---
title: 'LaCrGe3: Fragile Itinerant Ferromagnetism'
url: https://www.emergentmind.com/topics/lacrge3
type: topic
---

# LaCrGe3: Fragile Itinerant Ferromagnetism

Searching arXiv for LaCrGe3-related papers to ground the article in the current literature.
LaCrGe\(_3\) is a Cr-based intermetallic compound of composition \(1{:}1{:}3\) that crystallizes in the hexagonal BaNiO\(_3\)-type structure with space group \(P6_3/mmc\). It is a metallic ferromagnet whose ordered magnetism is carried by Cr \(3d\) states and is widely regarded as an itinerant, pressure-sensitive, or “fragile” ferromagnet. Although it first entered this literature partly as the non-\(4f\) reference compound for CeCrGe\(_3\), later work established LaCrGe\(_3\) as a benchmark system for avoided ferromagnetic quantum criticality, tricritical-wing phenomenology, and unusually complex ambient-pressure ferromagnetism [1402.1609, 1611.01212].

## 1. Crystal chemistry and structural framework

LaCrGe\(_3\) is consistently reported to adopt a hexagonal perovskite-type or BaNiO\(_3\)-type structure with space group \(P6_3/mmc\) [1402.1609]. In neutron refinements for the La end member of Ce\(_{1-x}\)La\(_x\)CrGe\(_3\), the room-temperature lattice parameters are \(a = 6.176(1)\) \AA\ and \(c = 5.745(1)\) \AA, while at 5 K they are \(a = 6.169(1)\) \AA\ and \(c = 5.752(1)\) \AA; the same work refines Ge on the \(6h\) site with \(x_{\mathrm{Ge}} = 0.1930(1)\), \(y_{\mathrm{Ge}} = 0.3860(2)\) at 295 K and \(x_{\mathrm{Ge}} = 0.1932(1)\), \(y_{\mathrm{Ge}} = 0.3865(1)\) at 5 K [2109.07366]. Earlier polycrystalline work reported \(a = 6.198\) \AA, \(c = 5.765\) \AA, and \(V_{\rm cell} = 191.79\) \AA\(^3\) [1402.1609].

The structural motif emphasized across later studies is a chain-like arrangement of Cr-centered Ge polyhedra along the crystallographic \(c\) axis. First-principles work describes the Cr-centered Ge octahedra as forming a one-dimensional line along \(c\), with a Cr–Cr distance of \(2.79\) \AA\ along \(c\) and \(6.078\) \AA\ in the basal plane in the relaxed LDA structure [1802.08398]. A 2025 Hall-effect study similarly described quasi-1D Cr chains with a nearest-neighbor Cr–Cr distance along \(c\) of about \(2.88\) \AA\ and a much larger minimum Cr–Cr distance in the basal plane of about \(6.2\) \AA\ [2508.21508]. This pronounced structural anisotropy is central to the magnetic easy-axis behavior and to pressure sensitivity.

Single crystals are rod-like, with the crystallographic \(c\) axis running along the rod direction [2303.02062]. That crystallographic fact is operationally important because many later measurements—magnetization, Hall effect, NMR, and pressure studies—apply field along \(c\), the magnetic easy axis.

## 2. Ambient-pressure ferromagnetism

At ambient pressure, LaCrGe\(_3\) is ferromagnetic with a transition temperature in the mid-80 to mid-90 K range, depending on probe, sample form, and criterion. Polycrystalline measurements reported \(T_c^{({\rm mag})}=88\) K from susceptibility and \(T_c^{(\rho-T)}=88\) K from resistivity, with a specific-heat anomaly near \(\sim 84\) K [1402.1609]. Single-crystal measurements gave \(T_C^{\rm mag}=88\) K, \(T_C^\rho=84\) K, and \(T_C^{C_p}=85\) K [1305.7258]. Neutron and susceptibility work on the La end member of Ce\(_{1-x}\)La\(_x\)CrGe\(_3\) reported \(T_C^{(\mathrm{DC})}=91.4(1)\) K, \(T_C^{(\mathrm{AC})}=96.8(8)\) K, and \(T_C^{(\mathrm{BT7})}=96(1)\) K [2109.07366]. More recent single-crystal magnetometry summarized the compound as having \(T_C \sim 86\) K [2303.02062].

