We report on the magnetic behaviour of Nd5Ge3 by investigating through magnetization, neutron diffraction and muon spin relaxation measurements. Temperature dependent-magnetization, muon depolarization rate (λ), initial asymmetry (A0) and the stretched exponent (β) show a clear anomaly at the Néel temperature TN ∼ 54 K. However, the short-range correlated ferromagnetic interactions below TN are inferred from the diffuse scattering mechanism as revealed by zero-field neutron diffraction data. Narrow first order phase transition is due to the competing interaction of a high temperature weak-antiferromagnetic and low temperature glassy states. Magnetic field-induced reentrant spin glass state from a magnetic glass state is observed, before it transforms to a ferromagnetic state.

Nd5Ge3 is reported to exhibit dual magnetic transitions; AFM order (TN ∼ 50 K) and a second AFM order (Tt ∼ 30 K).1–3 The second AFM transition is determined on the basis of the disappearance of a critical field (Hcr), remanent magnetization and a cusp in χ(T) at 26 K.2 The observation of an easy destruction of zero field cooled (ZFC)-Tt transition in field-cooled (FC) mode (in an applied field of 100 Oe) and absence of a specific heat anomaly at Tt (both under ZFC and FC) lead us to believe a spin-glass like structure coexisting with long-range AFM order. In Nd5Ge3, antiferromagnetic order is reported to occur at a temperature (52 ± 2) K.1 The strongly coupled degrees of freedom in Nd5Ge3 are inferred from the field-induced sudden jumps in isothermal magnetization, specific heat versus magnetic field and field-dependent resistivity below Tt by Maji et al.3 

Maji et al.,4 point out that the glassy state formation below Tt is due to geometric frustration originating from the triangular arrangement of Nd atoms in the 6g position, using χac, magnetic relaxation and thermoremanant magnetization measurements. At T < 10 K, magnetic structure of Nd5Ge3 is of the spin wave type.5 In the present work, we have reported/confirmed temperature driven first order phase transition and cluster-glass behaviour below 30 K and a weak antiferromagnetic state at 50 K. Neutron diffraction measurements suggest short-range magnetic correlations while Nd5Ge3 undergoes a field-induced ferromagnetic state eventually.

Nd5Ge3 was prepared by arc-melting method as discussed in Ref. 4. X-ray diffraction (Cu-Kα radiation) pattern was collected at room temperature. The magnetization was measured using 7 T/2 K SQUID-VSM (Quantum Design, USA), in ZFC, field-cooled cooling (FCC) and field-cooled warming (FCW) modes. Powder neutron diffraction (ND) time of flight and muon spin relaxation (μSR) measurements were performed on WISH diffractometer and EMU instrument at ISIS, Rutherford Appleton Laboratory, United Kingdom respectively. μSR measurements were performed down to 2 K in zero field (ZF) and longitudinal field (LF) configurations. Muon relaxation function is given by Pz(t) = [NF(t) − αNB(t)]/[NF(t) + αNB(t)], in which α is the calibration constant.

Nd5Ge3 crystallizes in Mn5Si3-type hexagonal structure (P63/mcm) as evident from the Rietveld refined6 x-ray diffraction pattern shown in Fig. 1(a). The lattice parameters a = b = 8.7512(3) Å and c = 6.6341(2) Å are in agreement with those reported in Refs. 2, 4, and 7. Figure 1(b) depicts the magnetization as a function of temperature M(T). In 200 Oe, ZFC curve shows two peaks around 46.5 and 32.8 K which are in agreement with the literature.3 However, FCC magnetization does not exhibit a peak at Tt, indicating that the low-T phase is more susceptible to the magnetic field due to prevailing FM interactions in the paramagnetic state (note that TtθW, Weiss temperature). TN is the AFM transition while Tt (Tf hereafter) is ascribed to spin-glass freezing temperature.3,4

FIG. 1.

(a) Rietveld refined x-ray diffraction of Nd5Ge3 at T = 300 K, crystallizing in the hexagonal structure. (b) M(T) measured in a ZFC, FCC and FCW protocols. Inset: An enlarged view of FCC and FCW magnetization curves, showing a narrow thermal hysteresis. (c) Refined neutron diffraction pattern at 3 K, after H is made zero from 60 kOe. The magnetic peaks are indicated by arrows enclosed in a box. (d) Magnetic structure. 4d (Nd1) and 6g (Nd2), depicted in blue and green, order ferromagnetically along c-direction with unequal moments 1.81(4) μB and 1.66(3) μB, respectively.

FIG. 1.

