Effect of magnetic fields on the relaxation of the thermoremanent magnetization in spin glasses

Chu, Dongliang; Kenning, G. G.; Orbach, Raymond Lee

doi:10.1080/01418639508238539

Cited by 32 publications

(36 citation statements)

References 17 publications

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“…A distribution of exchange energies is related to a distribution of energy barriers. In the phase-space representation, aging during t w at T 1 can be viewed as a random walk between the minima of the free energy 13,21,22 ͓Fig. 5͑b͔͒ by jumping over the barriers that are of the order k B T 1 or smaller.…”

Section: Discussionmentioning

confidence: 99%

“…Such a decreasing behavior was also found in a canonical SG CuMn ͑with 5 at. % Mn͒, 22 whereas the normalized TRM was found to be H fc independent in the geometrically frustrated icosahedral Tb-Mg-Zn and Tb-Mg-Cd QCs, 13 which was attributed to a superparamagnetic-cluster structure of the magnetic phase in these QC compounds.…”

Section: Thermoremanent Magnetization Versus Cooling Field H Fcmentioning

confidence: 99%

“…21,22 In this experiment ͓Fig. 5͑a͔͒, one cools the sample in a field H fc from above T f to a measuring ͑and, at the same time, aging͒ temperature T 1 Ͻ T f , where the spin system is let to age for a time t w .…”

Section: Thermoremanent Magnetizationmentioning

confidence: 99%

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Broken ergodicity, memory effect, and rejuvenation in Taylor-phase and decagonalAl3(Mn,Pd,Fe)complex intermetallics

et al. 2008

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The Taylor-phase complex intermetallic compound T-Al 3 Mn, its solid solutions with Pd and Fe, T-Al 3 ͑Mn, Pd͒ and T-Al 3 ͑Mn, Fe͒, and the related decagonal d-Al-Mn-Fe quasicrystal belong to the class of magnetically frustrated spin systems that exhibit rich out-of-equilibrium spin dynamics in the nonergodic phase below the spin-freezing temperature T f . Performing large variety of magnetic experiments as a function of temperature, magnetic field, aging time t w , and different thermal histories, we investigated broken-ergodicity phenomena of ͑i͒ a difference in the field-cooled and zero-field-cooled susceptibilities, ͑ii͒ the frequencydependent freezing temperature, T f ͑͒, ͑iii͒ hysteresis and remanence, ͑iv͒ ultraslow decay of the thermoremanent magnetization, ͑v͒ the memory effect ͑a state of the spin system reached upon isothermal aging can be retrieved after a negative temperature cycle͒, and ͑vi͒ "rejuvenation" ͑small positive temperature cycle within the nonergodic phase erases the effect of previous aging͒. We show that the phenomena involving isothermal aging periods ͑the memory effect, rejuvenation, and the ultraslow decay of the thermoremanent magnetization͒ get simple explanation by considering that during aging under steady external conditions, localized spin regions quasiequilibrate into more stable configurations, so that higher thermal energy is needed to destroy these regions by spin flipping, as compared to the thermal energy required to reverse a frustrated spin in a disordered spin-glass configuration that forms in the case of no aging. Common to all the investigated brokenergodicity phenomena is the slow approach of a magnetically frustrated spin system toward a global equilibrium, which can never be reached on accessible experimental time scales due to macroscopic equilibration times.

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Section: Discussionmentioning

confidence: 99%

Section: Thermoremanent Magnetization Versus Cooling Field H Fcmentioning

confidence: 99%

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Broken ergodicity, memory effect, and rejuvenation in Taylor-phase and decagonalAl3(Mn,Pd,Fe)complex intermetallics

et al. 2008

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“…Theoretically 18,19 and experimentally 20,21,22,23,24,25,26,27,28,29,30 it has been accepted that the time variation of χ ZF C (t) may be described by a product of a power-law form and a stretched exponential function…”

Section: B Stretched Exponential Relaxation In the Sg Phasementioning

confidence: 99%

Aging dynamics in a reentrant ferromagnet:Cu0.2Co0.8Cl2−FeCl3
Suzuki
¹
,
Suzuki
²

2005
Phys. Rev. B
3
2
4
0
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Aging dynamics of a reentrant ferromagnet Cu0.2Co0.8Cl2-FeCl3 graphite bi-intercalation compound has been studied using AC and DC magnetic susceptibility. This compound undergoes successive transitions at the transition temperatures Tc (= 9.7 K) and TRSG (= 3.5 K). The relaxation rate S(t) exhibits a characteristic peak at tcr close to a wait time tw below Tc, indicating that the aging phenomena occur in both the reentrant spin glass (RSG) phase below TRSG and the ferromagnetic (FM) phase between TRSG and Tc. The relaxation rate S(t) (= dχZF C (t)/d ln t) in the FM phase exhibits two peaks around tw and a time much shorter than tw under the positive T -shift aging, indicating a partial rejuvenation of domains. The aging state in the FM phase is fragile against a weak magnetic-field perturbation. The time (t) dependence of χZF C (t) around t ≈ tcr is well approximated by a stretched exponential relaxation: χZF C (t) ≈ exp[−(t/τ ) 1−n ]. The exponent n depends on tw, T , and H. The relaxation time τ (≈ tcr) exhibits a local maximum around 5 K, reflecting a chaotic nature of the FM phase. It drastically increases with decreasing temperature below TRSG.

