A New Geometrically Frustrated Cluster Spin-Glass

LiZn2V3O8: A new geometrically frustrated cluster spin-glass

S. Kundu,1, ∗ T. Dey,2 A. V. Mahajan,1 and N. Büttgen3 1Department of Physics, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India 2Experimental Physics VI, Center for Electronic Correlations and Magnetism, University of Augsburg, 86159 Augsburg, Germany 3Experimental Physics V, Center for Electronic Correlations and Magnetism, University of Augsburg, 86159 Augsburg, Germany (Dated: January 1, 2020) Abstract We have investigated the structural and magnetic properties of a new cubic spinel LiZn2V3O8 (LZVO) through x-ray diffraction, dc and ac susceptibility, magnetic relaxation, aging, memory effect, heat capacity and 7Li nuclear magnetic resonance (NMR) measurements. A Curie-Weiss fit of the dc susceptibility χdc(T ) yields a Curie-Weiss temperature θCW = -185 K. This suggests strong antiferromagnetic (AFM) interactions among the magnetic vanadium ions. The dc and ac susceptibility data indicate the spin-glass behavior below a freezing temperature Tf ' 3 K. The frequency dependence of the Tf is characterized by the Vogel-Fulcher law and critical dynamic scaling behavior or power law. 6 From both fitting, we obtained the value of the characteristic angular frequency ω0 ≈ 3.56×10 Hz, the dynamic −6 exponent zv ≈ 2.65, and the critical time constant τ0 ≈ 1.82×10 s, which falls in the conventional range for typical cluster spin-glass (CSG) systems. The value of relative shift in freezing temperature δTf ' 0.039 supports a CSG ground states. We also found aging phenomena and memory effects in LZVO. The asymmetric response of the magnetic relaxation below Tf supports the hierarchical model. Heat capacity data show no long-range or short-range ordering down to 2 K. Only about 25% magnetic entropy change (∆Sm) signifies the presence of strong frustration in the system. The 7Li NMR spectra show a shift and broadening with decreasing temperature. The spin-lattice and spin-spin relaxation rates show anomalies due to spin freezing around 3 K as the bulk magnetization.

PACS numbers: 75.50.Lk, 75.40.Cx, 76.60.-k

I. INTRODUCTION tem. With a frustrated geometry, it exhibits a resonating valence-bond condensed state [14]. The strong interplay between the spin, charge, lattice and orbital degrees of Spinel oxides with the general formula AB2O4 have freedom in these transition metal oxides (TMO) are the provided an excellent arena for studying the effects of source of these novel magnetic properties. Motivated by geometrical frustration [1,2] and have seen a surge of these exotic behaviors of the cubic spinels, we decided to interest in the past decade due to a series of excit- investigate the mixed valent system LiZn2V3O8 (LZVO). ing experimental observations. In the cubic spinel, the Only the structural and electrical properties of LZVO B-sites form a corner shared, 3D tetrahedral network were reported long back in 1972 by B. Reuter and G. like the pyrochlore lattice which is geometrically frus- Colsmann [15]. The magnetic properties of LZVO have trated. Geometrical frustration arises when magnetic not been reported so far. As zinc prefers the A-site in moments occupying the B-sites interact antiferromagnet- spinel like in ZnCr2O4 [16, 17] and ZnV2O4 [18, 19], we ically with each other. With the intention of unraveling expect the site occupancy of LZVO to be represented as novel magnetic properties arising due to geometric frus- [Zn1.0(Li0.25V0.75)2O4]2 - where the octahedral B-site is tration, we were in the quest for new B-site cubic spinel occupied by Li and V in the 1:3 ratio. It will be inter- compounds. In this category, 3d-transition metal oxide 3+ 4+ esting to observe how the 25% dilution via non-magnetic LiV2O4 [3–5] (V :V = 1:1) is a well-studied system. lithium affects the magnetic properties of LZVO. Also, It shows heavy fermion behavior [6]. But with non- this system is amenable to nuclear magnetic resonance magnetic impurity (Zn/Ti) doping, it shows spin-glass (NMR) local probe measurement of 7Li nuclei. From behavior [7–9]. Recently studied mixed valent spinel 3+ stoichiometry, LZVO is a mixed valent spinel as in this system Zn3V3O8 or [Zn1.0(Zn0.25V0.75)2O4]2 with V : 11 4+ compound the average vanadium valence is + 3 . So it V = 2:1 [10] has been suggested to possess a cluster will be interesting to see whether this leads to tetrava- spin-glass ground state. Similarly, Li2ZnV3O8 (better lent and trivalent V in a 2:1 ratio. written as [Zn0.5Li0.5(Li0.25V0.75)2O4]2) containing only V4+ (S = 1/2) magnetic ions shows spin-glass behav- The motivation behind studying the system arXiv:1807.05612v3 [cond-mat.str-el] 31 Dec 2019 ior at low temperatures[11]. LiZn2Mo3O8 [12, 13] is an- LiZn2V3O8 is to contrast its properties with those other system stoichiometrically similar to our probed sys- of the resonating valence bond solid and cluster magnet compound LiZn2Mo3O8, whereas Zn3V3O8 (ZVO) was motivated by Majumdar-Ghosh chain system Ba3V3O8. Also, in LZVO, the effective spin value is close to S ∗Electronic address: [email protected] = 1/2 whereas in ZVO the effective spin is close to