(a) Rietveld refined x-ray diffraction of Nd5Ge3 at T = 300 K, crystallizing in the hexagonal structure. (b) M(T) measured in a ZFC, FCC and FCW protocols. Inset: An enlarged view of FCC and FCW magnetization curves, showing a narrow thermal hysteresis. (c) Refined neutron diffraction pattern at 3 K, after H is made zero from 60 kOe. The magnetic peaks are indicated by arrows enclosed in a box. (d) Magnetic structure. 4d (Nd1) and 6g (Nd2), depicted in blue and green, order ferromagnetically along c-direction with unequal moments 1.81(4) μB and 1.66(3) μB, respectively.

Close modal

Figure 1(c) shows refined ND pattern at 3 K on d-spacing scale, measured after reducing the field to zero from 60 kOe. The magnetic peaks are indicated by arrows in the box. As evident from the magnetic structure of Nd5Ge3 shown in Fig. 1(d), Nd1 at 4d-position possesses 1.81(3) μB while Nd2 at 6g-position has 1.66(3) μB. This infers to the field-induced ferromagnetic state. The magnetic moment 1.72 μB/Nd, at 3 K in the irreversible state, obtained from the refinement agrees well with that of from the magnetization data. However, magnetic fields of the order of 500 kOe are required to reach the magnetization saturation (Ms = 3.5 μB of Nd+3) in the c-direction.2 At H = 0 kOe, after applying 60 kOe, the nearest neighbour Nd1–Nd1 (4d–4d) inter-atomic distance and Nd1–Nd2 (4d–6g) inter-layer distance are found to be 3.3150(1) and 3.7581(2) Å respectively. These values are slightly less compared to zero-field values. Under 60 kOe, the inter-layer distance is observed to reduce from 3.7866(2) to 3.7553(1) Å. The decrease in the inter-layer distance can cause an enhancement of ferromagnetic interactions between the 4d and 6g positions.

Shown in Figs. 2(a) and 2(b) are the zero-field (ZF) asymmetry A(t) plots for the temperatures below and above TN, respectively. A(t) curves are fit using a stretched exponential form of the muon decay function; A(t) = A0 exp[−(λt)β] + BG8–10 where A0 is an initial asymmetry, λ is the muon decay rate and β is the stretched exponent. A non-decaying function is used as the background (BG) function as the muon stops in the silver sample holder, fixed at BG = 0.013 746 for the present case. Figure 2(c) shows the temperature variation of initial asymmetry A0(T). It is nearly independent of temperature down to 60 K below which it abruptly increases. Nevertheless, A0 decreases rapidly between 0.2 (at 50 K) to 0.06 (at 30 K). At low temperatures, A0 varies very weakly with temperature. The rapid decrease of initial asymmetry below 60 K is suggestive of antiferromagnetic order while A0 is constant in the paramagnetic state. Further, a diverging relaxation rate λ(T) from T = 92 K is shown in the Fig. 2(d), λ is 0.11 μs−1 at 92 K and reaches to a value of about 1 μs−1 while approaching TN. λ in the paramagnetic state fits well to the critical scaling law λ(T)=λ(0)[(T/TN)1]βμSR11,12 where TN is the antiferromagnetic ordering temperature and βμSR (not to be confused with the stretched exponential β) is the critical exponent; TN and βμSR being equal to 54 K and 0.43, respectively. While the obtained TN from the fit is in close agreement with the magnetization measurements, the critical exponent is indicative of three-dimensional Heisenberg model (βcritical = 0.367).13 Further reducing the temperature below 30 K, λ exhibits a plateau down to 9 K with a value of ∼0.2 μs−1. Thereafter, λ drops to 0.04 μs−1 at 2 K. This transition, also reflected in A0(T) and β(T), is in good agreement with the freezing temperature observed in ZFC magnetization. Figure 2(e) shows the temperature variation of the stretched exponent β. β (= 1 at T > 100 K) decreases with decreasing temperature, exhibits a minimum of less than ∼0.2 around the Néel temperature, but then recovers, reaching a value of ∼0.6 at approximately Tf. Below Tf, β exhibits a plateau, with an average value of ∼0.6. Though, the reduced β indicates the spin-glass behaviour, it is twice that of reported for a concentrated spin glass (β ∼ 1/3 below Tg).8,11,12,14,15 In this case, β(T) should be somewhat less than 1 and should be independent of temperature.8 However, in Nd5Ge3, the low-temperature glassy state is a result of competing ferro and antiferro-magnetic interactions. βavg ∼ 0.6 below the freezing temperature for Nd5Ge3 may be the result of the same local cluster-moment environment for the muon relaxation below Tf with a unique single relaxation time and competing ferromagnetic and antiferromagnetic interactions.16,17

FIG. 2.

