Session W23: Frustrated Magnetism: Spin Glasses and Disordered Systems

Magnetization of the CuMn spin glass in high magnetic fields

High magnetic field (up to 35T) magnetization (M) measurements of five Mn doped Cu spin glass samples measured from above their respective glass temperatures to 4.2K is reported.  Three of the samples were polycrystalline with Mn concentrations of 4%, 7%, and 13.5% atomic and two were single crystals with concentrations of 2.6% and 7.92%.  The data were fitted to a Brillouin function with a Curie constant (Tc).  The fits were performed for all the data for a given M vs H and another set included only those data above 10T; both gave similar results.  The most notable feature is the M vs H data were only slightly temperature dependent.  This meant the effective T_c varied linearly from +40K for the 13.5% sample to the order of -20K at LHe temperatures for all concentrations.  A plot of the Tc values vs T for all the samples is approximately independent of the Mn concentration.  The magnetization measurements at a given temperature always followed heating above the glass temperature for a given alloy to the temperature of measurement in zero field.  The low field data were highly non-Brillouin like with the initial low field magnetization rising faster than linear up to approximately 5T followed by a significant decrease with increasing field to the order of 10T for all samples.   

Protocol Dependence of Out-of-Equilibrium Effects in Spin Glasses

Spin glass is a well-known example of an out-of-equilibrium system and is famous for displaying spectacular effects such as aging and rejuvenation. Aging is said to occur when a sample’s temperature is held fixed, and the system is allowed to relax¹. Rejuvenation occurs when the sample appears to "forget" this aging history upon further cooling². However, we propose that these effects compete more than this initial description suggests. Magnetization measurements of spin glasses are extremely sensitive to experimental protocol³, and we have used this dependence as a probe of the spin glass energy landscape. When cooling the sample at a constant, but finite rate, pockets of so-called spin glass order will grow, and the system will age. However, the energy landscape will also change as temperature chaos sets in and the system will rejuvenate. In this talk, we discuss our ac susceptibility experiments studying the interplay between aging and rejuvenation in a single crystal of CuMn with 7.92 at.% Mn. By studying how these two effects compete, we develop a more complete picture of spin glass behavior.

 

[1] Dupuis et al., “Aging, Rejuvenation and Memory Phenomena in Spin Glasses.”

[2] Baity-Jesi et al., “Temperature Chaos Is Present in Off-Equilibrium Spin-Glass Dynamics.”

[3] Freedberg et al., “On the Nature of Memory and Rejuvenation in Glassy Systems”   

Field dependence of spin glass transition temperature in Cu:Mn single crystals

The nature of the spin glass transition in the presence of a magnetic field is a subject of longstanding controversies. Prior studies [Phys. Rev. Lett. 66, 2923 (1991)] used polycrystalline Cu:Mn samples to explore magnetic field dependence of the spin glass transition temperature. They reported the presence of a single d’Almeida-Thouless (AT) transition temperature in low magnetic fields and the presence of two transition temperatures in high magnetic fields which are interpreted as the AT and Gabay-Toulouse (GT) transitions. However, a distribution of crystal sizes introduces multiple coherence length scales with a distribution of glass transition temperatures [Phys. Rev. B 91, 014434 (2015)] which introduces additional complexities in interpreting these results simply as the AT and GT transitions. Here we report preliminary results of magnetic field dependence of spin glass transition temperature for large single crystal Cu:Mn samples with different Mn concentrations. Our preliminary results show that in low fields, the temperature of the onset of irreversibility (M_FC - M_ZFC) decreases with increasing magnetic field strength, but the cusp of the temperature-dependent M_ZFC curve does not.   

Spin Glass Critical Dynamics just below Tg

Conventional critical dynamics are based on powers of 1/|T – T_g| in the vicinity of the glass temperature T_g.  For spin glasses, the precise value of T_g is difficult to obtain, leading to a breadth of values for critical exponents.  Recently, a scaling formalism was proposed¹ utilizing the coherence length, ξ(T,t_w) as the explicit variable, where t_w is the aging time at temperature T.  Recent experiments of Kenning et al ² on single crystals of CuMn, performed below and close to T_g, have exhibited extraordinary results. Our goal is to combine these two studies to develop a better method of calculating T_g from experimental data and predict T_g  for new materials. The characteristic relaxation time, t_w^eff drops by orders of magnitude and becomes independent of t_w as T approaches T_g from below.  Our analysis of these findings uses a scaling formalism for ln[t_w^eff(H)/t_w^eff(H→0)] in a power series in H². The interplay between the H² and H⁴ terms (of opposite signs) in the expansion are shown to be responsible for the drastic drop in t_w^eff, and for t_w^eff becoming independent of t_w as T approaches T_g from below.  This demonstrates that the scaling formalism is a powerful tool for examining critical dynamics below and in the vicinity of T_g spin glasses.  Comparison with data for super-cooled liquids shows that it may be rather general for glassy systems.