1 ˚ S = 1. As quantum fluctuations are more prominent temperature (RT) with Cu Kα radiation (λ = 1.54182 A) in low spin systems, quantum effects in LZVO might on a PANalytical X’Pert PRO diffractometer. Magneti- play a dominant role compared to classical ZVO. Also, zation measurements were carried out in the temperature 3+ 4+ Zn3V3O8 (ZVO) has the ratio of V :V = 2:1 whereas range 1.8 − 400 K and the field range 0 − 70 kOe using for LZVO it is 1:2. In contrast, Li2ZnV3O8 contains a Quantum Design SQUID VSM. For the low-field mag- only S = 1/2 V4+. The strength of the exchange netization measurements, the reset magnet mode option couplings reflected in the Curie-Weiss temperature θCW of the SQUID VSM was used to set the field to zero. is about -370 K for ZVO while for Li2ZnV3O8 it is about Heat capacity measurements were performed in the tem- -210 K. For both ZVO and Li2ZnV3O8 the irreversible perature range 1.8 − 295 K and in the field range 0 − 90 temperature is Tirr ' 6.0 K and freezing temperatures kOe using the heat capacity option of a Quantum De- (Tf ) is around 3.75 K and 3.50 K respectively. sign PPMS. The NMR measurements were carried out In this work, we report sample preparation, structural using a phase-coherent pulse spectrometer on 7Li nuclei analysis, bulk magnetic properties, heat capacity and 7Li in a temperature range 1.8 - 200 K. We have measured NMR measurements on LZVO. The system crystallizes field sweep 7Li NMR spectra, spin-spin relaxation rate Fd¯3m 1 1 in the centrosymmetric space group with a site ( T2 ) and spin-lattice relaxation rate ( T1 ) at two different sharing between the lithium and the vanadium atoms at fixed radio frequencies (rf) of about 95 MHz and 30 MHz, the crystallographic 16c sites. Our magnetization data respectively. The spectra were measured using a con- π show no long-range ordering down to 2 K but we found ventional spin-echo sequence ( 2 − τecho − π). We have a splitting between the zero field cooled (ZFC) and field used the spin-echo pulse sequence with a variable delay cooled (FC) data at 3 K in low fields. A large Curie- time τD to measure T2 and a saturation pulse sequence θ = π Weiss temperature, CW - 185 K indicates strong an- ( 2 − τD − π) is used after a waiting time or last delay of tiferromagnetic (AFM) interactions between the mag- three to five times of T1 between each saturation pulse netic ions. Our frequency dependent ac susceptibility to measure T1. results indicate a spin-glass ground state. To know the spin-dynamics of the glassy phase in detail, we have carried out further magnetization measurements below the III. RESULTS AND DISCUSSION freezing temperature (Tf ) and observed clear signature of magnetic relaxation, aging effect and memory phenomena which are thought to be typical characteristics A. Crystal structure of spin-glasses. In memory effects, we observed that a To check for phase purity, we have measured the XRD small heating cycle erases its previous memory and reini- pattern of polycrystalline LZVO. The Rietveld refine- tializes the relaxation process. This type of asymmetric ment of LZVO (shown in Fig.1) revealed that it crys- response favors by the hierarchical model [20, 21]. The tallizes in the centrosymmetric cubic spinel Fd¯3m (227) inferred magnetic heat capacity has a broad maximum at space group. The two phase refinement of LZVO in- T ∼ 7 K but no sharp anomaly indicative of long-range dicates the presence of non-magnetic impurity phase ordering (LRO) is observed. The field swept 7Li NMR Li3VO4 (less than 2%) together with the main phase. spectra down to 1.8 K indicate the presence of an NMR The atomic positions obtained after Rietveld refinement line shift and gradual broadening of the spectra as T de- (using Fullprof suite [22]) are given in TableI. After re- creases. The spin-lattice and spin-spin relaxation rates finement, we obtained the lattice parameters as : a = b both show anomalies at a freezing temperature of 3 K. = c = 8.364 Å, α = β = γ = 900. The goodness of the Rietveld refinement is inferred from the following param- 2 eters χ : 1.37; Rp: 21.8%; Rwp: 10.7%; Rexp: 9.14%. II. EXPERIMENTAL DETAIL Note that from Rietveld refinement we can rewrite the chemical formula of LiZn2V3O8 as The polycrystalline LiZn2V3O8 sample was prepared [Zn1.0(Li0.241V0.759)2O4]2 like the cubic spinel gen- by conventional solid-state reaction techniques using high eral formula AB2O4. One unit cell is shown in Fig.2(a). purity starting materials. The sample was prepared Here the Zn2+ ions are at the tetrahedral A-sites and 2+ in two steps. First, we prepared the LiZnVO4 precur- connected to other Zn ions like in a diamond structure sor from a stoichiometric mixture of preheated Li2CO3 and the octahedral B-sites are statistically occupied by 1+ 3+ 4+ (99.995% pure), ZnO (99.9% pure) and V2O5 (99.99% Li and vanadium ions (both V and V ) in a 1:3 pure) at 700oC for 15 hours in a box furnace. After that, ratio. The V-V bond distance is 2.95 Å. The vanadium LiZnVO4,V2O3 and ZnO were mixed well (in the molar occupies the octahedral B-site and among themselves ratio 1:1:1), pelletized and sealed in a quartz tube af- they form a corner shared tetrahedral network like in ter flushing with argon gas. The sample was then fired the pyrochlore lattice which is geometrically frustrated. in a box furnace for 24 hours with intermediate regrind- Random or statistical distribution between the Li1+, ing, pelletization and sealing. The temperatures during V3+ and V4+ ions dilutes the corner-shared tetrahedral successive firing were 600oC and 700oC. Powder x-ray magnetic network. This dilution works as an additional diffraction (XRD) measurements were performed at room source of disorder and forces the system to relieve

2 3

H = 10 kOe Yobs

1.54182 Å 8 (113) Ycalc

-1

T = 300 K Yobs-Ycalc 2 ( - )

0 )

Bragg position 3

CW fit 2

Li VO

3 4

count) 4 (022)

H = 25 Oe (044) (115) /mol V) /mol 3 8 mol V/cm mol

FC 3

1 4

ZFC

cm 6 1 /mol V) /mol (224)

3 -3 (10 1 - (004) (335) 4 cm ) -3 (026) (246) (10 (226) (133) (222) (444) (135) (244) Intensity(10 (111)

(155) 2 T = 3 K dc (10 * * * * *

(

0 0

1 10 100

T(K)