ZF-time dependence of asymmetry for temperatures (a) below and (b) above TN. The data is fit using stretched exponential function. (c) The temperature variation of the initial asymmetry, A0(T). Loss of A0 is evident below TN. (d) λ(T), showing an abrupt increase of λ at the magnetic transition temperature while recovering below TN. Again λ exhibits a slope change near Tf. Critical scaling fit to λ(T) in the paramagnetic region gives TN ∼ 54 K. (e) The temperature dependence of the stretched exponent β. It exhibits a minimum at TN and becomes temperature independent (βavg ∼ 0.6) below Tf ∼ 30 K.

FIG. 2.

ZF-time dependence of asymmetry for temperatures (a) below and (b) above TN. The data is fit using stretched exponential function. (c) The temperature variation of the initial asymmetry, A0(T). Loss of A0 is evident below TN. (d) λ(T), showing an abrupt increase of λ at the magnetic transition temperature while recovering below TN. Again λ exhibits a slope change near Tf. Critical scaling fit to λ(T) in the paramagnetic region gives TN ∼ 54 K. (e) The temperature dependence of the stretched exponent β. It exhibits a minimum at TN and becomes temperature independent (βavg ∼ 0.6) below Tf ∼ 30 K.

Close modal

In re-entrant spin glass (RSG) systems; (i) a second order phase transition (SOPT) occurs from high-T long-range order to low-T glassy state with overlapping FCC and FCW curves (no thermal hysteresis),18,19 (ii) large thermomagnetic irreversibility (TMI)20 in low fields due to ZFC and FCC separation starts to decrease with increasing H and becomes zero when the high-T long-range order phase is established below Tf, (iii) ZFC-magnetization relaxes with time while that of FCC does not relax and (iv) the sign reversal of CHUF (cooling and heating in unequal fields) protocol21 does not seem to affect the RSG transition except that the absolute TMI changes monotonically with sign. On the other hand, in MG systems; (i) a marked thermal hysteresis between FCC and FCW arises due to arrested kinetics of first order magnetic phase transition, (ii) TMI is observed to increase with H, (iii) FCC magnetization relaxes with time while ZFC does not relax, (iv) low-T magnetic behavior is affected by the sign inequality of the CHUF protocol (discussed later) and (v) M(H) virgin curve (H: 0 → Hmax) lies, completely or partially, outside the envelope (Hmax → 0 → −Hmax → 0 → Hmax).22–24 

Figures 3(a)3(f) show M(T) measured in ZFC, FCC and FCW processes. ZFC-M(T) in 200 Oe shows two peaks around 46.5 and 32.8 K respectively, denoted as TN (Néel temperature) and Tt, which are in agreement with the literature.3 As the field strength is increased, M(Tt) increases significantly and the peak becomes more pronounced and sharper while the peak at TN smears out. However, FCC-M(T) does not show a peak at Tt in 200 Oe indicating that the low-T phase is more susceptible to magnetic field. This also points out that the ZFC state is not an equilibrium state of the system. Eventually in higher fields, TN is suppressed and ferromagnetic state emerges. The enlarged view of FCC and FCW from 20–40 K is shown in the insets of Figs. 3(a)3(f). It is observed that the FCC and FCW curves exhibit a narrow thermal hysteresis in the temperature range T ∈ [15, 40 K]. The measurements were repeated to confirm the narrow thermal hysteresis betweeen FCC and FCW curves. Eventually, the thermal hysteresis ceases out in high magnetic fields.

FIG. 3.

(a)–(f) ZFC, FCC and FCW M(T) in a few representative fields. TN gets smeared out while ZFC-M(Tt) is enhanced as H is increased. FCC and FCW curves saturate below 15 K. Insets: Enlarged view of FCC and FCW. Above 15 K and below 40 K, a narrow but distinct thermal hysteresis of FCC and FCW is noticed up to about 10 kOe, above which it vanishes.

FIG. 3.

(a)–(f) ZFC, FCC and FCW M(T) in a few representative fields. TN gets smeared out while ZFC-M(Tt) is enhanced as H is increased. FCC and FCW curves saturate below 15 K. Insets: Enlarged view of FCC and FCW. Above 15 K and below 40 K, a narrow but distinct thermal hysteresis of FCC and FCW is noticed up to about 10 kOe, above which it vanishes.

