Structure and Spin-Glass Magnetism of the MnxNi2Zn11–x Pseudobinary γ-Brasses at Low Mn Contents

The pseudobinary MnxNi2Zn11–x γ-brass-type phases at low Mn dopant levels (x = 0.1–0.5) were investigated. Crystal structures were determined for the two loading compositions of x = 0.3 and 0.5. The structures were solved in the cubic space group of I43m and are described in close analogy to the Ni2Zn11 parent γ-brass that is based on the 26-atom cluster, consisting of inner tetrahedron (IT), outer tetrahedron (OT), octahedron (OH), and cuboctahedron (CO). The refined site occupancies of the MnxNi2Zn11–x (x = 0.3, 0.5) reveal that the cluster center, which is empty in the Ni2Zn11, shows a partial occupation by Zn, with a partial depletion of Zn at the IT sites. The OH sites show a mixed Zn/Mn occupation. The OT and CO sites remain intact with respect to Ni2Zn11. Magnetic properties were studied for the Mn0.3Ni2Zn10.7 composition. The temperature-dependent zero-field-cooled and field-cooled magnetization, the ac susceptibility, the M(H) hysteresis curves, the thermoremanent magnetization, and the memory effect demonstrate typical broken-ergodicity phenomena of a magnetically frustrated spin system below the spin freezing temperature Tf ≈ 16 K. The Mn0.3Ni2Zn10.7 γ-brass phase classifies as a spin glass, originating predominantly from the random distribution of diluted Mn moments on the octahedral partial structure.


INTRODUCTION
Complex metallic alloys (CMAs) are a class of intermetallic compounds that possess giant unit cells comprising from several tens up to many thousands of atoms arranged in welldefined atomic clusters of different polyhedral symmetry. 1,2 CMA structures possess various types of disorder, including configurational disorder due to a statistically varying orientation of a particular subcluster, chemical (substitutional) disorder, partial site occupation (occupancy smaller than 1), and split occupation, where two neighboring sites are alternatively occupied because they are too close in space. Many CMAs possess a solid-solution range, so that the composition of a single phase can be varied. The category of CMAs includes the family of γ-brasses, containing 52 atoms in the unit cell. 3 The structure of γ-brass-type phases is described in terms of a 26-atom cluster, made up of four successive shells. Starting from the empty cluster center (CC), the first shell is the inner tetrahedron (IT), followed by outer tetrahedron (OT), octahedron (OH), and cuboctahedron (CO). On the basis of the space group, γ-brasses are divided into four families: 3 (1) I-cell-type γ-brasses with space group I43m form a body-centered cubic (bcc) lattice with two identical 26-atom clusters in the unit cell, centered at the highly symmetric positions (0,0,0) and (1/2,1/2,1/2), (2) P-cell type with space group P43m adopt a CsCl structure composed of two different 26-atom clusters, (3) F-cell type with space group F43m form superstructures, and (4) R-cell type with space group R3m (a subgroup of P43m) are rhombohedral. The I-cell and P-cell types are the most numerous ones, found in 24 binary alloy systems. 3 Binary γ-brasses were widely investigated in the past, both experimentally and theoretically, and the state of the art in the field is summarized in the book by Mizutani. 3 Within the finite solid solution range of the γ-brass phase, the stoichiometric compositions can adopt one of the A 2 B 11 , A 4 B 9 , A 5 B 8 , A 7 B 6 , and A 10 B 3 formulas with space group I43m and a combination of these two with space group P43m. According to the classification in terms of a combination of constituent elements in the periodic table, the I-and P-cell γ-brasses are divided into three groups. Group I comprises 11 combinations of a monovalent noble metal (Cu, Ag) and a polyvalent element, whose valency is well-defined. Group II also includes 11 γbrasses, which consist of 3d transition-metal elements like TM = V, Mn, Fe, Co, and Ni and either divalent elements Be, Zn, Cd or trivalent elements Al, In. Group III includes γ-brasses consisting of a combination of two nontransition metal elements like Ag, Li, and Pb.