15 30 45 60 75 90 0 0

0 -185 0 200 400 600

T(K) Figure 1: Powder XRD pattern of LZVO at 300 K and its Rietveld refinement considering Fd¯3m space group is shown Figure 3: The dc susceptibility χdc(T ) (on left y-axis) and the along with its Bragg peak positions (pink vertical bars) and inverse susceptibility free from T -independent χ (on right y- the corresponding Miller indices (hkl). The black circles are axis) of LZVO in H = 10 kOe are depicted as a function of the observed data, the red solid line is the calculated Ri- temperature. The solid lines show the Curie-Weiss fit. In the etveld pattern, the blue solid line is the residual data and inset, the bifurcation between zero field cooled (ZFC) and field the olive vertical bars are the Bragg peak positions for the cooled (FC) data below Tf = 3 K is observed in an applied field of 25 Oe. non-magnetic impurity Li3VO4. The main peaks of Li3VO4 are indicated by blue asterisks. function of temperature (T ) at various applied magnetic M fields (H). The dc susceptibility (χdc(T ) = H ) is plotted as a function of temperature in an applied field H = 10 kOe in Fig.3. There is no long-range or short-range ordering down to 2 K. The χdc(T ) in H = 10 kOe is paramagnetic and follows a Curie-Weiss law. The zero field cooled (ZFC) and field cooled (FC) data in H = 10 kOe show no difference down to 2 K. From a Curie-Weiss C χdc(T ) χ(T ) = χ0 + fit of using the equation: (T −θCW) in the range of (200 - 400) K, we obtained the temperature −4 3 independent susceptibility χ0 = 4.62 × 10 (cm /mol 3 Figure 2: (a) One unit cell of LZVO. (b) Corner shared V), the Curie constant C = 0.28 Kcm /mol V and the tetrahedral network of magnetic vanadium atoms and corner Curie-Weiss (CW) temperature, θCW = -185 K. The ef- 2+ shared diamond structure of Zn ions. fective moment µeff is then about 1.50 µB which is less 1 than that of the µeff = 1.73 µB for a spin S = 2 system. From the stoichiometry of LZVO, one might have the frustration and a spin-glass or frozen state might expected two V4+ ions and one V3+ ion per formula unit emerge. Fig.2(a) and (b) shows (Li/V) 4 corner shared giving a Curie constant C = 0.583 cm3K/mol V. How- tetrahedra in 3D. ever, we inferred a much smaller value. This result is similar to the homologous cluster magnet LiZn2Mo3O8 3 Table I: Atomic positions in LiZn2V3O8 after Rietveld refine- [12] where the Curie constant (C = 0.24 Kcm /mol f.u.) ment of powder XRD at room temperature. was less than the expected value. In metallic LiV2O4, the Curie constant was found to be that corresponding to one S = 1 moment per vanadium whereas one has, Atom Wyckoff position x/a y/b z/c Occupancy 2 on an average, 1.5 electrons per vanadium. It is possible Zn 8b 0.375 0.375 0.375 1.000 that here as well, the moment is quenched to some extent Li 16c 0.000 0.000 0.000 0.241 due to frustration. The high CW temperature suggests V 16c 0.000 0.000 0.000 0.759 strong antiferromagnetic interactions between the mag- O 32e 0.239 0.0.239 0.239 1.000 netic vanadium atoms in the sample. In the inset of Fig. 3, the susceptibility, in a low field of 25 Oe, in ZFC (open circles) and FC (closed triangles) mode shows bifurcation B. DC susceptibility below Tf ' 3 K. This bifurcation suggests a spin-glass (SG) ground state of the system at low temperature. The M f = |θcw| ≈ 62 The magnetization ( ) of LZVO was measured as a inferred frustration parameter [1]( TN ) puts

3 the LZVO system in the highly frustrated category. it is intermediate between the values for canonical SG systems and superparamagnets (δTf ' 0.28). Also the C. AC susceptibility present value of δTf is close to that of the shape memory alloys showing re-entrant spin-glass (RSG) behavior [29], To further understand the nature of the SG states of 0.037 seen in metallic glasses [30] and 0.095 reported in LZVO, the ac magnetic susceptibility was measured in a LaCo0.5Ni0.5O3 [31]. ﬁxed ac ﬁeld of Hac = 3.5 Oe with T - range (2≤ T ≤ 4.2 K) and frequency range 1 ≤ ν ≤ 1000 Hz. The tem-

(a)

T perature variation of the in-phase component of the ac 3.3 0 f susceptibility, χ (T ), as shown in Fig.4, shows a cusp ac Vogel-Fulcher fit like behavior and a peak at Tf = 3.0 K for ν = 11 Hz. The peak position shifts towards higher temperatures as the 3.2 (K) f

ν T frequency increases from 11 Hz to 555 Hz. So the fre- = 3.56x10 rad/s

0 0 quency dependence of χac(T ) is evident with a downward E /k = 3.31 K

3.1 shift of the anomaly with increasing ν and is consistent a B

T = 2.78 K with SG systems. Even the out of phase component of 0 00 χ (T ) T ac susceptibility ac shows a peak at f which barely 3.0 shifts with frequency variation (shown in the inset of Fig. 0.08 0.10 0.12 0.14 0.16

1/ln( / ) 00

0 4). The value of χac(T ) is non-zero positive below Tf

and is negative above Tf . This indicates the SG state -1.0 (b) is associated with frustrated magnets. Such behavior is Expt. data

Critical exponent fit

-1.5

1.3 )

11 Hz

2 -2.0

-6 55 Hz

log( = 1.82x10 s 1

0 emu/Oe) 111 Hz -8

-2.5

T = 3.03 K 0 333 Hz

g (10 ''

1.2

555 Hz ac

z = 2.65 -1

-3.0 emu/Oe) -2

2.0 2.5 3.0 3.5 4.0 -6

-1.8 -1.6 -1.4 -1.2 -1.0

T(K) (10

log(T /T -1) '

f g ac

1.1

H = 0 dc Figure 5: Frequency dependence of the freezing temperature

H = 3.5 Oe

ac Tf along with (a) the ﬁt to the Vogel-Fulcher law. (b) the ﬁt to the critical slowing down formula (see text).