Close modal

Figure 4(a) shows magnetization, measured using CHUF protocol. Every time, the sample is cooled in the presence of 25 kOe (Hcool > Hcr) from 300 to 2 K and MCHUF(T) is measured in different magnetic fields as shown in the left panel of Fig. 4(a). Field-induced irreversible behaviour of FM state is evident from MCHUF > MZFC in fields of H < Hcr while the magnetization values are comparable when H > Hcr. MCHUF(T) exhibits two recognizable transitions [i.e., two peaks in dMCHUF/dT respectively at 26 and 52 K shown in Fig. 4(a)-right panel] for negative CHUF (Hmeas < Hcool) while one transition (i.e., one peak in dMCHUF/dT) for positive sign (Hmeas > Hcool). This behaviour is in resemblance of MG state in H < Hcr while RSG state in H > Hcr.

FIG. 4.

(a) Left-panel: MCHUF(T) in different labeled measuring fields (Hmeas) after cooling the system in 25 kOe (Hcool). For negative CHUF sign, two transitions while one transition for positive sign are noticed in terms of peaks represented by dMCHUF/dT in the right panel. (b) TMI-H phase diagram. TMI increases up to Hcr and decreases thereafter (see text for explanation).

FIG. 4.

(a) Left-panel: MCHUF(T) in different labeled measuring fields (Hmeas) after cooling the system in 25 kOe (Hcool). For negative CHUF sign, two transitions while one transition for positive sign are noticed in terms of peaks represented by dMCHUF/dT in the right panel. (b) TMI-H phase diagram. TMI increases up to Hcr and decreases thereafter (see text for explanation).

Close modal

An investigation of magnetic relaxation and dynamic behavior of ac-susceptibility by Maji et al.4,25 suggests RSG state. Nonetheless, the thermal hysteresis between FCC and FCW, initial increase of TMI with H up to a certain field [Fig. 4(b)] and non-overlapping of ZFC and FCC curves hint the presence of MG with ZFC state being the non-equilibrium state. Furthermore, the virgin curve is observed to lie partly outside the envelope at 2.2 K.3 However, the separation between virgin curve and envelope is small compared to some of the typical phase coexistence compounds; doped-CeFe2.26,27

Summarizing, the magnetic properties of Nd5Ge3 have been studied using magnetization, neutron diffraction and muon spin relaxation (μSR) measurements. Nd5Ge3 undergoes an antiferromagnetic transition at TN ∼ 54 K, followed by a low temperature glassy state. Zero-field neutron diffraction studies reveal short-range ferromagnetic correlations. Besides, a field-induced reentrant spin glass state from a magnetic glass state is reported before the system transforms to a ferromagnetic state.

S.S.S., Y.V. and K.G.S. acknowledge STFC for the Newton-Bhabha Fund to carry out neutron diffraction (ND) experiments (RB1610200) and JNCASR-Bangalore and DST-India for the financial support to perform muon spin relaxation measurements through Indian Access (RB1768039). S.S.S. thanks Akhilesh Kr. Patel for the help in ND experiments and Science and Engineering Research Board, India for Core Research Grant (CRG/2022/007993). This work was supported by the NSF, Launching Early-Career Academic Pathways in the Mathematical and Physical Sciences (LEAPS-MPS) program under Award No. DMR-2213412.

The authors have no conflicts to disclose.

S. Shanmukharao Samatham: Conceptualization (lead); Data curation (equal); Formal analysis (equal); Funding acquisition (lead); Investigation (lead); Methodology (equal); Writing – original draft (lead); Writing – review & editing (equal). Venkateswara Yenugonda: Data curation (equal); Formal analysis (equal). Gowrinaidu Babbadi: Data curation (supporting); Investigation (supporting). Muralikrishna Patwari: Writing – original draft (supporting). Arjun K. Pathak: Funding acquisition (lead); Writing – review & editing (supporting). P. Manuel: Data curation (equal); Formal analysis (equal); Writing – review & editing (supporting). D. Khalyavin: Data curation (equal); Formal analysis (equal); Writing – review & editing (supporting). Stephen Cottrell: Data curation (equal); Formal analysis (equal); Writing – review & editing (supporting). A. D. Hillier: Data curation (equal); Writing – review & editing (supporting). K. G. Suresh: Conceptualization (equal); Supervision (equal); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.