The ordered state is strongly uniaxial. The \(c\) axis is the easy axis; for \(H \parallel c\), magnetization saturates rapidly, whereas for \(H \parallel ab\) the response is much smaller and nearly linear over a wide field range [1305.7258, 2303.02062]. Prior work summarized in the single-crystal coercivity study quoted a saturated moment of about \(\mu_S \approx 1.2~\mu_B/\mathrm{Cr}\) and an anisotropy field of roughly \(40\)–\(50~\mathrm{kOe}\) [2303.02062]. The 2013 single-crystal study reported \(\mu_S \approx 1.25~\mu_B/\mathrm{Cr}\) for \(H \parallel c\) [1305.7258], while neutron diffraction later refined the ordered Cr moment as \(1.40(5)~\mu_B\) at 5 K with moments aligned along \(c\) [2109.07366].

Magnetic diffraction places the ferromagnetic intensity on nuclear Bragg positions, consistent with a ferromagnetic propagation vector \(\mathbf{k}=(0,0,0)\), although that notation is not written explicitly in the neutron paper. The La-rich compositions, including LaCrGe\(_3\), were refined in magnetic symmetry \(P6_3/mm'c'\) with \(\mu_{\rm Cr} \parallel c\) [2109.07366]. This distinguishes LaCrGe\(_3\) sharply from CeCrGe\(_3\), where the Cr moments were argued to order in the \(ab\) plane in the same series study [2109.07366].

## 3. Metallic transport and evidence for itinerant Cr magnetism

Multiple experimental lines point away from a robust local-moment Cr picture and toward itinerant ferromagnetism. In the single-crystal V-substitution study, the high-temperature susceptibility was analyzed with
\[
\frac{1}{\chi} = \frac{T-\theta_c}{C},
\qquad
\chi_{\rm ave} = \frac{1}{3}\left(\chi_c + 2\chi_{ab}\right),
\]
yielding for LaCrGe\(_3\) an effective moment \(\mu_{\rm eff}=2.5~\mu_B/\mathrm{Cr}\) and \(\theta_c=91.7\) K [1305.7258]. Polycrystalline work using the modified Curie–Weiss form
\[
\chi(T)=\chi_0+\frac{C}{T-\theta_P}
\]
reported \(\mu_{\rm eff}=2.66~\mu_B\) per formula unit and \(\theta_P=87\) K [1402.1609]. A later DC-susceptibility study in the Ce/La series obtained \(\theta_{CW}=98.6(2)\) K and \(\mu_{\rm eff}=2.46(2)~\mu_B\) for LaCrGe\(_3\) [2109.07366]. In all cases the effective moment is reduced relative to free-ion Cr\(^{3+}\), and the positive Weiss scale indicates dominant ferromagnetic interactions.

Transport and thermodynamics are metallic and weakly correlated by heavy-fermion standards. Polycrystalline LaCrGe\(_3\) shows “typical metallic behavior” over 2–300 K, with \(\rho_0 \sim 65~\mu\Omega\,{\rm cm}\) and \({\rm RRR}\sim 4.3\) [1402.1609]. Single crystals measured with current along \(c\) gave \(\rho_0 = 36~\mu\Omega\,{\rm cm}\) and a clear resistive anomaly at about \(84\) K [1305.7258]. Low-temperature specific heat is described by
\[
C(T)=\gamma T+\beta T^3,
\]
with \(\gamma = 2.89~{\rm mJ/mol\,K^2}\) and \(\Theta_D = 253\) K in the polycrystalline study [1402.1609]. In the single-crystal substitution study, the magnetic entropy at \(T_C\) was estimated as
\[
S_M(T_C) \approx 0.56\, R\ln 2,
\]
which was taken as further evidence against a simple local-moment description [1305.7258].

The same work also used the Rhodes–Wohlfarth ratio
\[
\mathrm{RWR} = \frac{\mu_c}{\mu_S},
\qquad
\mu_c(\mu_c+1)=\mu_{\rm eff}^2,
\]
finding \(\mathrm{RWR}\simeq 1.4\) for LaCrGe\(_3\), with larger values upon V substitution [1305.7258]. The discussion explicitly invoked the Stoner criterion
\[
U D(\varepsilon_F) \ge 1,
\]
as a useful frame for the substitution-induced weakening of ferromagnetism [1305.7258].