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“…Our approach, justified previously through magnetic field cycling [9] and used to determine the Parisi physical order parameter P (q), [1] makes use of the scaling relationship introduced by Vincent et al [2]. They show that barrier heights surmounted during aging are reduced upon a change in magnetic field by E z , a quantity related to the change in Zeeman energy.…”

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confidence: 99%

Extraction of the Spin Glass Correlation Length

et al. 1999

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The peak of the spin glass relaxation rate, S(t) = d[ − MT RM (t, tw)/H]/dℓnt, is directly related to the typical value of the free energy barrier which can be explored over experimental time scales. A change in magnetic field H generates an energy Ez = Nsχ f c H 2 by which the barrier heights are reduced, where χ f c is the field cooled susceptibility per spin, and Ns is the number of correlated spins. The shift of the peak of S(t) gives Ez, generating the correlation length, ξ(t, T ), for Cu : M n 6at.% and CdCr1.7In0.3S4. Fits to power law dynamics, ξ(t, T ) ∝ t α(T ) and activated dynamics ξ(t, T ) ∝ (ℓnt) 1/ψ compare well with simulation fits, but possess too small a prefactor for activated dynamics.PACS numbers: 75.50. Lk, 75.10.Nr, 75.40.Gb The study of the irreversible behavior of the spin glass magnetization under a change of magnetic field allows exploration of the available states of a random frustrated system. [1,2] There are various representations for the long time evolution and the dynamics of spin glasses, [3-5] but a coherent, overall accepted real space description remains lacking.[6] The purpose of this paper is to extract a time and temperature dependent spin glass correlation length from a specially structured set of experiments, and to compare our results with available theoretical predictions.The definition of a correlation length for a spin glass is difficult to express in measurable terms. Marinari et al. [7] and Kisker et al. [8] introduced the time dependent equal time correlation function at time t. In the notation of Ref. 7,where the average is done at time t, and σ i (σ i+x ) and τ i (τ i+x ) represent the z component of Ising spins at sites i (i + x) in two thermalized configurations in a box of volume V . To avoid accidental contributions to G(x, t), the two configurations are chosen to have zero overlap, q = V −1 i σ i τ i . Refs. 7 and 8 both observed, through their simulation studies, that for large times t the correlation function G(x, t) differs from zero for distances not too much larger than a dynamic correlation length ξ(t, T ). Simulations of Marinari et al. [7] obtain satisfactory fits for ξ(t, T ) ∝ (t/τ 0 ) αT /Tg , appropriate to power law dynamics, [4] while Kisker et al. [8] fit satisfactorily both this proportionality and equally well ξ(t, T ) ∝ [(T /T g )ℓn(t/τ 0 )] 1/ψ , appropriate to activated dynamics. [5] Our measurements consist of cooling a sample in a magnetic field through the glass temperature T g to the measuring temperature T , waiting a time t w , then cutting the field to zero and measuring the decay of the magnetization. This generates the response function,where M T RM (t, t w ) is the thermoremanent magnetization at time t after cutting the magnetic field to zero. Our approach, justified previously through magnetic field cycling [9] and used to determine the Parisi physical order parameter P (q), [1] makes use of the scaling relationship introduced by Vincent et al. [2]. They show that barrier heights surmounted during aging are reduced upon a...

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Effect of magnetic fields on the relaxation of the thermoremanent magnetization in spin glasses

Cited by 32 publications

References 17 publications

Broken ergodicity, memory effect, and rejuvenation in Taylor-phase and decagonalAl3(Mn,Pd,Fe)complex intermetallics

Broken ergodicity, memory effect, and rejuvenation in Taylor-phase and decagonalAl3(Mn,Pd,Fe)complex intermetallics

Aging dynamics in a reentrant ferromagnet:Cu0.2Co0.8Cl2−FeCl3
Suzuki
¹
,
Suzuki
²

2005
Phys. Rev. B
3
2
4
0
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Extraction of the Spin Glass Correlation Length

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Effect of magnetic fields on the relaxation of the thermoremanent magnetization in spin glasses

Cited by 32 publications

References 17 publications

Broken ergodicity, memory effect, and rejuvenation in Taylor-phase and decagonalAl3(Mn,Pd,Fe)complex intermetallics

Broken ergodicity, memory effect, and rejuvenation in Taylor-phase and decagonalAl3(Mn,Pd,Fe)complex intermetallics

Aging dynamics in a reentrant ferromagnet:Cu0.2Co0.8Cl2−FeCl3Suzuki1, Suzuki2 2005Phys. Rev. B3240View full textAdd to dashboardCite

Extraction of the Spin Glass Correlation Length

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About

Aging dynamics in a reentrant ferromagnet:Cu0.2Co0.8Cl2−FeCl3
Suzuki
¹
,
Suzuki
²

2005
Phys. Rev. B
3
2
4
0
View full text Add to dashboard Cite