1.
P.
Schobinger-Papamontellos
and
K.
Buschow
,
Journal of Magnetism and Magnetic Materials
49
,
349
356
(
1985
).
2.
T.
Tsutaoka
,
A.
Tanaka
,
Y.
Narumi
,
M.
Iwaki
, and
K.
Kindo
,
Physica B: Condensed Matter
405
,
180
185
(
2010
).
3.
B.
Maji
,
K. G.
Suresh
, and
A. K.
Nigam
,
EPL (Europhysics Letters)
91
,
37007
(
2010
).
4.
B.
Maji
,
K. G.
Suresh
, and
A. K.
Nigam
,
J. Phys.: Condens. Matter
23
,
506002
(
2011
).
5.
A. P.
Vokhmyanin
,
B.
Medzhi
,
A. N.
Pirogov
, and
A. E.
Teplykh
,
Physics of the Solid State
56
,
34
(
2014
).
6.
J.
Rodriguez-Carvajal
,
Physica B: Condensed Matter
192
,
55
69
(
1993
).
7.
K. H. J.
Buschow
and
J. F.
Fast
,
Physica Status Solidi (b)
21
,
593
600
(
1967
).
8.
I. A.
Campbell
,
A.
Amato
,
F. N.
Gygax
,
D.
Herlach
,
A.
Schenck
,
R.
Cywinski
, and
S. H.
Kilcoyne
,
Phys. Rev. Lett.
72
,
1291
(
1994
).
9.
R. M.
Pickup
,
R.
Cywinski
, and
C.
Pappas
,
Physica B: Condensed Matter
397
,
99
(
2007
).
10.
M. T. F.
Telling
,
J.
Dann
,
R.
Cywinski
,
J.
Bogner
,
M.
Reissner
, and
W.
Steiner
,
Physica B: Condensed Matter
289–290
,
213
(
2000
).
11.
R.
Cywinski
,
S. H.
Kilcoyne
, and
C. A.
Scott
,
J. Phys.: Condens. Matter
3
,
6473
(
1991
).
12.
M. T. F.
Telling
,
K. S.
Knight
,
F. L.
Pratt
,
A. J.
Church
,
P. P.
Deen
,
K. J.
Ellis
,
I.
Watanabe
, and
R.
Cywinski
,
Phys. Rev. B
85
,
184416
(
2012
).
13.
S. N.
Kaul
,
J. Magn. Magn. Mater.
53
,
5
(
1985
).
14.
A.
Keren
,
P.
Mendels
,
I. A.
Campbell
, and
J.
Lord
,
Phys. Rev. Lett.
77
,
1386
(
1996
).
15.
R.
Renzi
and
S.
Fanesi
,
Physica B: Condensed Matter
289–290
,
209
(
2000
).
16.
C.
Shravani
, “
Microscopic coexistence of antiferromagnetic and spin glass states in disordered perovskites
,” Ph.D. thesis,
ETH-Zürich
,
2015
.
17.
H.
Klauss
,
M.
Hillberg
,
W. W. M. A. C.
de Melo
,
F.
Litterst
,
M.
Fricke
,
J.
Hesse
, and
E.
Schreier
,
104
,
319
(
1997
).
18.
M.
Gabay
and
G.
Toulouse
,
Phys. Rev. Lett.
47
,
201
204
(
1981
).
19.
S.
Niidera
and
F.
Matsubara
,
Phys. Rev. B
75
,
144413
(
2007
).
20.
K.
Binder
and
A. P.
Young
,
Rev. Mod. Phys.
58
,
801
976
(
1986
).
21.
A.
Banerjee
,
A. K.
Pramanik
,
K.
Kumar
, and
P.
Chaddah
,
J. Phys.: Condens. Matter
18
,
L605
(
2006
).
22.
M. K.
Chattopadhyay
,
S. B.
Roy
, and
P.
Chaddah
,
Phys. Rev. B
72
,
180401
(
2005
).
23.
S. B.
Roy
,
M. K.
Chattopadhyay
,
P.
Chaddah
,
J. D.
Moore
,
G. K.
Perkins
,
L. F.
Cohen
,
K. A.
Gschneidner
, and
V. K.
Pecharsky
,
Phys. Rev. B
74
,
012403
(
2006
).
24.
V. K.
Sharma
,
M. K.
Chattopadhyay
, and
S. B.
Roy
,
Phys. Rev. B
76
,
140401
(
2007
).
25.
B.
Maji
and
K.
Suresh
,
Journal of Alloys and Compounds
605
,
29
33
(
2014
).
26.
S.
Roy
,
P.
Chaddah
,
V.
Pecharsky
, and
K.
Gschneidner
,
Acta Materialia
56
,
5895
5906
(
2008
).
27.
A.
Haldar
,
K. G.
Suresh
, and
A. K.
Nigam
,
Phys. Rev. B
78
,
144429
(
2008
).