Since the discovery of spin glasses in dilute magnetic systems, their study has been largely focused on understanding randomness and defects as the driving mechanism. The same paradigm has also been applied to explain glassy states found in dense frustrated systems. Recently, however, it has been theoretically suggested that different mechanisms, such as quantum fluctuations and topological features, may induce glassy states in defect-free spin systems, far from the conventional dilute limit. Here we report experimental evidence for existence of a glassy state, which we call a spin jam, in the vicinity of the clean limit of a frustrated magnet, which is insensitive to a low concentration of defects. We have studied the effect of impurities on SrCr
9pGa
12-9pO
19 [SCGO(
p)], a highly frustrated magnet, in which the magnetic Cr
3+ (
s = 3/2) ions form a quasi-2D triangular system of bipyramids. Our experimental data show that as the nonmagnetic Ga
3+ impurity concentration is changed, there are two distinct phases of glassiness: an exotic glassy state, which we call a spin jam, for the high magnetic concentration region (
p > 0.8) and a cluster spin glass for lower magnetic concentration (
p < 0.8). This observation indicates that a spin jam is a unique vantage point from which the class of glassy states of dense frustrated magnets can be understood.Understanding glassy states found in dense frustrated magnets has been an intellectual challenge since peculiar low-temperature glassy behaviors were observed experimentally in the quasi-2D SrCr
9pGa
12-9pO
19 (SCGO) (
1–
3) and in the 3D pyrochlore Y
2Mo
2O
7 (
4). Immediately following, theoretical investigations (
5–
9) were performed to see if an intrinsic spin freezing transition is possible in a defect-free situation, aided by quantum fluctuations, as in the order-by-fluctuations phenomenon (
10,
11). Quantum fluctuations at
T = 0 were shown to select a long-range ordered state in the 2D kagome isotropic antiferromagnet (AFM) (
5,
6), later expanded to the isotropic pyroclore and SCGO (
9). Anisotropic interactions were also considered as a possible origin of the glassy kagome AFM (
7). For an XY pyrochlore AFM, thermal fluctuations were found to induce a conventional Neel order (
8). Experimental works were also performed to investigate if the glassy states are extrinsic due to site defects or random couplings or intrinsic to the magnetic lattice (
12,
13). The consensus is that the low-temperature spin freezing transitions in SCGO(
p) near the clean limit (
p ≈ 1) is not driven by site defects (
13).The nature of the frozen state in SCGO has been investigated by numerous experimental techniques, including bulk susceptibility (
1–
3), specific heat (
2,
14), muon spin relaxation (μSR) (
15), nuclear magnetic resonance (NMR) (
13,
16), and elastic and inelastic neutron scattering (
17). Observed are spin glassy behaviors, such as field-cooled and zero-field-cooled (FC/ZFC) hysteresis in bulk susceptibility (
3), as well as non-spin-glassy behaviors, such as a quadratic behavior of specific heat at low
T,
Cv ∝
T2 (
14), linear dependence of the imaginary part of the dynamic susceptibility at low energies,
χ″(
ω) ∝
ω (
17), and a broad but prominent momentum dependence of the elastic neutron scattering intensity (
17). The interpretation of the frozen state below
Tf is still controversial. One possibility suggested was a spin liquid with unconfined spinons or resonating valence bond state, based on NMR and μSR studies (
15,
16). Many-body singlet excitations were also suggested to be responsible for the
Cv ∝
T2 behavior (
14).Recently, some of us presented an alternative scenario involving a spin jam state by considering the effects of quantum fluctuations in the disorder-free quasi-2D ideal SCGO lattice with a simple nearest neighbor (NN) spin interaction Hamiltonian ? =
J∑
NNSi ?