The γ-brass phases belong to the class of Hume−Rothery phases, where the crystal structure achieves stability at a specific valence electron concentration of e/a. 3−7 A pseudogap in the electronic density of states (DOS) is formed at the Fermi energy ε F , which efficiently lowers the kinetic energy of the conduction-electron system, making the structure more stable. γ-Brasses from the group I are stabilized at the value e/a = 21/13 = 1.615. For the group II, the situation is less clear, because the e/a value for the TM is not a-priori known. Theoretical band calculations using the Full-Potential Linearized Augmented Plane Wave (FLAPW) method applied to the stoichiometric TM 2 Zn 11 (TM = Fe, Co, Ni, Pd) γ-brasses from the group II have yielded e/a values between 1.70 and 1.80, 6 which is considered still acceptable to claim that the stability of these alloys follows the Hume−Rothery electron concentration rule. The γ-brass phase field for the TM 2 Zn 11 family is extended over 15−30 atom % of the TM element.
Inspired by the knowledge and understanding of the stabilization mechanism of binary γ-brasses, the research has been extended to ternary γ-brass phases. New pseudobinary/ ternary γ-brass phases were unraveled in the Co−Pd−Zn, 8 Fe−Pd−Zn, 9 and Ni−Zn-X (X = In, Ga) 10 systems, starting from the knowledge of electronic structures of the binary Co 2 Zn 11 , Fe 2 Zn 11 , Pd 2 Zn 11 , and Ni 2 Zn 11 . The Co−Pd−Zn and Fe−Pd−Zn ternary compounds show weak ferromagnetic or ferrimagnetic behavior, unlike their binary parent compounds. Recently, the phase diagram of the ternary Mn−Ni−Zn system has been studied. 11,12 Three new ternary compounds, denoted as T, τ 1 , and τ 1 , were found to exist at 400°C, and extended single-phase regions of the phases Mn 5 Zn 21 , Ni 2 Zn 11 , NiZn 3 , and NiZn were observed. In this work, we investigate experimentally the γ-brass-type Mn−Ni−Zn pseudobinary/ ternary phases based on the Ni 2 Zn 11 parent compound. 13 By introducing Mn as a dopant to the Ni 2 Zn 11 , the atomic radius of Mn (r Mn = 127 pm) is closer to Zn (r Zn = 134 pm) than Ni (r Ni = 124.6 pm). The Pauling electronegativity of Mn (1.55) is also closer to Zn (1.65) than Ni (1.91). For those reasons it can be assumed that Mn will preferentially substitute for Zn. Here we concentrate on the system Mn x Ni 2 Zn 11−x at low Mn dopant levels (x = 0.1−0.5), by determining the crystallographic structure for two nonstoichiometric compositions and the physical properties, with the emphasis on magnetism.

RESULTS
2.1. Structure Determination and Description. The materials, synthesis, and characterization by powder X-ray diffraction (PXRD), single-crystal X-ray diffraction (SCXRD), and energy-dispersive X-ray spectroscopy (EDS) are detailed in the Experimental Section. The phase purity of the samples was verified by PXRD and Rietveld refinement plots, confirming that the entire series of the Mn x Ni 2 Zn 11−x (x = 0.1−0.5) compounds were single-phase, belonging to the γbrass-type phase I43m.
The PXRD spectra and the Rietveld refinement plots for the loading compositions Mn 0 . 3 Ni 2 . 0 Zn 1 0 . 7 (C1) and Mn 0.5 Ni 2.0 Zn 10.5 (C2) are shown in Figure 1 with the goodness of fit (GOF) indicated. The crystal structures were subsequently determined by SCXRD for these two compositions. The complete crystallographic data are presented in Table 1 (additional crystallographic information is available regarding the Accession Codes), whereas the final atomic coordinates, site occupancies, and isotropic displacement parameters are given in Table 2.
