Canonical Spin Glass Systems Research Articles

Toward understanding the dimensional crossover of canonical spin-glass thin films

Spin-glass thin films exhibit many features different from the bulk. The freezing temperatures of spin-glass films are suppressed for reduced thickness and follow the Kenning relation. The dynamics are altered near the vacuum interface. These phenomena are closely related to the lower critical dimension of spin glasses, the spin-glass correlation length, and the dimensional crossover from d = 3 to d = 2. In this article, we review the experimental facts and theoretical perspectives for spin-glass thin films. We focus on canonical spin-glass systems with the Ruderman–Kittel–Kasuya–Yosida (RKKY) interaction between magnetic impurities in a nonmagnetic host. Open questions to be addressed are emphasized.

Evidence for canonical spin glass behaviour in polycrystalline Mn1.5Fe1.5Al Heusler alloy

Magnetic properties of magnetically frustrated polycrystalline Mn1.5Fe1.5Al Heusler type alloy with a β-Mn structure were systematically studied using dc magnetization, ac susceptibility, magnetic relaxation and magnetic memory effect measurements to understand its magnetic ground state. The Mn1.5Fe1.5Al alloy system exhibits a sharp peak at low temperature around 34.5 K with strong antiferromagnetic correlations (θCW ∼ −639 K) and a high degree of frustration (fp ∼ 18.7) which suggest the presence of competing magnetic interactions. Despite of strong antiferromagnetic correlations, this peak has spin-glass character as confirmed by the observations of bifurcation of the zero-field-cooled and field-cooled magnetization curves below the irreversibility temperature, field dependent shift of the irreversibility temperature, unidirectional exchange bias effect on the field-cooled M-H hysteresis loop, exponential decay of the temperature variation of remanence and coercivity, frequency dependent shift of the spin glass freezing temperature (Tf) as per the dynamic scaling laws given by the critical slowing down model and Vogel-Fulcher law, magnetic relaxation and magnetic memory effect below Tf. The observation of a clear asymmetric response with respect to the temperature cycling in the magnetic relaxation measurements validates the hierarchical model of the spin-glass magnetic relaxation in Mn1.5Fe1.5Al alloy. Since the behaviour exhibited by the Mn1.5Fe1.5Al alloy has perfect similarity with the well-known atomic spin glasses like CuMn, AuFe, therefore, it may be considered as canonical spin-glass system.

Non-equilibrium magnetic response of canonical spin glass and magnetic glass

Time and history dependent magnetization has been observed in a wide variety of materials, which are collectively termed as the glassy magnetic systems. However, such systems showing similar non-equilibrium magnetic response can be microscopically very different and they can be distinguished by carefully looking into the details of the observed metastable magnetic behavior. Canonical spin glass (SG) is the most well studied member of this class and has been extensively investigated both experimentally and theoretically over the last five decades. In canonical SGs, the low temperature magnetic state obtained by cooling across the SG transition temperature in presence of an applied magnetic field is known as the field cooled (FC) state. This FC state in canonical SG is widely believed as an equilibrium state arising out of a thermodynamic second order phase transition. Here, we show that the FC state in canonical SG is not really an equilibrium state of the system. We report careful dc magnetization and ac susceptibility measurements on two canonical SG systems, AuMn (1.8%) and AgMn (1.1%). The dc magnetization in the FC state shows clear temperature dependence. In addition, the magnetization shows a distinct thermal hysteresis in the temperature regime below the SG transition temperature. On the other hand, the temperature dependence of ac susceptibility has clear frequency dispersion below SG transition in the FC state prepared by cooling the sample in the presence of a dc-bias field. We further distinguish the metastable response of the FC state of canonical SG from the metastable response of the FC state in an entirely different class of glassy magnetic system namely magnetic glass, where the non-equilibrium behavior is associated with the kinetic-arrest of a first order magnetic phase transition.