1.0

1.8 2.4 3.0 3.6 4.2

T(K) To know the dynamic properties of the spins, we have fitted Tf with the empirical Vogel–Fulcher law: ω = 0 Ea ω0 exp[− ] ω0 Figure 4: The temperature dependence of the in phase χac kB (Tf −T0 ) in Fig.5(a). Here is the char- 00 (in main figure) and the out of phase χac component (in the acteristic angular frequency, ω is the angular frequency inset) of ac susceptibility (χac) at different frequencies are (ω = 2πν), E a and T0 are the activation energy and shown. Vogel–Fulcher temperature, respectively. The best fit, 6 shown in Fig.5(a), is obtained for ω0 ≈ 3.56 × 10 Hz, distinctive of the SG states and allows us to categorize Ea /kB ≈ 3.31±0.10 K, and T0 ≈ 2.78±0.01 K. As the the SG systems from the disordered antiferromagnetic measured frequency range is limited (only up to 1 kHz), (AFM) systems. In the disordered AFM systems, the the error bar will be high in the derived parameters from 00 value of χac(T ) is constant and remains zero below the such a fit. The Vogel-Fulcher fit of the variations of the transition temperature [23–25]. All these features con- freezing temperature (Tf ) with frequency suggests short- firm the formation of a SG ground state of LZVO. range Ising SG behavior [32]. The value of ω0 obtained The frequency dependence of Tf is often quantified in from the fitting is less than that of conventional SG sys- terms of the relative shift of the spin freezing tempera- tems, which is expected to be about 1013 rad/s. Such ture, defined as δTf = [ ∆Tf / Tf ∆log10(ν)] [26]. This a low value of ω0 is associated with the re-entrant spin- relative shift paramenter δTf which is also known as My- glass (RSG) systems like Ni2Mn1.36Sn0.64 [29] and cluster dosh parameter [27] is used to identify different SG sys- spin-glass (CSG) Zn3V3O8 [10]. Thus we might suggest tems. The calculated value is δTf ' 0.039 for our LZVO. that the spin glass state in LZVO is not atomic in origin; This value of δTf indicates that the sensitivity to the rather it is related to flipping of large number of spins frequency of LZVO is larger by an order of magnitude simultaneously or in a collective manner which leads to than that for canonical SG systems such as CuMn (δTf the formation of CSG states. = 0.005) [28] and AuMn (δTf = 0.0045) [24]. Indeed, On further analysis, the Tf is found to obey the critical

4 slowing down dynamics (see Fig.5(b)) governed by the the presence of metastable states in our LZVO system. Tf −zv τ = τ0( − 1) τ0 From the value of τ, it is evident that the decay is faster equation: Tg , where is spin flipping relaxation time of the fluctuating entities, zv is the dynamic as the temperature near Tf ' 3 K. This also signifies that LZVO system goes to a metastable and irreversible state exponent and Tg is the static freezing temperature [33]. below Tf on application of field. As expected, when T We found the best fit with Tg = 3.03±0.01 K, τ0 ≈ 1.82 ×10−7 s and zv ≈ 2.65. For the conventional SG systems, ≥ Tf , MIRM(t) is independent of time. −10 −13 the value of τ0 ranges within 10 to 10 s and zv in the range (4 - 13) [30]. The fact that the present value of 1.75

(a) Aging effect τ0, is higher than that of the conventional SG systems, suggests that in LZVO, the spin-dynamics develops at a 1.70 slower rate due to the presence of randomly magnetized /mol V) /mol interacting clusters, instead of individual spin random- 3 1.65 ness. Similar values have also been reported in SG sys- 10 s

H = 200 Oe (G cm (G tems such as Heusler alloys, LaCo0.5Ni0.5O3, pyrochlore 1000 s

T = 2.2 K M

1.60 molybdates etc. [29, 31, 34]. The value of zν falls in the 5000 s range of other typical CSG systems.

1.55

3 0 1 2 3

D. Aging eﬀect and relaxation t(10 s)

Isotherm al relaxation (b)

Aging eﬀect is a characteristic signature of any glassy 3 K

1.00 system [28, 35]. Aging indicates that the response of a 3.5 K system becomes slower and slower with time. Here, ag- 2.8 K

2.2 K

0.75 ing eﬀect has been studied with time evolution of zero 2.5 K (t = 0) = (t

2 K

ﬁeld cooled (ZFC) magnetization. The Fig.6(a) de- IRM

1.8 K picts the growth of the magnetization data as a func- M

0.50 Fit tion of time, in the frozen state. The sample was cooled (t)/ from RT to 2.2 K in the ZFC mode and then the sys- IRM M tem was allowed to age for a waiting time tw. Subse- 0.25 quently, a ﬁeld of 200 Oe was applied and the magneti- 0 2 4 6 8

3 zation was then recorded as a function of time. We have t(10 s) measured aging effect for three different waiting times 10 s, 1000 s and 5000 s. It is clear that the magnetiza- Figure 6: (a) Aging effect shows the growth of the magneti- tion growth is slower for larger waiting times, which indi- zation as a function of time with three different waiting times cates the metastability of the low temperature magnetic and (b) Isothermal remanent magnetic relaxations (normal- state. We also measured the isothermal remanent mag- ized with respect to the moment at t = 0) with their fitting (described in text) are shown as a function of time at several netization (MIRM) of LZVO to explore the metastable temperatures. behavior of the SG state around the SG transition temperature. To measure the MIRM, first we cooled the sample in the ZFC mode from RT to the desired temperature mainly below the transition point, then we applied Table II: The best fit (see text) result of isothermal remanent a field of 500 Oe and we switched off the field after 300 s magnetic relaxation of LZVO. and allowed the system to relax. During relaxation, we T (K) M∞ Stretching exponent α Relaxation time τ(s) recorded the magnetization as a function of time for two M0 hours. Fig.6(b) shows seven relaxation curves which 1.8 0.223 0.53 580 are normalized to the magnetization before making the 2.0 0.248 0.55 649 field zero, MIRM(t)/MIRM(0) at seven different temper- 2.2 0.372 0.46 593 atures. The time dependence of MIRM(t) is well fitted with the stretched exponential given as in equation 2.5 0.318 0.52 737 α 2.8 0.653 0.54 323 Mt(H) = M0(H)+[M∞(H)−M0(H)][1−exp{−(t/τ) }]. Here, M0 and M∞ are magnetizations at t → 0 and t → ∞, τ is the characteristic relaxation time and α is the stretching exponent, which ranges between 0 and 1. De- E. Memory effect pending on the value of α, one can have an estimation of the distribution of energy barriers present in the frozen Fig.7 shows a memory effect which is measured in the state. The obtained best fit parameters for each isotherm FC magnetization mode using the protocol introduced by are listed in TableII. We have found that the values of α Sun et al. [20]. In an applied field of H = 500 Oe, we for LZVO, varies within 0.45 to 0.55, is consistent with have recorded the magnetization of LZVO as a function earlier reported glassy systems [10, 27, 36]. Also α < of temperature from 100 K down to 2 K with a cooling 1 indicates the anisotropic nature of energy barries i.e. rate of 1 K/min. Below Tf , We interrupted the cooling

