Session V38: Spin Glasses and Disordered Magnetic Systems

A dynamic probe of finite-size effects near the spin-glass transition temperature

Using a high sensitivity dual DC SQUID magnetometer, we have measured the growth of the spin glass correlation length, through the aging and end of aging effects. Measurements were made on bulk CuMn5% and a CuMn12% thin film multilayer with CuMn layer thicknesses of 4.5 nm. As the glass temperature Tg is approached (0.9Tg < T<0.96Tg) in the bulk sample, we find that the waiting time effect (as measured by the time associated with the inflection point of the decay) as a function of increasing temperature, shifts to shorter timescales. For T >0.96Tg, there is no waiting time effect (end of aging) on the magnetization decay. and all decays collapse onto a single decay curve indicating an end of aging even for long waiting times (tw = 10,000s). For the thin film, all effects due to the waiting time disappear at around 0.89T_f, where T_f is the freezing temperature marking the onset of irreversibility. The end of aging results are interpreted in terms of the spin glass correlation length saturating due to finite size effects.   

Seeking the spin-glass state in a field through windows

Although the presence of a finite-temperature transition in the three-dimensional Ising spin-glass is well established in zero field, the behavior in the presence of an external magnetic field has been a matter of long-standing controversy. For the infinite-range Sherrington-Kirkpatrick spin glass, mean-field theory predicts a transition line known as Almeida-Thouless (AT) line that separates the paramagnetic and spin-glass phases in the temperature-field plane. Despite extensive numerical efforts, no consensus has been reached with regard to the presence of an AT line in short-range systems, mostly due to strong corrections to finite-size scaling. Here we investigate the transition in a three-dimensional system via a method in which we perform population annealing Monte Carlo simulations for a large system, but only consider the thermodynamic properties of the system restricted to a small window. By computing the wave-vector-dependent spin-glass susceptibility for the individual windows, as well as for the whole system, we investigate the effects of finite-size corrections to the two-point correlation function.   

Evidence of transition between Heisenberg and Ising-like phases in mesoscale Ge:Mn spin glass

The glassy dynamics of vector spin glasses in presence of a weak uniaxial anisotropy has been a subject of longstanding controversy. It has been predicted that in presence of such anisotropy Heisenberg-like spin glass system first undergoes longitudinal moment freezing, followed by a transverse moment freezing at even lower temperature. Evidence of such phase transition is seen in the temperature chaos experiments in thin film Ge:Mn spin glass. Here the sample temperature is increased from the quench temperature after the correlation length has reached its thickness. For large enough positive change of temperatures the maximum barrier height increases monotonically, which is consistent with a phase change of lower temperature Heisenberg-like phase to higher temperature Ising-like phase.   

Study of longitudinal fluctuations of the Sherrington-Kirkpatrick spin glass

Spin glasses are disordered systems with a complex behavior, caused by the very high degeneracy of low energy states. They have a phase transition between a paramagnetic phase and a spin glass phase, in which the ergodicity is broken in a hierarchical organization of states. This implies many peculiar properties such as aging, remanence and memory effect. In our work, we study finite-size corrections to the mean field model, the Sherrington-Kirkpatrick spin glass, whose solution is well-known. The behavior of these corrections in the low temperature phase has been debated for several years. Because of the complicated form of the theory around the mean field solution and of the difficulty to perform a numerical estimate, no final value has been found so far. We investigate the role of longitudinal fluctuations, neglecting the transverse contribution. Since they can be calculated directly into the full-replica symmetry breaking ansatz, it is easier to obtain a prediction for their behavior.   

Chaotic Behavior in CuMn13.5 Multilayer Thin Film Spin Glasses

The zero field cooled (ZFC) and field cooled (FC) magnetizations of an 11 nm CuMn_13.5 multilayer thin film spin glass was measured using a superconducting quantum interference device (SQUID) over the time scale where the correlation length has grown to the film thickness, i.e. for time scales where the thin films crossover from 3 D to 2 D. Temperature chaos, the vulnerability of the quasi-equilibrium state to temperature perturbations, was studied by a series of temperature drops after the crossover time. We find the ZFC and FC magnetization responses are sensitive to temperature changes after crossover. Both reversible and chaotic behavior, the latter characterized as rejuvenation, are observed. The traditional interpretation using a characteristic length for chaos, and the concept that chaos is “driven by rare events,” are discussed in comparison with experimental results.   

Experimental Observation of Room-temperature Anomalous Hall Mobility and Positive Magnetic Hysteresis in Amorphous Fe-Dy-O Thin Films

Fe-Dy-Tb-O thin film system was recently reported with very high transparency, conductivity and room temperature ferromagnetism driven by partially filled d - and f - subshells. Here, we have synthesized and studied the Fe-Dy-O thin films. The thin film system was prepared by e-beam evaporation and its structural, transport, magnetic and optical characterizations were performed. The as-grown films were amorphous, as evidenced by transmission electron microscopy and X-ray scattering. X-ray absorption spectra revealed a progressive oxidation of thin films on reducing the dimension. The films showed high ordinary (~10 cm²/V-s) and anomalous (~10² cm²/V-s) Hall mobility with n-type semiconducting behavior. Cryogenic magnetic behaviors evinced the existence of spin-glass-like transition at 79 K. Positive hysteresis loop and transverse magneto-resistivity up to 4% in the magnetic field of 5 T were observed at room temperature. Room-temperature optical studies showed the existence of a band gap of 2.42 eV in the visible range. These unique set of properties make the system a rich toolbox for not only understanding condensed matter behavior but also realizing multifunctional devices.   