Field-cooled state of the canonical spin glass revisited

Canonical spin-glass (SG) is an enigmatic system in condensed matter physics. In spite of the intense activities of last five decades several questions regarding the nature of the SG phase transition and the SG ground state are yet to be resolved completely. In this backdrop we have revisited the field cooled state of canonical spin-glass. We have experimentally studied magnetic response in two canonical spin-glass systems AuMn(1.8%) and AgMn(1.1%), both in the field cooled (FC) as well as zero field cooled (ZFC) state. We show that the well known magnetic memory effect, which clearly established earlier the metastable nature of the ZFC state in SG, is also present in the FC state. The results of our experimental study indicate that the FC state also is a non-equilibrium state, and hence the energy landscape involved is a non-trivial one. This in turn seriously questions the picture of spin-glass transformation as a second order thermodynamic phase transition.

Possible glass-like random singlet magnetic state in 1T-TaS2

Two-dimensional layered transition-metal-dichalcogenide compound 1T-TaS2 shows the rare coexistence of charge density wave (CDW) and electron correlation driven Mott transition. In addition, atomic-cluster spins on the triangular lattice of the CDW state of 1T-TaS2 give rise to the possibility of the exotic spin-singlet state in which quantum fluctuations of spins are strong enough to prevent any long range magnetic ordering down to the temperature absolute zero (0 K). We present here the evidences of a glass-like random singlet magnetic state in 1T-TaS2 at low temperatures through a study of temperature and time dependence of magnetization. Comparing the experimental results with a representative canonical spin-glass system Au(1.8%Mn), we show that this glass-like state is distinctly different from the well established canonical spin-glass state.

Electron doping induced exchange bias and cluster glass magnetism in multiferroic Sc0.8Zr0.2MnO3

Since few decades, several studies on hole-doping in rare-earth manganites (RMnO3) have been reported exploring various novel phenomena. Comparatively electron-doping studies in RMnO3 are scarcely found and the intrinsic properties are still unidentified. We report on the occurrence of exchange bias phenomenon and glassy magnetic interaction in multiferroic compound Sc0.8Zr0.2MnO3 induced by electron doping. The compound possesses long-range antiferromagnetic ordering, (TN = 90 K) and electron doping was found to induce additional ferromagnetic interaction (TC = 60 K) in it. The study provides compelling experimental evidences that the system behaves more like a cluster glass compound than a canonical spin glass system with a freezing temperature (Tf) of 13 K. Field-cooled magnetic hysteresis loops are found to shift in the field axis (HE) and show asymmetry in remanent magnetization (ME). The direction of loop shift depends on the sign of the cooling field used. We present details of field cooling and temperature dependence of HE and ME and training effect in Sc0.8Zr0.2MnO3. A comparison with the commonly observed exchange bias phenomena in typical phase separated systems is also presented. The present study assumes significance as it helps the understanding of new phenomena consequent to electron doping.

Large magnetic cooling power involving frustrated antiferromagnetic spin-glass state inR2NiSi3(R=Gd,Er)

The ternary intermetallic compounds ${\mathrm{Gd}}_{2}{\mathrm{NiSi}}_{3}$ and ${\mathrm{Er}}_{2}{\mathrm{NiSi}}_{3}$ are synthesized in chemically single phase, which are characterized using dc magnetization, ac magnetic susceptibility, heat capacity, and neutron diffraction studies. Neutron diffraction and heat capacity studies confirm that long-range magnetic ordering coexists with the frustrated glassy magnetic components for both compounds. The static and dynamical features of dc magnetization and frequency-dependent ac susceptibility data reveal that ${\mathrm{Gd}}_{2}{\mathrm{NiSi}}_{3}$ is a canonical spin-glass system, while ${\mathrm{Er}}_{2}{\mathrm{NiSi}}_{3}$ is a reentrant spin cluster-glass system. The spin freezing temperature merges with the long-range antiferromagnetic ordering temperature at 16.4 K for ${\mathrm{Gd}}_{2}{\mathrm{NiSi}}_{3}$. ${\mathrm{Er}}_{2}{\mathrm{NiSi}}_{3}$ undergoes antiferromagnetic ordering at 5.4 K, which is slightly above the spin freezing temperature at 3 K. The detailed studies of nonequilibrium dynamical behavior, viz., the memory effect and relaxation behavior using different protocols, suggest that both compounds favor the hierarchical model over the droplet model. A large magnetocaloric effect is observed for both compounds. Maximum values of isothermal entropy change $(\ensuremath{-}\mathrm{\ensuremath{\Delta}}{S}_{M})$ and relative cooling power (RCP) are found to be 18.4 J/kg K and 525 J/kg for ${\mathrm{Gd}}_{2}{\mathrm{NiSi}}_{3}$ and 22.6 J/kg K and 540 J/kg for ${\mathrm{Er}}_{2}{\mathrm{NiSi}}_{3}$, respectively, for a change in field from 0 to 70 kOe. The values of RCP are comparable to those of the promising refrigerant materials. A correlation between large RCP and magnetic frustration is discussed for developing new magnetic refrigerant materials.