Microscopic probes sharpen this itinerant picture. \(^{139}\)La NMR at ambient pressure found nearly isotropic Knight shift and \(1/T_1\) in the paramagnetic state, with Korringa ratios \(\alpha_\parallel\) and \(\alpha_\perp\) falling from about \(0.07\) at room temperature to below about \(0.008\) near \(120\) K, strongly indicating ferromagnetic correlations [1906.00249]. Within SCR theory, the observed scaling favored three-dimensional ferromagnetic fluctuations:
\[
\frac{1}{T_1 T K_s} \approx {\rm const.},
\]
rather than the 2D form involving \(K_s^{3/2}\), and the extracted spin-fluctuation parameters were \(T_0 = 89\) K and \(75\) K, and \(T_A = 998\) K and \(793\) K for in-plane and out-of-plane fluctuations, respectively [1906.00249]. ESR on polycrystalline LaCrGe\(_3\) at X band found a symmetric Lorentzian line at \(290\) K with \(g = 2.10 \pm 0.02\) and \(\mu_0\Delta H = 55 \pm 2\) mT, which was interpreted as a resonance of narrow Cr \(d\)-bands rather than a conventional local-ion Cr\(^{3+}\) signal [2109.09341].

## 4. Complexity inside the ferromagnetic state

Although LaCrGe\(_3\) is often introduced as a simple itinerant ferromagnet, several ambient-pressure studies indicate that the ordered state is more structured. Pressure-transport work identified a lower-temperature anomaly at \(T_x \approx 71\) K already at ambient pressure, visible as a broad maximum in \(d\rho/dT\), and labeled the higher-temperature ferromagnetic region FM1 and the lower-temperature one FM2 by analogy with UGe\(_2\) [1611.01212]. That interpretation was inferential in the original transport work, but later Hall measurements reported direct boundary signatures near \(T_x \approx 70\)–75 K and explicitly described two ferromagnetic phases, FM\(_1\) and FM\(_2\) [2508.21508].

The single-crystal coercivity study showed that for \(H \parallel c\) the low-temperature loops can become nearly rectangular once the sample is driven above roughly \(1.5\)–\(2~\mathrm{kOe}\), with the coercive field saturating near \(\sim 0.5~\mathrm{kOe}\) at 5 K for maximum applied fields of \(5~\mathrm{kOe}\) and above [2303.02062]. The sample remains in a fully saturated magnetization state at zero field and reverses sharply and completely only when a finite reverse field is reached. The temperature dependence of \(H_c\) is nonmonotonic: large below \(\sim 40\) K, essentially zero through roughly the 40–55/60 K region, reappearing with a local maximum around \(75\) K, and vanishing again at \(T_C \sim 86\) K [2303.02062]. The same work identified an AC-susceptibility feature near \(55\) K and argued that the ferromagnetic state likely changes character near \(50\)–\(55\) K, while stopping short of claiming a definitive thermodynamic phase transition [2303.02062].

Hall transport adds a complementary perspective. For \(B \parallel z\), continuous \(\rho_{yx}(T)\) at fixed low fields shows a sharp onset at \(T_\mathrm{C}\approx 85\) K and a dip-like anomaly near \(T_\mathrm{x}\), while the remanent Hall resistivity and coercive field both peak around \(73\) K [2508.21508]. The ordinary Hall coefficient \(R_0\) for \(B\parallel y\) shows a minimum near the same temperature. A plausible implication is that the FM\(_1\)–FM\(_2\) boundary involves a change in electronic structure, and the Hall paper explicitly suggested Fermi-surface reconstruction [2508.21508]. It also reported a large anomalous Hall conductivity \(\sigma_{yx}^A = 1160\ \Omega^{-1}\mathrm{cm}^{-1}\) at 2 K for \(B\parallel z\), versus \(\sigma_{xz}^A = 289\ \Omega^{-1}\mathrm{cm}^{-1}\) for \(B\parallel y\), with low-temperature behavior interpreted as dominated by intrinsic effects [2508.21508].