The crystal structures were solved in the cubic space group I43m (No. 217). The structure solution has generated four crystallographically independent positions in the unit cell. The preliminary stage of refinement for the crystal C1 converged at the R(F) value of 4.8%. It was challenging to identify the exact atomic positions of Ni and Zn in the crystal structure on the basis of electron density due to their very similar X-ray scattering factors. Thus, at this stage, the positions of Ni and Zn were allocated based on the model established for ordered γ-brass type Ni 2 Zn 11 . 14,15 Of the four crystallographic sites, one 8c site was assigned to Ni, whereas the remaining three (8c, 12e, 24g) were assigned to Zn, and the subsequent refinement converged at the R(F) value of 4%. The 12e site discerned a relatively larger isotropic atomic displacement parameter (ADP) of ∼0.021 Å 2 with respect to the average value. An Inorganic Chemistry pubs.acs.org/IC Article independent refinement of the 12e site assigned as Zn resulted in a site occupancy factor (SOF) lower than unity, whereas the site assigned as Mn led to the occupancy (SOF) higher than unity. Hence, the 12e site was modeled by partially replacing Mn for Zn (Zn2/Mn2) assuming these sites to be fully occupied overall. The subsequent refinement resulted in the R(F) value of 3.5%. The 8c site occupied by Zn also discerned a slightly larger isotropic ADP (∼0.018 Å 2 ) and was tested for partial occupancy. At this stage, additional residual electron density was identified at the 2a site in the cluster center (CC) located at (0.5, 0.5, 0.5) and included as Zn. The 2a (Zn) site was also examined for partial occupancy, as the distance between the 2a and 8c sites is too short (∼1.63 Å). The local structural disorder was modeled by introducing split positions. In no case does the sum of site occupancy factors (SOFs) of two such sites exceed unity, but the splits are explainable in terms of a set of locally ordered clusters. Both sites were independently refined, following the relation of SOF(Zn(CC)) + SOF(Zn(IT)) ≈ 1.00. The harmonic ADPs for all atoms including the isotropic extinction correction were taken into account at the final stage of the refinement, and the R(F) value converged at 2.4%. The SCXRD refined model for the C1 crystal was used as the initial model for the refinement of the SCXRD data collected for the C2 crystal. The refined (Z = 4) compositions Mn 0 . 3 9 6 Ni 2 Zn 1 0 . 3 8 for the C1 and Mn 0.491 Ni 2 Zn 10.376 for the C2 were checked by EDS, and good matching was obtained (Table 1). Each structure (C1 and C2) was tested for possible twinning by an inversion and absolute configuration. The Flack parameters for C1 and C2 after the refinement resulted in −0.1(2) and −0.03 (16), respectively. Hence, the structures are not twinned by an inversion. It is worth mentioning that these data were tentatively truncated to test for any trend in the occupancy of the Zn2/Mn2 site. No such trend was detected, that is, the data are stable toward a high-order truncation. An artificial truncation of the data to lower reciprocal space vectors resulted in similar values for the occupancy of the Zn2/Mn2 site. The structure can be described in close analogy to the Ni 2 Zn 11 parent γ-brass compound, in which Ni occupies solely the 8c(OT) position with full occupancy, whereas the remaining three sites 8c(IT), 12e(OH), and 24g(CO) are fully occupied by Zn. The pseudobinary structures C1 and C2 adopt the same structure type, described by the 26-atom γcluster. The refined site occupancies for the C1 composition reveal that the central (CC) site, which is empty in the γcluster of the Ni 2 Zn 11 , is partially occupied by Zn (SOF(CC) = 0.107(13)) with a simultaneous depletion of Zn at the IT sites (SOF(IT) = 0.861 (7)). The OH site shows a Zn/Mn substitutional disorder. The OT and CO sites that are occupied by Ni and Zn, respectively, remain unaffected by the Mn insertion. The structure for the C1 composition is shown in Figure 2. The five successive shells of the distorted γcluster are presented in Figure 2a, with the OH sites showing mixed Zn/Mn occupation of 0.87/0.13, whereas one complete γ-cluster is shown in Figure 2b. The bcc unit cell is shown in Figure 2c, whereas the magnetic lattice with diluted Mn spins on the OH sites (see later) is shown in Figure 2d. The partial structure of the partially populated CC and IT sites (both occupied by Zn) is shown in Figure 2e. The C2 crystal shows a similar occupancy pattern and crystal structure, where the occupancy of the CC site slightly decreases (SOF(CC) = 0.082(11)), with a further increase of Zn occupation at the IT sites (SOF(IT) = 0.913(5)).