Spin glass behavior of the antiferromagnetic Heisenberg model on scale free network

Randomness and frustration are considered to be the key ingredients for the existence of spin glass (SG) phase. In a canonical system, these ingredients are realized by the random mixture of ferromagnetic (FM) and antiferromagnetic (AF) couplings. The study by Bartolozzi et al. [Phys. Rev. B73, 224419 (2006)] who observed the presence of SG phase on the AF Ising model on scale free network (SFN) is stimulating. It is a new type of SG system where randomness and frustration are not caused by the presence of FM and AF couplings. To further elaborate this type of system, here we study Heisenberg model on AF SFN and search for the SG phase. The canonical SG Heisenberg model is not observed in d-dimensional regular lattices for (d ≤ 3). We can make an analogy for the connectivity density (m) of SFN with the dimensionality of the regular lattice. It should be plausible to find the critical value of m for the existence of SG behaviour, analogous to the lower critical dimension (dl) for the canonical SG systems. Here we study system with m = 2, 3, 4 and 5. We used Replica Exchange algorithm of Monte Carlo Method and calculated the SG order parameter. We observed SG phase for each value of m and estimated its corersponding critical temperature.

Inhomogeneous Ferromagnetism and Spin-Glass-Like Behavior in <inline-formula> <tex-math notation="TeX">$({\rm Nd}_{1-x}{\rm Y}_{x})_{0.7}{\rm Sr}_{0.3}{\rm MnO}_{3}$ </tex-math></inline-formula> With <inline-formula> <tex-math notation="TeX">$x=0.21{-}0.35$ </tex-math></inline-formula>

The magnetic properties of polycrystalline ceramic samples $({\rm Nd}_{1-x}{\rm Y}_{x})_{0.7}{\rm Sr}_{0.3}{\rm MnO}_{3}$ with $x=0.21-0.35$ were studied by means of dc magnetization and ac susceptibility measurements. Experimental results reveal a strong decrease of the ferromagnetic (FM)-paramagnetic phase-transition temperature $(T_{C})$ from 97 to 65 K as increasing $x$ from 0.21 to 0.35, respectively. There is magnetic inhomogeneity associated with short-range FM order. Particularly, the samples undergo a spin-glass (SG) phase transition at the so-called blocking temperature $(T_{B})$ below $T_{C}$ , which shifts toward lower temperatures with increasing the applied field, $H_{\rm ex}$ ; $T_{B}\to T_{g}$ (the SG phase-transition temperature) as $H_{\rm ex}\to 0$ . The existence of the SG behavior in these samples was also confirmed by frequency $(f)$ dependences of the ac susceptibility. For the in-phase/real component, $\chi^{\prime}(T)$ , it shows a frequency-dependent peak at the SG freezing temperature $(T_{f})$ ; $T_{f}\to T_{g}$ as $f\to 0$ . Dynamics of this process were analyzed by means of the slowing down scaling law, $\tau/\tau_{0}\propto (T_{f}/T_{g}-1)^{-zv}$ , where $\tau_{0}$ and $zv$ are the characteristic time and critical exponent, respectively. Fitting the experimental $T\!_{f}(f)$ data to the scaling law gave the results of $zv=10.1{-}12.3$ and $\tau_{0}=10^{-21}{-}10^{-15}~{\rm s}$ . These values are different from those expected for canonical SG systems with $zv={10}$ and $\tau_{0}=10^{-13}~{\rm s}$ , revealing the cluster-SG behavior of $({\rm Nd}_{1-x}{\rm Y}_{x})_{0.7}{\rm Sr}_{0.3}{\rm MnO}_{3}$ samples. Notably, the increase in Y content leads to the shift of $\tau_{0}$ and $zv$ values toward those of canonical SG systems, which is ascribed to an expansion of SG clusters.