Sj (
18,
19). The spin jam framework provided a qualitatively coherent understanding of all of the low-temperature behaviors such as that a complex energy landscape is responsible for the frozen state without long-range order (
18), and Halperin−Saslow (HS)-like modes for the
Cv ∝
T2 and
χ″(
ω) ∝
ω behaviors (
5,
18). In this system, which we refer to as the ideal SCGO model (iSCGO), semiclassical magnetic moments (or spins) are arranged in a triangular network of bipyramids and interact uniformly with their NN (
18,
19). The microscopic mechanism for the spin jam state is purely quantum mechanical. The system has a continuous and flat manifold of ground states at the mean field level, including locally collinear, coplanar, and noncoplanar spin arrangements. Quantum fluctuations lift the classical ground state degeneracy (order by fluctuations), resulting in a complex rugged energy landscape that has a plethora of local minima consisting of the locally collinear states separated from each other by potential barriers (
18). Although the work of ref.
18 dealt with a similar phase space constriction by quantum fluctuations as the aforementioned other theoretical works did, we would like to stress here the difference between the two: Whereas the other works mainly focused on the selection of the long-range-ordered (LRO) energetic ground state, the work of ref.
18 showed that the short-range-ordered (SRO) states that exist at higher energies are long-lived, dominate entropically over the LRO states, and govern the low-
T physics.The introduction of nonmagnetic impurities into a topological spin jam state breaks some of the constraints in the system, and possibly allows local transitions between minima, with a time scale dependent on the density of impurities. At a sufficiently high vacancy concentration, the system exits the spin jam state and becomes either paramagnetic or an ordinary spin glass at lower temperatures. Here we try to identify and explore the spin jam regime in an experimentally accessible system. The three most important signatures we seek for the existence of a spin jam state, different from conventional spin glass states, are (
i) a linear dependence of the imaginary part of the dynamic susceptibility at low energies,
χ″(
ω) ∝
ω, (
ii) intrinsic short range static spin correlations, and (
iii) insensitivity of its physics to nonmagnetic doping near the clean limit. In the rest of the paper, we provide experimental demonstration of these properties.Experimentally, there are, so far, two materials, SrCr
9pGa
12-9pO
19 [SCGO(
p)] (
1–
3,
13–
17,
20) and qs-ferrites like Ba
2Sn
2ZnGa
3Cr
7O
22 (BSZGCO) (
21), in which the magnetic Cr
3+ (3d
3) ion surrounded by six oxygen octahedrally, form distorted quasi-2D triangular lattice of bipyramids (
20,
21) as shown in , and thus may realize a spin jam state. We would like to emphasize that these systems are very good insulators (resistivity
ρ > ?10
13?Ω ? cm at 300 K) and the Cr
3+
ion has no orbital degree of freedom. Furthermore, the neighboring Cr ions share one edge of oxygen octahedral, and thus the direct overlap of the
orbitals of the neighboring Cr
3+ ions make the AFM NN Heisenberg exchange interactions dominant and further neighbor interactions negligible (
22,
23), as found in Cr
2O
3 (
24) and ZnCr
2O
4 (
25).
Open in a separate window(
A) In SrCr
9pGa
12-9pO
19 [SCGO(
p)], the magnetic Cr
3+ (3d
3,
s = 3/2) ions form the kagome−triangular−kagome trilayer (
Top). The blue and red spheres represent kagome and triangular sites, respectively. When viewed from the top of the layers, they form the triangular network of bipyramids (
Bottom). (
B) The
p−
T phase diagram of SCGO(
p) constructed by bulk susceptibility and elastic neutron scattering measurements on powder samples with various
p values. The freezing temperatures,
Tf, marked with blue square and black circle symbols are obtained by bulk susceptibility and elastic neutron scattering measurements, respectively. Note that the values of
Tf are much lower than the Curie–Weiss temperatures (see ). Filled blue squares represent the data obtained from samples whose crystal structural parameters including the Cr/Ga concentrations were refined by neutron diffraction measurements (see and −), and open blue squares represent samples with nominal
p values. For nominal
p = 0.2, no freezing was observed down to 50 mK (see ).
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