A Lower Lower-Critical Spin-Glass Dimension from Quenched Mixed-Spatial-Dimensional Spin Glasses: Continuously Variable Dimension in Physically Realizable Systems

By quenched-randomly mixing local units of different spatial dimensionalities, we have studied Ising spin-glass systems on hierarchical lattices continuously in dimensionalities 1=<d =<3. The global phase diagram in temperature, antiferromagnetic bond concentration, and spatial dimensionality is calculated. We find that, as dimension is lowered, the spin-glass phase disappears to zero temperature at the lower-critical dimension dc=2.431. Our system being a physically realizable system, this sets an upper limit to the lower-critical dimension in general for the Ising spin-glass phase. As dimension is lowered towards dc, the spin-glass critical temperature continuously goes to zero, but the spin-glass chaos fully sustains to the brink of the disappearance of the spin-glass phase. The Lyapunov exponent, measuring the strength of chaos, is thus largely unaffected by the approach to dc and shows a discontinuity to zero at dc.
[1] B. Atalay and A.N. Berker, Phys. Rev. E 98, 042125 (2018).
[2] B. Atalay and A.N. Berker, Phys. Rev. E 97, 052102 (2018).   

Luttinger Quantum Paramagnet from Dimensional Recombination in the Frustrated Spin-1/2 Trimer Magnet Ba4Ir3O10

We report a highly frustrated spin state persisting down to 0.2 K in the monoclinic Ba₄Ir₃O₁₀ with Ir⁴⁺(5d⁵) ions, which consists of Ir₃O₁₂ trimers of face-sharing IrO₆ octahedra and wavy two-dimensional Ir-O sheets. This iridate conspicuously avoids any long-range magnetic order down to 0.2 K despite strong antiferromagnetic interaction with Curie-Weiss temperature -766 K. The corresponding frustration ratio reaches an astonishing value of 3830. This frustrated spin state is further evidenced by a sizable, linear heat capacity, indicating substantial residual entropy even at milli-Kelvin temperatures. It is equally striking that a mere 2% nonmagnetic Sr substitution for Ba readily lifts frustration and precipitates a long-range antiferromagnetic order at 130 K, suggesting proximity to a quantum critical point potentially with emergent random spin nucleation.   

Weird scaling for 2-D avalanches: curing the faceting, and scaling in the lower critical dimension

The non-equilibrium random-field Ising model (NE-RFIM) is very well studied and yet there are outstanding questions. In two dimensions, power law scaling approaches fail and the critical disorder is difficult to pin down. Additionally, the presence of faceting on the square lattice creates avalanches that are lattice dependent at small scales. We propose two methods which we find solve these issues. First, we perform large scale simulations on a Voronoi lattice to mitigate the effects of faceting. Secondly, the form of the nonlinear functions necessary to perform scaling collapses can be directly determined using our recent normal form theory of the Renormalization Group. This method has proven useful in cleanly capturing the complex behavior which occurs in both the lower and upper critical dimensions of systems and well describes the NE-RFIM in two-dimensions. The obtained scaling collapses span over a range of a factor of ten in the disorder and a factor of 10⁴ in avalanche size. They are consistent with a critical disorder at zero and with a lower critical dimension for the model equal to two.   

Critical behavior of the Ising model on a lattice with fractional space dimension

Disorder can have a drastic effect on the critical behavior of a magnetic system. The Harris criterion states that if the critical exponent of the correlation length $\nu$ fulfills the inequality $\nu \ge 2/d$, with $d$ the space dimension, disorder does not affect the universality class of the magnetic systems. A recent study reported a violation of this criterion for a two-dimensional three-state Potts model on a Voronoi lattice. To better understand the effects of disorder on the critical behavior of magnetic systems on disordered lattices, we study the critical behavior of a two-dimensional Ising ferromagnet on the largest component of a percolating cluster on a two-dimensional square lattice. There are two possible scenarios: In the weak universality scenario the disordered structure of the underlying lattice slowly changes the critical exponents, whereas in the strong universality scenario the critical exponents are not affected by the fractional space dimension of the system. Our results suggest a strong universality scenario with weak (logarithmic) corrections.   