Critical property of spin-glass transition in a bond-disordered classical antiferromagnetic Heisenberg model with a biquadratic interaction

Motivated by puzzling spin-glass behaviors observed in many pyrochlore-based magnets, effects of magnetoelastic coupling to local lattice distortions were recently studied by the authors for a bond-disordered antiferromagnet on a pyrochlore lattice [arXiv:1010.5625v2]. Here, we extend the analyses with focusing on the critical property of the spin-glass transition which occurs concomitantly with a nematic transition. Finite-size scaling analyses are performed up to a larger system size with 8192 spins to estimate the transition temperature and critical exponents. The exponents are compared with those in the absence of the magnetoelastic coupling and with those for the canonical spin-glass systems. We also discuss the temperature dependence of the specific heat in comparison with that in canonical spin-glass systems as well as an experimental result.

Ferromagnetism and spin-glass-like behavior in (Nd0.65Y0.35)0.7Sr0.3MnO3

We have studied the ferromagnetism and spin-glass-like behavior in polycrystalline perovskite (Nd0.65Y0.35)0.7Sr0.3MnO3 based on investigations of the magnetization, magnetic AC susceptibility, and electron spin resonance (ESR). Magnetization measurements versus temperature reveal a spin-glass phase-transition temperature Tg at about 53 K. For the in-phase susceptibility x′(T), a frequency-dependent peak called the spin-freezing temperature Tf is observed. A lowering of the frequency to zero leads to Tf → Tg. The dynamics of this process was analyzed by means of the slowing-down scaling law τ/τo = (Tf /Tg-1)−zv, where the characteristic time τo and critical exponent zv obtained by fitting the experimental Tf data were about (i.e., 1.6 × 10−15 s) and 10.12, respectively, quite different from those expected for canonical spin-glass systems with τo = 10−13 s and zv = 10. The spin-glass phenomenon is related to the magnetic frustration phenomenon caused by strong competition between ferromagnetic and anti-ferromagnetic interactions, together with the strong magnetic disorder. The dynamics of the magnetic interactions in (Nd0.65Y0.35)0.7Sr0.3MnO3 was studied further by means of ESR.

Critical phenomena of canonical spin glass systems with large Dzyaloshinsky–Moriya anisotropy

We have studied critical phenomena of spin glass transition for larger Dzyaloshinsky–Moriya anisotropy Heisenberg spin glass system, PtMn. The analysis of nonlinear magnetizations in the framework of the existence of a phase transition at Tg yields the critical exponents δ = 2.5 ± 0.3, γ = 1.5 ± 0.3 and β = 1 ± 0.3. These results suggest that the universality class of spin glass transition on PtMn is the same as those of CuMn, AgMn and AuFe systems. Experimentally, there is an indication of a unique universality class for Heisenberg spin glass materials.

Signatures of spin-glass behaviour in PrIr2B2 and heavy fermion behaviour in PrIr2B2C