5 4.6 and then we have measured the magnetization for a time t FCC 2 = 1 hr. Finally, we restored the sample temperature

M Ref to T1 = 2.75 K and measured the magnetization for a

FCW

M Mem period of t3 = 1 hr. The relaxation curve obtained in

FCC

M 4.4 this way is shown in Fig.8(a). In each relaxation pro-

Stop /mol V) /mol 3 cess, the magnetization increases logarithmically with t and the system remembers its previous value it reached

(G cm (G before the temporary cooling started. This determines

M that the negative T - cycle does not erase the memory in

4.2 2.5 K ZFC mode. For the FC mode, we field cooled the sample to T1 = 2.75 K first in a field of 500 Oe. Once we reached 2.2 K the measuring temperature, we switched off the field and subsequently measured the magnetization as a function

4.0 of time. Fig.8(b) shows the FC relaxation process where 2 3 4 the magnetization decays exponentially with t. Similarly, T(K) the FC method also preserves the state of the system even Figure 7: The memory eﬀect in LZVO as a function of tem- after a temperature cooling. Inset of Fig.8 (a) and (b) perature is observed in FC magnetization mode at H = 500 shows that in both ZFC and FC methods, the magnetic FCC t3 Oe. The MStop curve was obtained during cooling the sam- relaxation during is a continuation of the relaxation ple with intermediate stops of 3 hours duration each at 2.5 K curve during t1. This is a simple demonstration of the FCW FCC and 2.2 K. The MMem and MRef curves were measured dur- memory eﬀect. ing continuous heating and cooling of the sample respectively at H = 500 Oe. 4.6

(a) ZFC

T = 2.00 K H = 500 Oe T = 2.75 K

4.4

4.48

T = 2.75 K /mol V)

1 process twice at 2.5 K and 2.2 K for a waiting time tw = 3

4.44

3 hr each. We switched oﬀ the ﬁeld during tw and let the ZFC T

T 3

(Gcm 4.2 1 system to relax. We resumed the FC process after each M ZFC

4.40 M

0 2 8 10 12 stop and wait period. The stops at 2.5 K and 2.2 K are 3 FCC t(10 s) obvious as step-like features obtained in the MStop curve

shown in Fig.7. After reaching 2 K, we heated the sam- (b) FC

0.04

H = 500 Oe ple continuously in the same magnetic ﬁeld and recorded 0.04

0.02 FC

the magnetization data simultaneously. The magnetiza- M

T /mol V)

T FCW 1 3 tion obtained in this way, referred to as MMem , exhibits 0.00 3 a slight inﬂexion at 2.5 K and a pronounced minimum 0 2 8 10 12 3

0.02

t(10 s) (Gcm

at 2.2 K. This indicates that somehow the system has FC M

T = 2.75 K its previous behavior imprinted as a memory during the T = 2.00 K 1 T = 2.75 K

2 cooling process. Similar behavior has been noticed earlier 3

0 2 4 6 8 10 12 in intermetallic compounds such as GdCu [36], Nd5Ge3 3

t(10 s) [37] and in super-spin-glass nanoparticle systems [20, 38]. This is nothing but the typical aspect of SG systems. The Figure 8: The magnetic relaxation in LZVO at 2.75 K with a M FCW inflexion point or dip at 2.5 K in the Mem curve is weak negative heating cycle at H = 500 Oe for (a) the ZFC and (b) because at 2.5 K the system is not much below the freez- the FC methods. The insets show the relaxation data during ing temperature (i.e.Tf = 3.0 K at H = 500 Oe). A T1 and T3 which are merged in a seamless manner. FCW reference curve (MRef ) was also measured by cooling the sample continuously at H = 500 Oe. It is worth not- Positive heating cycle: The droplet model [39, 40] of ing that there was no memory effect when we wait at a SG systems supports a symmetric behavior in the mag- temperature above Tf . netic relaxation concerning either heating or cooling cy- Negative heating cycle: The memory effect was further cles whereas the hierarchical model [20, 21] predicts a clarified by the ZFC and FC method with a negative asymmetric response. To compare the response of in- heating cycling as shown in Fig.8. In the ZFC mode, termittent heating and cooling cycles, we performed the we cooled the sample below the spin freezing tempera- relaxation experiment with a positive heating cycle also. ture (Tf ) in zero field from the paramagnetic state to the The results are shown in Fig.9(a) and (b). One might measuring temperature T1 = 2.75 K. Then we recorded notice that a positive temperature cycle erases the ear- the magnetization as a function of time (t) for 1 hr in lier memory and re-initializes the relaxation process in an applied field of 500 Oe. The magnetization increases both ZFC and FC mode. This confirms that the mag- logarithmically with t. After that, we cooled the sample netic response of the our system irrespective of heating temperature to a lower value T2 = 2.0 K in the same field or cooling cycle is not symmetric. So this study sup-

6 4.50 the system temperature from T0 to T0 + ΔT , then the (a) ZFC T =1.90 K

H = 500 Oe barriers between the free energy primary valleys becomes

T =2.75 K

/mol V) /mol low or sometimes they even get merged. Then, the re-

4.25 3

T =1.90 K

1 4.5 laxations can easily take place within diﬀerent valleys. T 3 T T When the temperature is lowered back to 0, the relative

1 (Gcm

4.2

ZFC 4.00 occupancy of each energy valley does not remain the same M ZFC

3.9 M t(10 s) as before even though free energy surface goes back to the

0 2 8 10 12 original state. Thus the state of the system varies after 0.6 a temporary heating cycle and results without a memory (b) FC

0.4

T H = 500 Oe eﬀect. The behavior we found in our system, has been 1 FC

0.4 0.2 /mol V) /mol M seen in some other SG systems too [10, 20, 36, 37, 41]. 3 T

0.0

T =1.90 K 300

1 0.2

0 2 8 10 12 (Gcm

3 0 kOe

t(10 s) FC

25 kOe M

0.0 T =2.75 K T =1.90 K 50 kOe

2 3

75 kOe

0 2 4 6 8 10 12

90 kOe

200 t(10 s)

(1D+3E) f it

0.27 Figure 9: The magnetic relaxation in LZVO at 1.9 K with a ) positive heating cycle in H = 500 Oe (a) the ZFC and (b) the (J/molK) 2 p 0.18 FC methods. Insets show the relaxation data during T1 and C T3 which are not merged. 100

0.09 (J/molK /T p C

0.00

2 3 4 5 6 7 8 910 20 30

T(K)

0 100 200 300

T(K)

Figure 11: The heat capacity Cp(T ) of LZVO as a function of temperature in different fields is plotted. The pink solid line represents the (Debye + Einstein) fit (see text) as well as the lattice heat capacity. The inset shows low temperature anomaly of Cp/T vs. T plot in semi-log scale.