¹ I. Paga et al J Stat. Mech. (2021) 033301.

² G.G. Kenning et al Phys. Rev. B 102, 064427 (2020).   

Transition to Temperature Chaos in Spin Glasses

The concept of temperature chaos (TC) in spin glasses has been a controversial issue.  Recently, two independent observations of TC have been reported^1,2 along with justification of its existence in off-equilibrium spin glass dynamics.³  A remaining issue is the nature of the onset of TC as the temperature change, ΔT, passes from reversible to chaotic, appearing narrower in experiment as compared to simulations.  We invoke a temperature cycling protocol to determine the nature and width of the transition.  The coherence length, ξ₀(T₁ ,t_w1), is extracted at an initial temperature T₁ after aging t_w1.  The temperature is reduced by ΔT_R within the reversible range and held for t_w2 (t_w2 > t_w1).  It is then raised back to T₁ and the coherence length ξ_R(T₁) measured.  A separate experiment replicates the first step, but lowers the temperature by ΔT_C to reach the chaotic regime (ΔT_C > ΔT_R).  The system is aged t_w2, then heated back to T₁ and ξ_C(T₁) measured.  Validation of reversibility and chaoticity: ξ_C(T₁) < ξ₀(T₁) < ξ_R(T₁) enables the determination of the temperature width of the transition to chaos.  Results on single crystals of CuMn will be reported.   

The waiting time effect in spin glass thin films

Large finite size effects are well known in spin glass multilayer films (Phys. Rev Lett., vol.59, 22, 1987). These effects are likely due to the Lower Critical Dimension (LCD)  of the spin glass state lying between 2D and 3D. Previous dynamic studies have shown that a 3 nm multilayer film displays significantly faster dynamics than bulk samples, and a likely T = 0 K fixed point (Phys. Rev. B, vol. 40, 1, 1989). In this study we use High sensitivity DC SQUID magnetometry to probe the waiting time effect in multilayer spin glass films with spin glass layer thicknesses between 1 nm and 10 nm. The waiting time effect is an important signature of the spin glass phase and has been used extensively in the past to analyze the energy structure of the spin glass phase space (see for e.g., Phys. Rev. B 100 (9), 09420, 2109). We find a waiting time effect down to at least 5 nanometers and we will report on samples with thinner layer thicknesses.   

Modulated magnetism in metallic ferromagnets close to quantum criticality

We demonstrate that strong electronic particle-hole fluctuations near to an avoided ferromagnetic quantum critical point give rise to the formation of helimagnetic order. In the presence of small magnetic anisotropy it is possible to tune through this phase reconstruction by small transverse magnetic field and to stabilise a modulated fan state in between the homogeneous ferromagnetic phase and the field polarised state. We show that our theory can explain the rich behaviours observed in the metallic ferromagnetic PrPtAl.   

Chemical disorder induced electronic orders in correlated metals

In strongly correlated metals, long-range magnetic order is sometimes found only upon introduction of a minute amount of disordered non-magnetic impurities to the unordered clean samples. To explain such anti-intuitive behavior, we propose a ``rekindled failed order'' scenario of inducing electronic (magnetic, orbital, or charge) order via chemical or lattice disorder in systems with coexisting local moments and itinerant carriers. By disrupting the damaging long-range quantum fluctuation originating from the itinerant carriers, the electronic order preferred by the local moment can be re-established. We demonstrate this mechanism using a realistic spin-fermion model and show that the magnetic order can indeed be recovered as a result of enhanced disorder once the length scale of phase coherence of the itinerant carriers becomes shorter than a critical value. The proposed simple idea has a general applicability to strongly correlated metals, and it showcases the rich physics resulting from interplay between mechanisms of multiple length scales.   

