonlinearity based on the effect of H on Δ(tw). Superposition is preserved if Δ(tw) is linear in the Hamming distance Hd (proportional to the difference between the self-overlap qEA and the overlap q[Δ(tw)]). However, superposition is violated if Δ(tw) increases faster than linear in Hd. We have previously shown, through experiment and simulation, that the barriers Δ(tw) do increase more rapidly than linearly with Hd through the observation that the growth of ξ(t,tw;H) slows down as ξ(t,tw;H) increases. In this paper, we display the difference between the zero-field-cooled ξZFC(t,tw;H) and the thermoremanent magnetization ξTRM(t,tw;H) correlation lengths as H increases, both experimentally and through numerical simulations, corresponding to the violation of the extended principle of superposition in line with the finding of the Uppsala Group. 000136058 536__ $$9info:eu-repo/grantAgreement/EC/H2020/694925/EU/Low Temperature Glassy Systems/LoTGlasSy$$9This project has received funding from the European Union’s Horizon 2020 research and innovation program under grant agreement No H2020 694925-LoTGlasSy$$9info:eu-repo/grantAgreement/ES/MCIU/FPU18/02665$$9info:eu-repo/grantAgreement/ES/MICINN-AEI-FEDER/PID2019-103939RB-I00$$9info:eu-repo/grantAgreement/ES/MICINN AEI/PID2022-136374NB-C21$$9info:eu-repo/grantAgreement/ES/MICINN/PID2021-125506NA-I00$$9info:eu-repo/grantAgreement/ES/MINECO-AEI-FEDER/PGC2018-094684-B-C21$$9info:eu-repo/grantAgreement/ES/MINECO-AEI-FEDER/PGC2018-094684-B-C22$$9info:eu-repo/grantAgreement/ES/MINECO-AEI-FEDER/PID2020-112936GB-I00 000136058 540__ $$9info:eu-repo/semantics/openAccess$$aAll rights reserved$$uhttp://www.europeana.eu/rights/rr-f/ 000136058 592__ $$a1.345$$b2023 000136058 590__ $$a3.2$$b2023 000136058 591__ $$aMATERIALS SCIENCE, MULTIDISCIPLINARY$$b201 / 439 = 0.458$$c2023$$dQ2$$eT2 000136058 591__ $$aPHYSICS, CONDENSED MATTER$$b31 / 79 = 0.392$$c2023$$dQ2$$eT2 000136058 591__ $$aPHYSICS, APPLIED$$b62 / 179 = 0.346$$c2023$$dQ2$$eT2 000136058 593__ $$aCondensed Matter Physics$$c2023$$dQ1 000136058 593__ $$aElectronic, Optical and Magnetic Materials$$c2023$$dQ1 000136058 594__ $$a6.3$$b2023 000136058 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/acceptedVersion 000136058 700__ $$aZhai, Q. 000136058 700__ $$aBaity-Jesi, M. 000136058 700__ $$aCalore, E. 000136058 700__ $$0(orcid)0000-0002-7934-7271$$aCruz, A.$$uUniversidad de Zaragoza 000136058 700__ $$aCummings, C. 000136058 700__ $$aFernandez, L. A. 000136058 700__ $$0(orcid)0000-0003-2903-3044$$aGil-Narvion, J. M. 000136058 700__ $$aPemartin, I. Gonzalez-Adalid 000136058 700__ $$aGordillo-Guerrero, A. 000136058 700__ $$0(orcid)0000-0003-2916-5493$$aIñiguez, D. 000136058 700__ $$aKenning, G. G. 000136058 700__ $$0(orcid)0000-0002-0340-5199$$aMaiorano, A. 000136058 700__ $$aMarinari, E. 000136058 700__ $$0(orcid)0000-0002-3376-0327$$aMartin-Mayor, V. 000136058 700__ $$0(orcid)0000-0002-0420-8605$$aMoreno-Gordo, J. 000136058 700__ $$0(orcid)0000-0002-3613-3302$$aMuñoz-Sudupe, A. 000136058 700__ $$0(orcid)0000-0002-0795-8743$$aNavarro, D.$$uUniversidad de Zaragoza 000136058 700__ $$aOrbach, R. L. 000136058 700__ $$aParisi, G. 000136058 700__ $$0(orcid)0000-0001-8425-7345$$aPerez-Gaviro, S.$$uUniversidad de Zaragoza 000136058 700__ $$aRicci-Tersenghi, F. 000136058 700__ $$aRuiz-Lorenzo, J. J. 000136058 700__ $$aSchifano, S. F. 000136058 700__ $$aSchlagel, D. L. 000136058 700__ $$0(orcid)0000-0002-5967-2827$$aSeoane, B. 000136058 700__ $$0(orcid)0000-0003-2772-3762$$aTarancon, A.$$uUniversidad de Zaragoza 000136058 700__ $$0(orcid)0000-0001-7276-2942$$aYllanes, D. 000136058 7102_ $$15008$$2785$$aUniversidad de Zaragoza$$bDpto. Ingeniería Electrón.Com.$$cÁrea Tecnología Electrónica 000136058 7102_ $$12004$$2405$$aUniversidad de Zaragoza$$bDpto. Física Teórica$$cÁrea Física Teórica 000136058 773__ $$g107, 21 (2023), 214436 [21 pp.]$$pPhys. Rev. B$$tPhysical Review B$$x2469-9950 000136058 8564_ $$s1508800$$uhttps://zaguan.unizar.es/record/136058/files/texto_completo.pdf$$yPostprint 000136058 8564_ $$s2760670$$uhttps://zaguan.unizar.es/record/136058/files/texto_completo.jpg?subformat=icon$$xicon$$yPostprint 000136058 909CO $$ooai:zaguan.unizar.es:136058$$particulos$$pdriver 000136058 951__ $$a2025-03-19-14:32:19 000136058 980__ $$aARTICLE