Maximally Random Discrete-Spin Systems with Symmetric and Asymmetric Interactions and Maximally Degenerate Ordering

Discrete-spin systems with maximally random nearest-neighbor interactions that are symmetric or asymmetric, ferromagnetic or antiferromagnetic, including off-diagonal disorder, are studied for q=3,4 states in d dimensions, using renormalization-group theory exact for hierarchical lattices and approximate (Migdal-Kadanoff) for hypercubic lattices. For all d>1 and all non-infinite temperatures, the system eventually renormalizes to a random single state, signaling qxq degenerate ordering, which is maximally degenerate ordering. For high-temperature initial conditions, the system crosses over to this highly degenerate ordering after many renormalization-group iterations near the disordered infinite-temperature fixed point. Thus, a temperature range of short-range disorder in presence of long-range order occurs, as previously seen in underfrustrated Ising spin-glasses. The calculated entropy behaves similarly for ferromagnetic and antiferromagnetic interactions and shows a derivative maximum at the short-range disordering temperature. The system is disordered at all temperatures for d=1.
[1] B. Atalay and A.N. Berker, Phys. Rev. E 97, 052102 (2018).
[2] B. Atalay and A.N. Berker, Phys. Rev. E 98, 042125 (2018).   

Direct Observation of Magnetic Long-range Order in Ammann-Beenker Artificial Quasicrystals

Magnetic long-range order (LRO) in 3D Ammann-Beenker tilings (ABT) has been modeled in simulations^1,2, but has yet to be experimentally observed³. We fabricated artificial ABT composed of a connected wire network of elongated Permalloy film segments that mimic classical Ising spins interacting via long-range dipolar and short-range exchange interactions. Our MC analysis of ABT (NN interactions) generated a magnetic ground state built upon distinct sublattices, similar to fivefold Penrose tilings^4,5. High-resolution images of the in-plane magnetization of ABT were acquired with scanning electron microscopy with polarization analysis (SEMPA). An annealing protocol that yielded improved agreement with the MC ground state. We developed a novel cluster covering that introduces frustration among neighboring clusters, and suggests low-energy, long-range interactions are required for full LRO, and provides a possible explanation for the non-existence of magnetic LRO in atomic quasicrystals.
1) E. Y. Vedmedenko et al., Phys. Rev. Lett. 93, (2004) 076407
2) S. Thiem, J. T. Chalker, EPL 110 (2015) 17002
3) F. Hippert, J. J. Préjean, Philos. Mag. 88 (2008) 2175
4) B. Farmer et al., Phys. Rev. B. 93 (2016) 134428
5) D. Shi et al., Nat. Phys.14 (2917) 309   

Simulating spin-waves in strongly disordered magnets

Many scientifically important magnets contain disorder which complicates the theoretical analysis of their magnetic excitations. Examples include Sr2(Ir,Ru)O4 [1] with 50% (Ir,Ru) substitutions, Mn1.13Sb [2] with 13% Mn interstitials and Fe2.7GeTe2 [3] with 30% of Fe vacancies. To simulate magnons in these types of strongly disordered magnets we combine linear spin-wave theory [4] with the supercell approximation. [5] [1] Y. Cao, T. Berlijn et al PRB 95 (12), 121103 (2017) [2] A. E. Taylor, T. Berlijn, R. S. Fishman et al, PRB 91 (22), 224418 (2015) [3] G. D. Nguyen, T. Berlijn et al, PRB 97, 014425 (2018). [4] J. T. Haraldsen & R. S. Fishman, JPCM 21, 216001 (2009) [5] T. Berlijn et al, PRL 106, 077005 (2011).   

Study of a generalized XY model using the correlation length

The correlation length is examined in a generalized XY model where, together with the usual ferromagnetic interaction between spins, there is an additional nematic interaction that allows for half-vortices. The power of the correlation length is demonstrated in distinguishing different phases, thus fully reconstructing the phase diagram of the model. Moreover, it allows for further investigation of the tricritical region in the phase diagram where the paramagnetic, the nematic and the quasi-long-ranged phases meet. It shows that the Ising-type transition between the nematic and the quasi-long-range ordered phases stops at the tricritical point. Starting from this tricritical point, there is an intermediate range of different physics separates the two regions corresponding to the Ising-type and the Berzinskii-Kosterlitz-Thouless-type transitions.   

Dangerously Irrelevant Field at Clock Models - A study with the Monte Carlo Based RG Flows

The phase transitions between the paramagnetic phase and the $Z_q$ symmetry-breaking phase in the three dimensional XY model with $Z_q$-anisotropic field is now well accepted as belonging to the 3D XY universality class for $q>q_c$, with the $Z_q$-anisotropic field being irrelevant at the critical point. However, when $T<T_c$ it is always relevant as the symmetry is broken discretely. This is ”dangerous” because it leads to a larger length scale $\xi'$ than the normal correlation length $\xi$, which, by definition, governs the crossover behavior from $U(1)$ to $Z(q)$ symmetry breaking. While RG theory has provided generic pictures of the RG flow in coupling space, we here construct a quantitative Monte Carlo based RG flow using corresponding physical observables, where not only the crossover behaviors can be observed explicitly but also the critical exponents $\nu$ and $\nu'$ can be extracted accordingly. For this purpose, we have firstly restudied the anisotropy order parameter and confirm that its scaling dimension at the critical point is the same as that of the $Z_q$ field. We also clarify unsettled issues in several recent studies of this quantity.