Not all probes resolve sub-\(T_C\) complexity in the same way. Neutron diffraction on LaCrGe\(_3\) found a single well-defined second-order ferromagnetic transition and no evidence for spin reorientation or AFM/FM coexistence near the small bump around 80 K in bulk magnetization; that work attributed the lower-temperature anomalies primarily to magnetic domains and domain-wall pinning [2109.07366]. The resulting picture is therefore not that a second thermodynamic phase boundary has been universally established by all probes, but that domain physics, hysteresis, and transport anomalies reveal a nontrivial internal structure of the ferromagnetic state.

The same Hall study also identified “goniopolarity” in the paramagnetic phase: at 150 K and 200 K, \(\rho_{yx}(B_z)\) has a positive slope while \(\rho_{xz}(B_y)\) has a negative slope, and the Seebeck coefficients satisfy \(S_{xx}>0\) above 108 K and \(S_{zz}<0\) below 257 K, producing opposite transport polarities along different directions in the interval \(108\ \mathrm{K} < T < 257\ \mathrm{K}\) [2508.21508]. The authors attributed this to anisotropic Fermi-surface geometry.

## 5. Fragile magnetism, substitution, and pressure-tuned phase behavior

LaCrGe\(_3\) is one of the standard transition-metal examples of “fragile magnetism,” a term used for systems in which tuning weakens not only \(T_C\) but the moment scales themselves [1601.04931]. In the single-crystal series \(\mathrm{LaV_xCr_{1-x}Ge_3}\), accessible compositions were \(x_{\rm WDS}=0, 0.04, 0.09, 0.16, 0.19, 0.21, 1.00\), with ferromagnetism persisting up to \(x=0.21\) and the transition temperature falling monotonically from \(88\) K to \(36\) K [1305.7258]. Over the same range, the saturated moment for \(H\parallel c\) decreased from \(1.25\) to \(0.30~\mu_B/\mathrm{Cr}\), the effective moment from \(2.5\) to \(1.9~\mu_B/\mathrm{Cr}\), and \(\theta_c\) from \(91.7\) to \(6.7\) K [1305.7258]. That collapse of both ordered and paramagnetic moment scales is precisely the behavior later overviewed as fragile, rather than robust, magnetism [1601.04931].

Pressure suppresses ferromagnetism even more efficiently. The 2016 overview summarized that \(T_C\) “drops precipitously” and goes to zero near \(p \sim 2\) GPa, while a “probably antiferromagnetic phase transition” appears near \(T \sim 50\) K and \(p \sim 1.6\) GPa and is itself suppressed near \(6\) GPa [1601.04931]. Subsequent single-crystal resistivity work refined this into a detailed \(T\)-\(p\)-\(H\) phase diagram: at zero field, \(T_C = 86\) K at ambient pressure, a modulated phase denoted \(\mathrm{AFM}_Q\) appears near a Lifshitz point around \(1.3\) GPa, and zero-field ferromagnetism disappears near \(p_c \approx 2.1\) GPa [1611.01212]. The same study located a tricritical point near
\[
p_{\mathrm{TCP}} \approx 1.75~\mathrm{GPa}, \qquad
T_{\mathrm{TCP}} \approx 40~\mathrm{K},
\]
and established a double-wing structure in field, with first-order \(\mathrm{AFM}_Q \rightarrow \mathrm{FM1}\) and \(\mathrm{FM1} \rightarrow \mathrm{FM2}\) transitions [1611.01212]. At \(p=2.39\) GPa, the wing critical points were around \((13.5~\mathrm{K},\,5.1~\mathrm{T})\) and \((12~\mathrm{K},\,7.7~\mathrm{T})\), while the quantum wing critical points near \(0\) K, \(p \sim 3\) GPa, and \(H \sim 30\) T were explicitly described as extrapolated and approximate [1611.01212].

Under pressure, local probes show that the magnetic instability is subtler than a simple collapse of the Cr moment. \(^{139}\)La NMR up to \(2.64\) GPa found that the ordered-state internal field remains \(|B_{\rm int}| \sim 4\) T and changes by less than \(5\%\), implying robust local Cr \(3d\) moments, even though the ordering or crossover scale inferred from \(1/|K|\) is pushed down to \(63\pm3\) K at \(1.65\) GPa, \(53\pm5\) K at \(2.23\) GPa, and \(45\pm5\) K at \(2.64\) GPa in a field of about \(7.2\) T [2105.03479]. The same pressure NMR work found that the paramagnetic-state fluctuations remain three-dimensional ferromagnetic throughout the measured pressure range [2105.03479]. This suggests that pressure destabilizes long-range zero-field ferromagnetism without immediately removing the underlying ferromagnetic character of the Cr subsystem.