The magnetic and transport properties of PrIr2B2 and PrIr2B2C have been investigated by dc and ac magnetic susceptibility, specific heat, electrical resistivity and magnetoresistance measurements. PrIr2B2 forms in CaRh2B2-type orthorhombic crystal structure (space group Fddd). At low fields the dc magnetic susceptibility of PrIr2B2 exhibits a sharp anomaly near 46 K which is followed by an abrupt increase below 10 K with a peak at 6 K, and split-up in ZFC and FC data below 46 K. In contrast, the specific heat exhibits only a broad Schottky type hump near 9 K which indicates that there is no long range magnetic order in this compound. The thermo-remanent magnetization is found to decay very slowly with a mean relaxation time τ = 3917 s. An ac magnetic susceptibility measurement also observes two sharp anomalies; the peak positions strongly depend on the frequency and shift towards high temperature with an increase in frequency, obeying the Vogel–Fulcher law as expected for a canonical spin-glass system. The two spin-glass transitions occur at freezing temperatures Tf1 = 36 K and Tf2 = 3.5 K with shifts in the freezing temperatures per decade of frequency δTf1 = 0.044 and δTf2 = 0.09. An analysis of the frequency dependence of the transition temperature with critical slowing down, τmax/τ0 = [(Tf−TSG)/TSG]−zν, gives τ0 = 10−7 s and exponent zν = 8, and the Vogel–Fulcher law gives an activation energy of 84 K for Tf1 and 27.5 K for Tf2. While zν = 8 is typical for spin-glass system, the characteristic relaxation time τ0 = 10−7 s is very large and comparable to that of superspin-glass systems. An addition of C in PrIr2B2 leads to PrIr2B2C which forms in LuNi2B2C-type tetragonal structure (space group I4/mmm) and remains paramagnetic down to 2 K. The specific heat data show a broad Schottky type anomaly, which could be fairly reproduced with CEF analysis which suggests that the ground state is a CEF-split singlet and the first excited state singlet is situated 15 K above the ground state. The Sommerfeld coefficient γ∼300 mJ mol−1 K−2 of PrIr2B2C is very high and reflects a heavy fermion behaviour in this compound. We believe that the heavy fermion state in PrIr2B2C has its origin in low lying crystal field excitations as has been observed in PrRh2B2C.

Effect of pressure on temperature-induced spin-state transition in La1−xSrxCoO3 single crystals

The temperature dependence of magnetization (M) and resistivity (ρ) of La1−xSrxCoO3(x=0.10, 0.33) single crystals have been analyzed. For x=0.10, the temperature dependence of field-cooled magnetization (MFC) and zero-field-cooled magnetization (MZFC) is similar to that expected for a canonical spin-glass system. The thermal response of MZFC for x=0.33 indicates a glassy ferromagnetic state. We observe that the ferromagnetic transition temperature TC decreases and ρ increases rapidly with increasing pressure (P) for the metallic sample (x=0.33), while the dependence of ρ on P for the insulating sample (x=0.10) is quite complicated; the pressure coefficient of resistivity (dρ/dT) is sensitive to temperature and applied pressure due to the strong interplay between the pressure-induced band broadening and spin-state transition phenomenon. dρ/dT is large and negative at low-pressure and low-temperature regime while small and positive at high pressures (P>5.4 GPa) and high temperatures (T>110 K).

Pressure- and temperature-induced spin-state transition in single-crystallineLa1−xSrxCoO3(x=0.10and 0.33)

We report on the temperature dependence of magnetization $(M)$ and resistivity $(\ensuremath{\rho})$ of ${\text{La}}_{1\ensuremath{-}x}{\text{Sr}}_{x}{\text{CoO}}_{3}$ ($x=0.10$ and 0.33) single crystals. For $x=0.10$, the temperature dependence of field-cooled magnetization $({M}_{\text{FC}})$ and zero-field-cooled magnetization $({M}_{\text{ZFC}})$ are similar to that expected for a canonical spin-glass system. The thermal response of ${M}_{\text{ZFC}}$ for $x=0.33$ indicates a glassy ferromagnetic state. We observe that the ferromagnetic transition temperature ${T}_{C}$ decreases and $\ensuremath{\rho}$ increases rapidly with increasing pressure $(P)$ for the metallic sample $(x=0.33)$ while the dependence of $\ensuremath{\rho}$ on $P$ for the insulating sample $(x=0.10)$ is quite complicated; the pressure coefficient of resistivity $(d\ensuremath{\rho}/dT)$ is sensitive to temperature and applied pressure due to the strong interplay between the pressure-induced band broadening and spin-state transition phenomenon. $d\ensuremath{\rho}/dT$ is large and negative at low-pressure and low-temperature regimes while small and positive at high pressures $(Pg5.4\text{ }\text{GPa})$ and high temperatures $(Tg110\text{ }\text{K})$.