F. Heat capacity Figure 10: Schematic diagram of the hierarchical model for spin-glass states. The different curves represent the free en- We have measured the heat capacity of the LZVO sam- ergy at that particular temperatures. The metastable states ple at a constant pressure Cp(T ) by the thermal relax- of the spin-glass are depicted by the lobs at T = T0 - ∆T . ation method in different fields (0 - 90 kOe) at the temperature range (2 - 280) K for zero field and (2 - 50) K for higher fields. The Fig. 11 shows the tempera- ports the hierarchical model proposed for SG systems. ture dependence of the specific heat at constant pressure Fig. 10 depicts the schematic diagram of the hierarchi- Cp(T ) of LiZn2V3O8. Absence of sharp anomaly in the cal model. At a given temperature T0, there exists a Cp(T ) vs. T data implies a lack of long-range order in multi-valley {α,β, γ} free-energy surface for a frustrated LZVO and supports our dc susceptibility data in H = system. When we cool the system from T0 to T0−ΔT , 10 kOe. Below 10 K, in the Cp/T vs. T plot (see inset each valley splits into many sub-valleys {αi}, {βi}, {γi}. of Fig. 11), there is a broad hump or anomaly at low When ΔT is large, the energy gaps between the primary temperature. These anomalies are field dependent and valleys become high and the system fails to overcome this appear to be Schottky anomalies. To extract the mag- energy barrier within a finite waiting time t2. There- netic contribution to the heat capacity, we have to sub- fore, the relaxation occurs only within the sub-valleys or tract the lattice and Schottky contributions from the to- metastable states. When the temperature of the system tal heat capacity i.e. (Cm(T ) = [Cp(T ) − Clat − CSch]), is restored to its initial value T0, then the sub-valleys where Clat and CSch are the lattice and Schottky merge back to the original free energy surface and relax- heat capacities respectively. As there is no suitable ation at T0 resumes without being perturbed by the in- non-magnetic analog, we attempted to fit the specific termediate relaxations at T0− ΔT . But, if we increased heat capacity data with a combination of one Debye

7 h xD 4 x i ∆ T 3 x e g exp( k T ) term Cd 9nR( ) x 2 dx and several Ein- ∆ 2 0 B θD 0 (e −1) tem CSch = f R( k T ) ( g ) g0 ∆ 2 [42, 43]; B 1 [1+( g )exp( k T )] ´ θE 1 B θ exp( i ) P C 3nR( Ei )2 T where f is the fraction of free spins within the system, ∆ stein terms ei T θE to deter- (exp( i )−1)2 T is the Schottky gap, R is the universal gas constant, kB mine the Clat. Among them, one Debye function plus is the Boltzmann constant and g0 and g1 are the degen- three Einstein functions (1D+3E) fit was the best in the eracies of the ground state and excited state, respectively fit range 18 - 135 K. Here the coefficient Cd is the rela- (in this case, g = g0 = 1). Here, with respect to the 25 tive weight of the acoustic modes of vibration and coef- kOe data, we have derived the Schottky contribution at C C C ficients e1, e2 and e3 are the relative weights of the higher fields as the zero field data have the same kind of optical modes of vibrations. After fitting we obtained anomaly present which might be a result of some intrinsic C C C C d: e1: e2: e3 = 1:6:4:3. The sum of these coefficients interactions present within the system. From the fitting is equal to the total number of atoms (n = 14) per for- of ∆Cp(T )/T , we obtained the energy gap ∆ at different mula unit of LZVO. In the absence of an applied field, fields which are plotted in the inset of Fig. 12(a) and show a linear dependence. From the slope of ∆/kB vs.

0.02

50 kOe H plot, we obtained the value of Land´e g factor, g = 2.05 (a)

75 kOe which is close to the value for free spin. From our ﬁts,

90 kOe 1 0.01 the fraction of S = entities contributing to the heat ca-

) 2 Schottky fit 2 pacity is about 2-5 %. The large intercept in the ∆/kB

H 0.00 vs. shows that the internal magnetism exists even in 30

g = 2.05

zero applied ﬁeld as might be expected in a spin-glass. (J/mol K (J/mol 20 After subtracting the lattice and Schottky contribution,

-0.01 /T

p (K) C /k

B we obtained the magnetic heat capacity m at 50 kOe,

C 10 B /k

Linear Fit 75 kOe and 90 kOe. Fig. 12(b) shows the magnetic heat

-0.02 0 capacity (Cm) on the left y-axis. The Cm is indepen- 0 25 50 75 100

H(kOe) dent of the applied ﬁeld and it shows a hump around 7.5

5 10 15 20 25 30 K. Fig. 12(b) also shows the derived magnetic entropy

T(K) change (∆Sm(T )) on the right y-axis. The maximum 1.5 30 Cm

50 kOe value of ∆Sm(T ) (= dT ) is 1.75 (J/mol K) which (b) T

75 kOe is only 25% of the expected´ Rln(2S + 1) = 6.89 (J/mol 1 4+ 90 kOe K) for two S = 2 spin (V ions) and one S = 1 spin 3+ 1.0 20 (V ion) per formula unit of LZVO. A large reduction +1) (%) +1)

50 kOe of entropy change indicates quenching of moments due S

(J/mol K) (J/mol 75 kOe to frustration and/or the presence of many degenerate m ln(2

90 kOe C low-energy states at low temperature. R

0.5 10 / / m S

1.00 f = 95 MHz

0.0 0

Li reference line 0 5 10 15 20 25

143.5 K T(K)

0.75

108.0 K

Figure 12: (a) It shows the low temperature Schottky 46.6 K anomaly fitting in different fields. The inset shows the linear 23.9 K