2.2. Spin-Glass Magnetism of the γ-Brass Type Mn 0.3 Ni 2 Zn 10.7 . Magnetic properties were studied via the magnetic experiments and the specific heat for the loading composition Mn 0.3 Ni 2 Zn 10.7 (C1). The structure contains two kinds of magnetic elements, namely, Mn and Ni, where Mn is antiferromagnetic (AFM) as a pure metal, whereas Ni is ferromagnetic (FM). In an electrically conducting medium, the interaction between the moments is the conduction-electron mediated Ruderman−Kittel−Kasuya−Yosida (RKKY) indirect exchange, which oscillates in space on the scale of many  Temperature-Dependent Magnetization and Magnetic Susceptibility. The temperature-dependent zero-field-cooled (zfc) and field-cooled (fc) direct-current (dc) magnetization in a low magnetic field of μ 0 H = 5 mT, measured in the temperature range of 300−1.8 K, is shown in Figure 3a. The magnetization is given in Bohr magnetons μ B per one Mn 0.033 Ni 0.148 Zn 0.819 average "atom" (i.e., per one formula unit (fu)). When cooled, a paramagnetic growth of the magnetization is observed down to 16 K, where M zfc exhibits a cusp and decreases toward zero when further cooled, whereas M fc stays approximately constant below that temperature. Such behavior is typical of a kinetic spin-freezing transition in spin glasses, 16 where the temperature of the M zfc cusp is associated with the spin-freezing temperature T f . Below T f , the ergodicity of the spin system is broken; that is, the spin fluctuation times   Inorganic Chemistry pubs.acs.org/IC Article become so long that the system cannot reach an equilibrium state on the accessible experimental frequency scale, which is the origin of the M zfc − M fc splitting. The magnetic susceptibility χ = M/H in the paramagnetic phase (T > T f ) was analyzed by the Curie−Weiss law, χ = χ 0 + C CW /(T − θ). Here C CW is the Curie−Weiss constant, θ is the Curie−Weiss temperature, and χ 0 is the temperatureindependent term of the susceptibility. χ 0 is a sum of the negative (diamagnetic) Larmor core susceptibility, the positive Pauli paramagnetic spin susceptibility of the conduction electrons, and the negative Landau susceptibility due to the conduction-electron orbital circulation in the magnetic field, where all three contributions are of the same order of magnitude. The Larmor susceptibility was estimated from literature tables 17 as χ Larmor ≈ − 2 × 10 −10 m 3 mol −1 . The fit yielded the value χ 0 = −6.6 × 10 −10 m 3 mol −1 , which is of the correct order of magnitude. The plot of the susceptibility (χχ 0 ) −1 vs T and the Curie−Weiss fit (solid line) are shown in Figure 3b. Excellent fit was obtained in the entire paramagnetic regime above T f ≈ 16 K. The mean effective Bohr magneton number p ̅ eff , obtained from 18 p eff ̅ = (797.7 mol/m K ) 3 C CW × has yielded the mean effective paramagnetic moment μ ̅ eff = p ̅ eff μ B = (0.84 ± 0.05)μ B . This value is strongly reduced with regard to the experimental paramagnetic free-ion values of localized ions Mn 3+ , Mn 2+ , Ni 3+ , and Ni 2+ that amount to 4.9, 5.9, 4.8, and 3.2 μ B , respectively. On the basis of the Curie− Weiss analysis we are, however, unable to discriminate between a small number of magnetic ions with large magnetic moments and a large number of magnetic ions with small magnetic moments in the Mn 0.3 Ni 2 Zn 10.7 structure. Likewise, we are unable to discriminate between the magnetic moments of Mn and Ni.
The Curie−Weiss temperature was determined from the fit as θ = 0 K (with an estimated error of ±1 K). This temperature is generally an indication of the dominant type of interspin interactions, being either AFM (θ < 0) or FM (θ > 0). The Mn 0.3 Ni 2 Zn 10.7 3d magnetic alloy is an exchange-dominated spin system, where the randomness of the Mn positioning on the magnetic sublattice introduces a distribution of the exchange coupling constants . The zero value of the Curie−Weiss temperature suggests that the distribution function P( ) extends to both positive ( 0 > , FM coupling) and negative ( 0 < , AFM coupling) values. 19 It also indicates that the average exchange interaction is close to zero, 0 ̅ = , which is characteristic of spin glasses. This supports that the magnetic state below T f ≈ 16 K is of a spin-glass type, where the AFM and FM interactions are both present in similar proportions.