First-principles calculations provide a concrete microscopic mechanism for this fragility. DFT-LDA found the ferromagnetic state lower in energy than the nonmagnetic state by \(\Delta E_{\mathrm{FM-NM}}=-34.9~\text{meV/f.u.}\), with a calculated Cr moment of \(1.17~\mu_B\) and a total moment of \(1.09~\mu_B/\text{f.u.}\) [1802.08398]. The decisive electronic-structure feature is a large Cr-derived DOS peak only about \(\sim -0.15\) eV below \(E_F\) at ambient pressure. Compression reduces the Cr–Cr spacing along \(c\), pushes this peak toward \(E_F\), and destabilizes ferromagnetism when the peak crosses the Fermi level [1802.08398]. In the simplified FM-versus-NM comparison, the calculated suppression occurs near \(7\) GPa, while experiment gives about \(2.2\) GPa; the paper attributes that discrepancy to ordinary DFT pressure errors and, more importantly, to the neglect of intermediate AFM or modulated states [1802.08398]. The same study inferred an empirical critical spacing \(d_{\mathrm{Cr-Cr,crit}}^{(c)} \approx 2.72\) \AA, close to the ambient-pressure value, which rationalizes why hydrostatic pressure is so effective in LaCrGe\(_3\) [1802.08398].

## 6. Comparative role and broader significance

LaCrGe\(_3\) occupies a distinctive position in several neighboring research programs. In the CeCrGe\(_3\)/LaCrGe\(_3\) comparison, LaCrGe\(_3\) is the non-\(4f\) reference that isolates ordinary Cr-based metallic ferromagnetism from Ce-\(4f\) Kondo and heavy-fermion physics. The 2014 comparative study used LaCrGe\(_3\) precisely as that baseline: unlike CeCrGe\(_3\), it shows no \(-\ln T\) Kondo-like resistivity, no enhanced Sommerfeld coefficient, and no heavy-fermion thermopower signatures [1402.1609]. In the Ce\(_{1-x}\)La\(_x\)CrGe\(_3\) series, LaCrGe\(_3\) is also the high-volume end member with the highest \(T_C\) and the largest ordered Cr moment, while CeCrGe\(_3\) is the contrasting endpoint with Cr moments in the \(ab\) plane rather than along \(c\) [2109.07366].

In the broader phenomenology of itinerant ferromagnets, LaCrGe\(_3\) is one of the few systems in which both canonical tricritical-wing physics and a pressure-induced modulated magnetic phase appear in the same material [1611.01212]. Review work accordingly uses it as a model case for fragile transition-metal magnetism, contrasting it with LaCrSb\(_3\), whose ferromagnetism is described as non-fragile under comparable tuning [1601.04931]. NMR further places LaCrGe\(_3\) within the class of three-dimensional itinerant ferromagnets that follow the generalized Rhodes–Wohlfarth relation, while still showing a relatively high degree of real-space localization compared with several better-known itinerant ferromagnets [1906.00249].

A concise contemporary picture is therefore possible. LaCrGe\(_3\) is a metallic, strongly uniaxial Cr ferromagnet in hexagonal \(P6_3/mmc\), with ordered moments along \(c\), \(T_C\) in the upper-80 to mid-90 K range depending on probe, and a modest ordered moment of about \(1.2\)–\(1.4~\mu_B/\mathrm{Cr}\). Its reduced moment scales, metallic thermodynamics, SCR-consistent NMR response, and substitution trends establish itinerant Cr magnetism. Its low-pressure ordered state is magnetically richer than a minimal single-phase ferromagnet label would imply, as shown by nonmonotonic coercivity, square-loop behavior, and FM\(_1\)/FM\(_2\)-like transport anomalies. Under pressure, it becomes a canonical example of avoided ferromagnetic quantum criticality, with both tricritical wings and a competing modulated magnetic phase.

Source: https://www.emergentmind.com/topics/lacrge3