16.0 K dependence of the Schottky gap (∆) with the ﬁeld strength 0.50 11.8 K (H ). (b) The magnetic heat capacity (C ) on left y-axis and m 7.8 K

the magnetic entropy change (∆Sm) on right y-axis of LZVO 5.4 K

0.25 as a function of temperature is shown. 3.5 K

1.8 K

the Cp(T ) data at H = 0 kOe, Cp(0, T ) contains lat- (normalized) Intensity

0.00 tice Clat(T ), as well as a magnetic Cm(H , T ) part but lacks a Schottky contribution. So we consider Cp(0, T ) 57.0 57.2 57.4 57.6 57.8 58.0 as a reference and subtract it from the higher ﬁeld data

H(kOe) Cp(H , T ) to obtain Schottky contribution in that particular field, CSch(H,T ) = [Cp(H,T ) − Cp(0,T )] = ∆Cp. Figure 13: The 7Li NMR spectra of LZVO at different tem- Now this ∆Cp represents the Schottky contribution pro- peratures measured at a fixed frequency of 95 MHz. The blue vided that Cm(H , T ) is field independent in that tem- 7 ∆C /T dashed vertical line represents the reference position for Li perature range. In Fig. 12(a). we have plotted p nuclei at RT. vs. T and the Schottky contributions (CSch) to the total heat capacity are well fitted by a two level Schottky sys-

7 0.08

7 G. Li NMR spectra and shift K (%) at 95 MHz

-750 K 2.5

Linear fit 1

0.07 In LZVO, the non-magnetic Li ions and magnetic vana- Linear fit 2 (%)

K 0.06 dium ions share the B-site. Due to a strong onsite cou- ) 7 2.0 -2

A = (95 ± 5) Oe/ m pling between the nuclear moment and the electronic mo- hf B

0.05

A = (119 ± 5) Oe/ m ment it is diﬃcult to detect NMR signal from the mag- hf B (10

1.5 H netic vanadium ions yielding very short relaxation times. -600 / 1+ (ppm) 0 5 10 15 20

-3 3 H S K For Li ions, the electronic spin is zero ( = 0), with a c(10 cm /mol ) 7

3 7 D nuclear spin I = 2 . Additionally, the Li nuclei exhibit

1.0 a high natural abundance (92.6%) and a high gyromag- FW HM γ netic ratio 2π = 1.6546 MHz/kOe resulting in strong nuclear magnetization detectable in NMR experiments. 7Li 0.5 NMR spectra have been measured at 95 MHz down to -450 1.8 K. The spin-lattice and spin-spin relaxation rates also 0 50 100 150 200 have been measured to probe the low energy excitations. T(K) Fig. 13 shows the spectra at different temperatures from 143 K to 1.8 K. The spectra get broadened and Figure 14: The 7Li NMR shift (left y-axis) and the FWHM nominally shift towards higher fields (i.e. negative shift (right y-axis) of the 7Li NMR spectra as a function of tem- concerning frequency) as temperature decreases. By fit- perature behave like the paramagnetic bulk susceptibility. In ting the spectra at different temperatures to Gaussian the inset, the linear variation of 7 K (%) vs. χ with tempera- functions we derived the full width at half maximum ture as an implicit parameter is shown and from the slope we 7 (FWHM) and NMR line shift K (using the relation determine the hyperfine coupling constant Ahf . 7 Href −Hres K Hres = Href ; where denotes the resonance field

which is estimated by considering the peak position of 200

15 95 MHz that spectrum, while Href represents the reference ﬁeld T = 2.9 K 30 MHz

7 ) of the Li nuclei at room temperature). The calculated -1 s

10 shift (7K) varies from -450 ppm (200 K) to -750 ppm 3

7 (10 (1.8 K) with respect to the Li NMR reference ﬁeld Href 2

/T 5

T = 2.8 K 1 = 57.415 kOe at 95 MHZ. The temperature dependence ) 7 -1 of FWHM and K are shown in Fig. 14 on the right 100 0 (s

1 and left y-axis, respectively. Both exhibit paramagnetic 1 10

T(K) behavior according to the Curie-Weiss law of the bulk /T χ(T ) 1 susceptibility . In the inset of Fig. 14, we have 95 MHz 7 plotted the K(%) vs. dc susceptibility χ(T ) with tem- 30 MHz perature as an implicit parameter and the linear behavior

Ahf 0 Kshift = χ(T ) is seen. As NAµB ; the slope of the linear fit gives the hyperfine coupling constant (Ahf ). We have fitted the 7 K -χ plot by a linear equation in two different 1 10 100 T(K) ranges which are designated as linear fit 1 and linear fit 2. In linear fit 1, we have considered the whole temper- 1 Figure 15: The spin-lattice relaxation rate ( T ) and (in the ature range and it gives us Ahf = (95±5) Oe/µB. On 1 inset) the spin-spin relaxation rate ( 1 ) of 7Li are shown in T2 the other hand, in linear fit 2, we have neglected a few semi-log scale. Both were measured at two different frequen- low-temperature points (as, here, there could be some cies (95 MHz and 30 MHz) with a prominent peak at around extrinsic Curie contribution due to paramagnetic impu- Tf ' 3 K in lower frequency according to a lower applied rities in the bulk susceptibility data) and this fit yields magnetic field. The connecting lines are a guides to the eye. Ahf = (119±5) Oe/µB. H. Spin-lattice and spin-spin relaxation = 3 K (see Fig. 15). This is in agreement with the 7 The spin-lattice relaxation time (T1) of Li at vari- bulk dc susceptibility, where, in high fields, the anomaly ous temperatures was measured using a saturation re- is suppressed. The spin-spin relaxation data are well fit- ( −2t ) covery sequence at two fixed frequencies 95 MHz and ted with the single exponential M(t) = M0e T2 . The 30 MHz. The data are well fitted with a single expo- 1 M(t) ( −t ) spin-spin relaxation rates ( T ) (see inset of Fig. 15) also 1 − = Ae T1 2 nential M(0) in the temperature range show an anomaly around the SG transition temperature 7 1 Tf ' (150 - 7 K). Around 3 K the data are best fitted with 3 K. The Li NMR T1 data at high-field is nearly a stretched exponential. At low fields, the spin-lattice unchanged with temperature, which is different from the relaxation rate shows a prominent peak around 2.9 K published data of undoped LiV2O4 [4] and doped LiV2O4 which is close to the spin-glass ordering temperature Tf [44] (see Fig. 16 where published data are shown along