The alternating-current (ac) magnetic susceptibility was measured between 300 and 1.8 K in a sinusoidal magnetic field of amplitude μ 0 H 0 = 0.2 mT at logarithmically spaced frequencies between 0.1 and 1000 Hz. The real part of the susceptibility χ′ is presented in Figure 4a, where a peak at ∼16 K that shifts with frequency to higher temperatures is evident (the details are shown in Figure 4b). Such a frequency dependence indicates a spin-freezing transition from an ergodic to a nonergodic state. The frequency-dependent spin-freezing temperature T f (ν) is conveniently defined as the temperature of the χ′ peak, and the corresponding T f (ν)/T f (1 Hz) relation is shown in the inset of Figure 4b. The fractional shift of ΔT f / T f per log ν was determined as Γ = ΔT f /T f Δ(log ν) = 6.1 × 10 −3 . This value falls into the range typical for spin glasses, where the values of Γ from 10 −2 to 10 −3 are common. 20 The The theoretical fit of the 10 K curve with the above model is presented in Figure 5b. The fit yielded the parameter values M 0 = 1.2 × 10 −2 μ B /fu, μ = 22μ B , and k = 2.6 × 10 −3 μ B /(fuT). The small FM group moments of 22μ B suggest FM spin domains of a couple of nanometers in size. The fit qualitatively confirms the spin-glass-type P( ) distribution with vanishing average exchange interaction, 0 ̅ = . This is in accord with the zero Curie−Weiss temperature.
Specific Heat. Specific heat is suitable for the characterization of phase transitions (structural, magnetic, superconducting), where an ordering of some degree of freedom takes place at the phase transition temperature. The energy of the ordered state is lower than the energy of the high- Inorganic Chemistry pubs.acs.org/IC Article temperature disordered state, so that the energy released upon ordering exits the system as a heat in the form of an exothermic peak. The low-temperature specific heat of a magnetic alloy can be written as C = γT + αT 3 + C m , where γT, αT 3 , and C m are the electronic, lattice, and magnetic contributions, respectively. For canonical spin glasses (denoting a noble metal host like Cu or Ag with diluted magnetic impurities Fe, Mn, etc.), C m usually exhibits a broad peak upon spin freezing, with the peak maximum located at T max ≈ 1.4T f . 21 The exothermic peak in the region of the spin-freezing temperature indicates that the spins adjust locally to their neighbors in an energetically favorable configuration to reduce the exchange energy, although no long-range magnetic ordering takes place. For a purely kinetic spin freezing transition, however, the spins or small spin clusters gradually freeze into random directions during continuous cooling, so that no heat is released at T f , and the specific heat does not show any anomaly. The specific heat of the Mn 0.3 Ni 2 Zn 10.7 γ-brass was determined in the temperature range of 1.8−300 K in magnetic fields between 0 and 9 T. The C(T) graphs below 30 K are shown in Figure 6, where it is evident that there is no anomaly at the spin-freezing temperature T f ≈ 16 K, and the specific heat also does not show any field dependence. This is in favor of a kinetic spin-freezing transition from an ergodic to a nonergodic state. The specific heat below 10 K is presented in the inset of Figure 6 in a C/T versus T 2 plot, wherefrom the electronic specific heat coefficient was determined as γ = 4.71 mJ mol −1 K −2 . This value is almost the same as that reported for the Ni 2 Zn 11 parent γ-brass (γ = 4.5 mJ mol −1 K −2 ). 22 Since γ = (π 2 /3) k B 2 g (ε F ) is directly proportional to the electronic DOS at the Fermi level g (ε F ), this indicates that the DOS at ε F of the Mn-doped Mn 0.3 Ni 2 Zn 10.7 is not changed much with respect to the Ni 2 Zn 11 . The lattice specific heat coefficient α yielded the Debye temperature of θ D = 283 K (for comparison, the θ D values of the constituent metals are θ D Zn = 329 K, θ D Ni = 477 K, and θ D Mn = 409 K). Thermoremanent Magnetization. The broken-ergodicity state of a spin glass (as well as of other magnetically frustrated systems) can be further characterized by measuring the time decay of the thermoremanent magnetization (TRM), which is logarithmically slow below the spin-freezing temperature T f . 23−31 This reflects the slow approach of the spin system toward a thermal equilibrium, which cannot be reached on the available frequency scale of a given experimental technique due to a broad distribution of spin relaxation times. The TRM time-decay measurement protocol involves (1) continuous cooling of the spin system in a magnetic field H fc through T f into the nonergodic state, (2) stopping the cooling at a certain measuring (or aging) temperature T m < T f for a waiting (aging) time t w , (3) cutting the field to zero after t w , and (4) recording the M TRM magnetization decay as a function of time t. The TRM decay depends on T m , t w , and H fc .