Magnetic and caloric properties of magnetic nanoparticles: an equilibrium study

The static or thermal equilibrium properties of non-interacting magnetically anisotropicnanoparticles are studied in the framework of classical theory. Various important thermalequilibrium properties, e.g. internal energy, specific heat, magnetization and susceptibility,are derived from basic thermodynamic functions such as the partition function andthermodynamic potentials. The central issue in this paper is to study the effect ofanisotropic potential on these thermal equilibrium properties. We extensively study thelinear and nonlinear susceptibilities and their temperature dependence. We also give acomparative study of the magnetic properties of a superparamagnetic fine particle systemand a canonical spin-glass system and thus invoke the similarities and differences betweenthe two.

Transport and magnetic properties of Ce 2NiIn 3

We report results on transport and magnetic properties for the title compound. Spin-glass (SG) features arise below the temperature of T f = 2.8 K for Ce 2NiIn 3, as determined from ac and dc magnetic susceptibility. The low temperature specific heat presents an anomaly with a maximum located near T f which is unusual when compared with other compounds of the type Ce 2TX 3 (where T = transition metal and X = Si, Ge) and canonical SG systems. The anisotropic SG behavior or inhomogeneous magnetic ordering have been proposed as the possible causes for the arising magnetic ground state. The results for Ce 2NiIn 3 are compared with those obtained for Ce 2NiGe 3, isotypic compound.

Spin-glass behavior in the A1:Mn quasicrystalline alloys

We report dynamical scaling analysis of the ac magnetic susceptibility data for the quasicrystalline A1 75 Mn 20 Si 5 alloy near the critical temperature T. The critical exponents obtained are β = 1.0 and zν = 5.5. The value of β is higher than that obtained from static scaling analysis made in the decagonal Al 78 Mn 22 alloy which yielded β = 0.6 and γ = 4.4. The overall values obtained for the critical exponents are similar to those measured in canonical spin-glass systems.

Scaling of the nonlinear susceptibility in the spin-glass TAl 78Mn 22 quasicrystalline alloy

It is shown for the first time that the non-linear susceptibility, X NL = X − M/ H, of the quasicrystalline TAl 78Mn 22 alloy has a scaling behavior similar to canonical spin-glass systems. A good scaling is obtained for magnetic fields from 1. kOe up to 50. kOe and for temperatures above 14. K. The scaling yields the critical exponents γ = 4.4 and β = 0.6, and the critical temperature T g = 7.6 K, consistent with values obtained in canonical spin-glasses.

Comparison of the resistivity ofPdCr with canonical spin-glass systems

The electrical resistivity of several PdCr alloys, with between 11- and 18-at.% Cr, has been investigated between 1.4 and 300 K, and found to resemble that of canonical spin glasses (CSG). At low temperatures $\ensuremath{\Delta}\ensuremath{\rho}(T)\ensuremath{\propto}A{T}^{\frac{3}{2}}$, with $A\ensuremath{\propto}\ensuremath{-}logc$ over the concentration range investigated; the range of validity of this ${T}^{\frac{3}{2}}$ variation ($T<{T}_{1}$) is small in PdCr (where $A$ is comparatively large) as in AgMn. At higher temperatures $\ensuremath{\Delta}\ensuremath{\rho}(T)$ passes through an inflection point (at ${T}_{m}$) reaching a maximum (at ${T}_{\ensuremath{\mu}}$) above which it decreases with increasing temperature. The ratio $\frac{{T}_{m}}{{T}_{1}}$ is found to be roughly constant, as predicted by recent spin-glass theories, but as in CSG its magnitude is smaller than predicted. There are, however, several quantitative differences between PdCr and CSG; specifically both ${T}_{\ensuremath{\mu}}$ and $\ensuremath{\Delta}\ensuremath{\rho}({T}_{\ensuremath{\mu}})\ensuremath{-}\ensuremath{\Delta}\ensuremath{\rho}(0)$ are typically an order of magnitude smaller than in CSG of comparable concentration, whereas the slope of $\ensuremath{\Delta}\ensuremath{\rho}(T)$ above ${T}_{\ensuremath{\mu}}$ is about an order of magnitude larger than in CSG. This latter point in particular lends support to the assertion that such differences may arise from the fact that CSG are good moment systems (${T}_{K} or {T}_{S}\ensuremath{\ll}{T}_{m}$), but PdCr is not (${T}_{S}\ensuremath{\sim}{T}_{m}$).