9 with our data). In low-ﬁeld i.e. at 30 MHz, we observed nature. But these need not to be fully FM entities; they 1 7 an increase in our T1 data of Li nuclei for LZVO near the can be mostly random with some correlation length which freezing temperature Tf = 3 K (see Fig. 15). Likewise rigidly couples more than two spins. in case of Li1−xZnxV2O4 (x = 0.1) and Li(V1−yTiy)2O4 (y = 0.1) [45], an anomaly or peak in the T -dependence 7 1 of Li NMR T1 was seen close to the SG transition tem- 7 1 perature. Also, Li NMR studies of S = 2 geometrically frustrated systems, Li2ZnV3O8 [11] and LiZn2Mo3O8 [13] have been reported with an almost temperature invari- 1 ant spin-lattice relaxation rate ( T1 ) of the order of 10 s−1 similar to what we have seen for our LZVO at 95 MHz. As the earlier reported spin-lattice relaxation data on pure and doped LiV2O4 systems are measured at different frequencies, we have mentioned them in bracket for clarity in Fig. 16. Figure 17: Illustration of conventional spin-glass and cluster

Sample (frequency) [Ref.] spin-glass. The colors indicate the diﬀerent domains formed

LiV O (135 MHz) [4]

2 4 by group of spins which are oriented in a particular direction

LiV Ti O (17.3 MHz) [45]

1.8 0.2 4 with diﬀerent magnetic strength.

10000

Li Zn V O (17.3 MHz) [45]

0.9 0.1 2 4

Li ZnV O (155 MHz) [11] 2 3 8 Among the spinels where the pyrochlore lattice of ) LiZn Mo O (88.5 MHz) [13]

2 3 8 -1 the magnetic B-sites is diluted by non-magnetic ions 1000 LiZn V O (95 MHz) [this work]

2 3 8 (s

1 in the ratio 1:3, for LiZn2V3O8 the Curie-Weiss tem- LiZn V O (30 MHz) [this work]

2 3 8 T perature (θCW = -185 K) is somewhat lower than in 1/ (θ 100 Li2ZnV3O8 CW = -214 K) and much lower compared to Zn3V3O8 (θCW = -370 K). In all cases, the disorder at B-site of the spinel and the dilution of the corner-

10 shared tetrahedral network in 3D due to the presence 2+ 1+ of 25% non-magnetic ions (Zn for Zn3V3O8, Li for Li2ZnV3O8 and LiZn2V3O8) triggers the system to form

1 a spin–frozen state (cluster spin-glass rather than a con- 1 10 100 ventional one) at about the same temperature. Consid- T(K) ering the ratio of V3+ and V4+ ions, the expected Curie C 3 7 constant per vanadium is = 0.79 Kcm /mol for ZVO Figure 16: The spin-lattice relaxation rate (1/T1) of Li nuclei and C = 0.58 Kcm3/mol for LZVO; whereas the ob- in LZVO is compared to the pure and doped LiV2O4 systems tained values are C = 0.75 Kcm3/mol and C = 0.28 from literature. Kcm3/mol, respectively. We speculate that the much lower Curie constant in LZVO might indicate the presence of some degree of itinerancy like in the metallic LiV2O4 system. It would be interesting to see how these IV. DISCUSSION parameters evolve with the extent of dilution.

Theoretical studies by M. Schmidt et al.[46], Gang Chen et al.[47–49] and E. C. Andrade et al.[50] show V. CONCLUSION that when a geometrically frustrated system (like the Kagomé lattice) is driven by disorder then it often man- The cubic spinel LiZn2V3O8 has been successfully syn- ifests spin-glass (SG) and sometimes cluster-spin-glass thesized. It crystallizes in the centrosymmetric cubic (CSG) properties. A sketch of the outcome is given in spinel Fd¯3m space group. From a CW-fit of our 10 kOe Fig. 17 which depicts a cartoon of spin orientation in dc susceptibility data, we obtained the Curie constant C 3 a conventional SG and a CSG. The individual spins are = 0.28 Kcm /mol V and CW temperature θCW = -185 locked in place for conventional SG systems whereas in K. The Curie constant suggests a possible suppression CSG, a group of spins are locked to form a pair, triplet or partial quenching of local moments and the CW tem- or even domains. The remaining spins which are not perature suggests strong AFM interactions among the participating in the cluster are independent, but help to magnetic vanadium ions. A high value of frustration pa- mediate the interactions between the clusters such that rameter (f ' 60) is inferred from our data. The ZFC-FC the clusters can change their sizes and response time. bifurcation below Tf ' 3 K indicates SG nature which is The bigger the cluster size, the slower is the relaxation confirmed by frequency dependence of the ac susceptibil- rate. The clusters can be short-range ferromagnetic in ity, the Vogel-Fulcher law and critical power law of the

10 1 Tf . The low value of the characteristic angular frequency dence of the spin-lattice relaxation rate ( T ), and the 6 1 ω0 ≈ 3.56×10 Hz and the high value of the critical spin-spin relaxation rate ( 1 ) of the 7Li nuclei indicates −6 T2 time constant τ0 ≈ 1.82×10 s, corroborates the CSG that they are sensitive to the fluctuations of the magnetic ground state. The magnetic relaxation, aging phenom- ions and show an anomaly near Tf . All experimental re- ena and memory effect support the metastability of the sults and observations point towards the formation of a CSG ground state. The asymmetric response in a posi- CSG ground state in LZVO. tive temperature cycle obeys the hierarchical model proposed for the SG systems. Absence of any sharp anomaly in heat capacity data indicates lack of long-range ordering down to 2 K. The significant contribution of magnetic VI. ACKNOWLEDGMENTS heat capacity shows a hump around 7.5 K which is independent of the applied field strength. The small entropy SK acknowledges the central facility and financial sup- change (∆Sm ' 25%) presumably arises from a large de- port from IRCC, IIT Bombay. AVM would like to thank generacy of the ground states. The field swept 7Li NMR the Alexander von Humboldt foundation for financial spectra show a line shift (7K) as T decreases. The plot support during his stay at Augsburg Germany. We kindly of line shift 7K(%) vs. bulk susceptibility χ follows a lin- acknowledge support from the Deutsche Forschungsge- ear behavior and the derived hyperfine coupling constant meinschaft (DFG, German Research Foundation) – Pro- amounts to Ahf = 119 Oe/µB. The temperature depen- jektnummer 107745057 – TRR 80.

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