The TRM versus T m experiments, performed on the Mn 0.3 Ni 2 Zn 10.7 γ-brass, are shown in Figure 7. A small field of μ 0 H fc = 0.5 mT was applied, and the aging stops were performed at eight different temperatures T m between 16 and 2 K in steps of ΔT m = 2 K, where aging for t w = 1 h was employed at each stop. After H fc → 0, the TRM decays were recorded up to t ≈ 150 min. The normalized decays M TRM (T m , t)/M fc (T m ), where M fc (T m ) is the fc magnetization just before the field cutoff, are shown in Figure 7a, where an increase in amplitude with the decreasing T m is evident. The inset shows the normalized initial (t = 0) amplitude M TRM (T m , t = 0)/M fc (T m ) as a function of T m . The TRM at T m = T f = 16 K is zero, because the spin system is ergodic at that temperature. The decays slow down strongly with decreasing T m , owing to an increased remanence of the spin system at lower temperatures. This is demonstrated in Figure 7b, where the TRM decays normalized to their t = 0 amplitudes, M TRM (T m , t)/M TRM (T m , t = 0), are shown.
The TRM time decays versus the aging time t w at T m = 8 K, obtained after field cooling in μ 0 H fc = 0.5 mT, are presented in Figure 8. Eight different aging times between 1 min and 8 h, roughly logarithmically spaced, were employed. The normalized decay curves M TRM (t w ,t)/M fc (t w ) are shown in Figure 8a. The TRM increases for longer t w , which is additionally  shown as a function of t w . The decay shapes also change with t w , where a slowing-down for longer t w values is evident. This is demonstrated in Figure 8b, where the TRM decays normalized to their t = 0 amplitudes, M TRM (t w ,t)/M TRM (t w ,t = 0), are shown. The TRM time decays versus the field H fc , measured at T m = 8 K for the aging time t w = 1 h, are shown in Figure 9a. Fifteen field values between μ 0 H fc = 0.5 mT and 7 T, roughly logarithmically spaced, were used. The normalized TRM time decays, M TRM (H fc ,t)/M fc (H fc ), demonstrate a strong decrease of the TRM with increasing H fc . The inset in Figure 9a shows the normalized initial (t = 0) TRM amplitude M TRM (H fc ,t = 0 )/M fc (H fc ), as a function of H fc . A large decrease by 2 orders of magnitude within the investigated field range is evident. The change of the shape of the decay curves with H fc is presented in Figure 9b, where each curve is shown normalized to its t = 0 amplitude, M TRM (H fc ,t)/M TRM (H fc ,t = 0). The decays show a tendency to slow down for smaller H fc values.
Memory Effect. The memory effect (ME) 27,30,32−35 is another manifestation of the out-of-equilibrium, ultraslow dynamics of a nonergodic spin system, where the spin state formed upon isothermal aging can be retrieved after a reverse temperature cycle. The ME measurement protocol involves (1) continuous cooling of the spin system in a zero magnetic field through T f into the nonergodic phase, (2) stopping at a certain temperature T m1 < T f , and letting the system age isothermally for a macroscopic time t w , ranging from a few minutes to many hours, (3) resuming the zero-field cooling after t w , by performing eventually one or more additional consecutive aging stops at lower temperatures T mi , (4)   showing a diminution (a dip) in the M zfc at each T mi , with respect to the no-aging case (t w = 0). In addition to the aging temperatures, the spin system remembers also the duration t w of each aging stop. By heating into the ergodic phase, all the memorized information is erased, and the spin system is the same as before aging, a phenomenon known as rejuvenation.
The ME on the Mn 0.3 Ni 2 Zn 10.7 γ-brass was performed by stopping at T m1 = 8 K and employing a series of aging times between t w = 1 min and 8 h, approximately logarithmically spaced (each t w was used in a separate experiment). A no-stop reference run (t w = 0) was also performed. At 2 K (the lowest temperature of the cooling run), a field μ 0 H zfc = 0.5 mT was applied. The M zfc values for all t w values, measured when heated, are shown in Figure 10a, where a dip at T m1 in the aged curves is observed. The M zfc s in the vicinity of T m1 are shown on the expanded scale in Figure 10b, where it is seen in more detail how the dip increases with the increasing t w . The normalized difference between the reference (t w = 0) curve and the aged curves, ΔM = [M zfc (t w = 0) − M zfc (t w )]/M zfc (t w = 0), is shown in Figure 10c. ΔM is peaked at the aging temperature T m1 and increases in amplitude with t w .