Bulk Magnetic Properties and Vibrational Raman Scattering Spectroscopy of Four Boron Imidazolate Frameworks

Metal Organic Frameworks (MOFs), compounds consisting of metal ions connected by organic ligands, offer a possibility for tunable magnetic interactions between magnetic metal ions through ligands, creating an ideal space to explore exotic magnetism in real materials. Four MOFs in the boron imidazolate framework (BIF) family containing various magnetic ions connected with a boron imidazolate organic ligand have been studied by magnetization measurements and Raman scattering spectroscopy . Magnetization data reveal four distinct magnetic behaviors, including spin crossover in a paramagnetic system due to crystal electric field effects and superparamagnetism in single-domain ferromagnetic nanoparticles.The different energy regions of lattice modes, metal environment vibrations, and molecular vibrations are shown to act as a reliable fingerprint of the framework lattice, metal environment, and ligand respectively in room temperature Raman spectra.  These results establish an efficient method of understanding and assigning vibrational features in metal-organic framework Raman spectra, and demonstrate the existence of magnetic interactions in these MOFs despite extended superexchange pathways between magnetic metal centers.   

Magnetic properties of the rare-earth aluminides RECo2Al8 (RE = La, Ce, Pr, Nd and Sm).

We present the magnetic, thermal and transport properties of single crystals of the RECo2Al8 (RE = La, Ce, Pr, Nd and Sm) rare-earth aluminides. The Ce-based material is characterized as a Kondo system and moderate heavy fermion, for which the Sommerfeld coefficient is about ten times that determined for the La-based material ( γ^Ce= 138 mJ/mol.K and γ^La = 14 mJ/mol.K, respectively). The Pr-, Nd- and Sm-based materials all present antiferromagnetic (AFM) order that develops below 4.93 K, 8.2 K and 21.4 K, respectively. In the cases of the Nd- and Sm-based materials, frustrated in plane AFM interactions are observed. For the Pr-based compound, indeed two consecutive AFM transitions are observed in heat capacity and magnetization measurements (at 4.77 K and 4.93 K). Supported by isothermal magnetization and heat capacity measurements, we construct the T vs. H phase diagrams for the Pr- and Nd- based materials. Metamagnetic transitions from the low field AFM phase to a high field FM phase are observed. The FM phase is suppressed at further higher fields. Resistivity measurements are compatible with metallic behavior.   

Large Anisotropic Magnetoresistance and Magnetic properties of Single Crystalline, Tb2Al3Si2

Large magnetoresistance (LMR) materials, with their remarkable ability, are increasingly pivotal in various cutting-edge applications spanning from data storage technology to magnetic sensing and spintronic devices. The compound Tb₂Al₃Si₂ crystallizes in the C-centered monoclinic YAl₃Si₂-type, which contains wavy layers of Al and Si atoms linked together by additional Al atoms and linear Si-Al-Si bonds, has been reported to show antiferromagnetic order below T_N~16 K. However, there is a lack of extensive data concerning its magnetic and transport characteristics. In response to this deficit, we grew high-quality single crystals through the self-flux method, resulting in needle-shaped formations. Magnetic and transport measurements were carried out with the magnetic field aligned parallel and perpendicular to the needle's presumed direction along the b-axis. Due to the low symmetry (monoclinic), the orientation of the a- and c-axes to the magnetic field remained undetermined. Detailed temperature and field-dependent magnetic and transport results exposed a pronounced magnetic anisotropy in the system. Notably, transport measurements unveiled a substantial anisotropic magnetoresistance (AMR) in Tb₂Al₃Si₂. We will delve into a thorough discussion of all the aforementioned results to provide a comprehensive understanding of the compound's properties.   

A flat-band-induced ferromagnetic instability in the kagome metal Sc3Mn3Al7Si5

Kagome systems with rich electronic structures have become an intense research arena in the context of quantum spin liquids (QSL), charge density wave, and superconductivity. A Mn-based kagome system, Sc₃Mn₃Al₇Si₅, is proposed as an itinerant QSL via magnetic susceptibility and heat capacity measurements, and a possible ferromagnetic instability is reported with magnetization and nuclear magnetic resonance measurements [1,2]. To elucidate the ground state of this system, we conducted transport measurements of single crystals of Sc₃Mn₃Al₇Si₅ at low temperatures and high magnetic fields. The temperature dependence of resistivity at 0 T exhibits logarithmic divergence below 1 K. Magnetic fields suppress the logarithmic divergence and resistivity in high magnetic fields shows Fermi-liquid (FL) behavior. We find a scaling relation in magnetoresistance, suggesting that Sc₃Mn₃Al₇Si₅ is a ferromagnetic quantum critical metal due to flat-band-induced electron correlations and can be an exceptional example of interplay between electron correlation and topology of the underlying lattice. We will also discuss pseudogap-like behavior observed in soft-point-contact spectroscopy.

 

[1] H.He et al., Inorganic Chemistry 53,17 (2014) 

[2] S.Samanta et al., arXiv:2304.04928