The ME involving multiple consecutive isothermal aging stops for t w = 1 h within the same zfc cooling run was observed by performing three stops at T m1 = 12.5 K, T m2 = 9.5 K, and T m3 = 5 K. The no-stop reference run was also recorded. The corresponding M zfc s are presented in Figure 11a, showing a dip at each T mi . The normalized difference ΔM with three wellresolved peaks at T mi is shown in Figure 11b. The M zfc s for seven consecutive stops for t w = 1 h each at the temperatures T mi (i = 1−7) between 14 and 5 K in steps of ΔT mi = 1.5 K are shown in Figure 11c, whereas the corresponding ΔMs are shown in Figure 11d. All seven consecutive aging stops have been memorized by the nonergodic spin system.

DISCUSSION
Randomness, as one of the reasons responsible for the spinglass behavior of the Mn 0.3 Ni 2 Zn 10.7 γ-brass, is emerging from the random distribution of diluted Mn moments at the OH sites, because Ni occupies the OT sites with the full occupancy of 1, and there is no randomness in the Ni sublattice. Another    22 which has revealed that no long-range magnetic ordering of Ni moments takes place down to 0.35 K. The reported C/T = 4.5 mJ mol −1 K −2 value in the T → 0 limit can be attributed entirely to the electronic specific heat (the electronic specific heat coefficients of the Ni and Zn metals are γ Ni = 7.04 mJ mol −1 K −2 and γ Zn = 0.64 mJ mol −1 K −2 ), so that there is no magnetic specific heat, suggesting that Ni ions do not possess sizable magnetic moments. Doping with a small amount of Mn is not expected to change significantly the magnetic state of Ni in the Mn 0.3 Ni 2 Zn 10.7 pseudobinary γbrass, so it is reasonable to assume that the magnetism of the Mn-doped compound originates predominantly from the Mn ions. The diluted Mn moments are positioned randomly on the octahedral partial structure. The long-range oscillating RKKY interaction then frustrates the Mn spins, which are subjected to competing AFM/FM interactions, and a spin-glass state is consequently formed. The magnetic state of the Mn 0.3 Ni 2 Zn 10.7 γ-brass exhibits broken-ergodicity phenomena below the spin-freezing temperature that are typical for spin glasses and other magnetically frustrated spin systems. The memory effect has already found an important technological application as a thermal memory cell for the thermal storage of digital information, in the absence of an electric, magnetic, or electromagnetic field. 36 The observed broken-ergodicity phenomena are not restricted to spin glasses but are present also in other nonergodic magnetically and electrically frustrated systems. A theoretical understanding of these out-of-equilibrium phenomena is still incomplete, because the experimentally measured physical quantities are frequency-dependent, depending on the frequency scale of the employed experimental observation technique. A comprehensive literature on the subject exists, 16,25−36 and for details, the reader is invited to consult those articles. Here we emphasize that the TRM and the ME in the Mn 0.3 Ni 2 Zn 10.7 γ-brass exhibit the same type of the T m , t w , and H fc dependence as reported before for other spin systems belonging to the broad class of spin glasses, either diluted or concentrated, electrically conducting or insulating, sitedisordered or site-ordered with geometric frustration. Such systems include canonical spin glasses, 16,[27][28][29][30]33,34 geometrically frustrated quasicrystals, 31,37 and complex metallic alloys, 32 high-entropy alloys, 35,38,39 and magnetic nanoparticles. 40,41 The Mn 0.3 Ni 2 Zn 10.7 pseudobinary γ-brass can be classified as a spin glass, representing the first alloy from the family of γbrasses belonging to this class.

CONCLUSIONS
The Mn x Ni 2 Zn 11−x (x = 0.1−0.5) pseudobinary γ-brass type phases were synthesized by a high-temperature synthesis. The crystal structures for two nonstoichiometric loading compositions x = 0.3 and 0.5 were determined by XRD and solved in the cubic space group I43m. Like the binary Ni 2 Zn 11 parent γbrass, the structures are described by the 26-atom γ-cluster, distributed on a bcc lattice. The 8c(OT) and 24g(CO) sites of the γ-cluster are occupied solely by Ni and Zn, respectively, whereas the 12e(OH) site is Zn/Mn mixed populated. The 2a(CC) and 8c(IT) sites show a positional disorder, both being partially occupied by Zn. According to the space group type and the combination of chemical elements, the investigated Mn x Ni 2 Zn 11−x compounds belong to the I-cell γbrasses from the group II.
It is worth mentioning that, due to the similar X-ray scattering factors of the constituent elements (Mn, Ni, and Zn), a site occupancy and substitution pattern could be accurately addressed by a combination of X-ray and neutron diffraction analyses. The neutron powder diffraction analysis of the γ-brass type pseudobinary phases will be the subject of our future investigations.
Magnetic properties were studied for the low-Mn loading composition of Mn 0.3 Ni 2 Zn 10.7 . On the basis of the measurement of the temperature-dependent zfc and fc magnetization, the ac susceptibility, the M(H) hysteresis curves, the thermoremanent magnetization, and the memory effect, we found that the spin system exhibits typical broken-ergodicity phenomena of a magnetically frustrated spin system below the spin-freezing temperature T f ≈ 16 K. Specific heat measurements support a kinetic spin-freezing transition. The above results allow a classification of the Mn 0.3 Ni 2 Zn 10.7 pseudobinary γ-brass as a spin glass.

EXPERIMENTAL SECTION
Samples of several loading compositions Mn x Ni 2 Zn 11−x (x = 0.1−0.5) were prepared from high-purity elements Mn (99.98%), Ni (99.99%), and Zn (99.999%) from Alfa Aesar. The amounts of elements were weighted according to the loading compositions and kept in one-endclosed silica tubes. The other ends of the ampules were sealed under high vacuum (pressure < 10 −5 mbar). Sealed ampules were placed into a programmable furnace, which was heated to 600°C at a rate of 2°C/min, and then kept at that temperature for 24 h. After that, the samples were heated to 900°C at a rate of 0.2°C/min and annealed at that temperature for 6 h, followed by a cool-down to 450°C at a rate of 0.1°C/min. Next, they were annealed at that temperature for 107 h. A rapid cooling was then performed to 100°C at a rate of 1.2°C /min and kept at that temperature for 54 h. Finally, the furnace was turned off and left to cool naturally to room temperature.
The phase purity was verified for all samples by PXRD. A small fraction of each ingot was crushed and ground into a fine powder using an agate mortar and pestle. The PXRD data were collected at ambient temperature using a Rigaku MiniFlex 600 diffractometer (Bragg−Brentano geometry) with a 600 W X-ray tube (Cu Kα 1 radiation, λ = 1.540 56 Å) and D/teX Ultra silicon strip detector. The data were collected for the 2θ range from 10°to 80°with a step size of 0.02°. The JANA2006 program 42 was used to refine the PXRD data.
The structural model was elaborated from SCXRD data and analysis. Single crystals were selected from crushed ingots of the loading compositions Mn 0.3 Ni 2.0 Zn 10.7 and Mn 0.5 Ni 2.0 Zn 10.5 , for which the PXRD patterns are shown in Figure 1. The crystals were glued to the tip of a glass fiber and mounted on the goniometer head. Each data set was collected at room temperature with a Bruker Photon II diffractometer equipped with graphite-monochromatic Mo Kα radiation (λ = 0.710 73 Å). The data reduction was performed by Apex III software. The structure solution and refinement were made by using the JANA2006 package program. 42 An EDS analysis of the chemical composition was performed on Tungsten Environmental Scanning Electron Microscope ESEM Quanta 650 equipped with an Oxford Instruments Aztec Live Ultim Max SDD 40 mm2 EDS detection system.
Magnetic measurements were conducted on a Quantum Design MPMS3 magnetometer, equipped with a 7 T magnet and operating at temperatures between 1.8 and 400 K. The thermoremanent magnetization in low magnetic fields and the memory effect experiments were conducted using a copper AC/ULF coil of the MPMS3 magnetometer to ensure an accurate and repeatable magnetic field. Prior to the low-field experiments, the Ultra-Low Field option was used to compensate for the residual magnetic field of the superconducting magnet. A needle-shaped sample of dimensions 5 × 1 × 1 mm 3 was cut from the ingot and contained several differently oriented crystal grains. The long axis was parallel to the magnetic field, to minimize the demagnetization effect. The specific heat was measured on a Quantum Design Physical Property Measurement System (PPMS 9T), equipped with a 9 T magnet and operating in the temperature range between 1.9 and 400 K.