Magnetic fluctuations in the itinerant ferromagnet ${\mathrm{LaCrGe}}_3$ studied by ${}^{139}\mathrm{La}$ NMR

${\mathrm{LaCrGe}}_3$ is an itinerant ferromagnet with a Curie temperature of $T_{\mathrm{C}}=85$ K and exhibits an avoided ferromagnetic quantum critical point under pressure through a modulated antiferromagnetic phase as well as tricritical wing structure in its temperature-pressure-magnetic field ($T\text{−}p\text{−}H$) phase diagram. In order to understand the static and dynamical magnetic properties of ${\mathrm{LaCrGe}}_3$, we carried out ${}^{139}\mathrm{La}$ nuclear magnetic resonance (NMR) measurements. Based on the analysis of NMR data, using the self-consistent-renormalization (SCR) theory, the spin fluctuations in the paramagnetic state are revealed to be isotropic ferromagnetic and three dimensional (3D) in nature. Moreover, the system is found to follow the generalized Rhodes-Wohlfarth relation which is expected in 3D itinerant ferromagnetic systems. As compared to other similar itinerant ferromagnets, the Cr $3d$ electrons and their spin fluctuations are characterized to have a relatively high degree of localization in real space.

Figure 1

Generic temperature-pressure-magnetic field ($T\text{−}p\text{−}H$) phase diagrams for clean itinerant ferromagnets. (a) Schematic $T\text{−}p\text{−}H$ phase diagram with a tricritical wing (TCW) structure. The second-order phase transition (solid line) becomes first order (dashed line) at a tricritical point (TCP). Under a magnetic field, the TCW structure shown in red emerges from the TCP. (b) Schematic $T\text{−}p\text{−}H$ phase diagram with an antiferromagnetic (AFM) phase in blue. The AFM phase emerges from the Lifshitz point (LP) that is suppressed under $H$.

Figure 2

(a) Typical field-swept ${}^{139}\mathrm{La}$-NMR spectra of ${\mathrm{LaCrGe}}_3$ in the PM state at $f$ = 42.5 MHz and $T$ = 230 K for $H\left|\right|c$ and $H\left|\right|ab$. (b) Temperature dependence of ${}^{139}\mathrm{La}$-NMR spectrum for $H\left|\right|c$. (c) Field-swept ${}^{139}\mathrm{La}$-NMR spectra in the FM state ($T$ = 1.65 K) for $H\left|\right|c$ and $H\left|\right|ab$. Blue and green curves represent spectra for $H\left|\right|c$ and $H\left|\right|ab$, respectively, and the red curves are the calculated spectra with ${\nu }_{\mathrm{Q}}$ = 0.66 MHz for the PM state and ${\nu }_{\mathrm{Q}}\sim$ 0.49 MHz for the FM state. The vertical dashed black lines in (a) and (b) represent the zero-shift position ($K$ = 0).

Figure 3

(a) ${}^{139}\mathrm{La}$ NMR spectra at various frequencies for $H\left|\right|c$ at $T$ = 1.65 K. Inset: Resonance magnetic field ($H_{\mathrm{res}}$) dependence of $B_{\mathrm{int}}$ for $H\left|\right|ab$ (green circles) and $H\left|\right|c$ (blue squares). The arrows show the positions of the central transition line of the spectra measured at different frequencies.

Figure 4

Temperature dependence of ${}^{139}\mathrm{La}$ Knight shift for both $H\left|\right|ab$ (green) and $H\left|\right|c$ (blue) directions measured at $H\sim$ 7 T. Inset: $K_{ab}$ vs ${\chi }_{ab}$ and $K_c$ vs ${\chi }_c$ plots. The solid lines are linear fits as described in the text.

Figure 5

Temperature dependence of ${}^{139}\mathrm{La}1/T_{1}T$ for $H\left|\right|ab$ (green circles) and $H\left|\right|c$ (blue squares). The inset shows the semilog plots of 1/($T_{1}T{K}_{\mathrm{s}}$) and 1/($T_{1}T{K}_{\mathrm{s}}^{3/2}$) for two different magnetic fluctuation directions (in-plane and out-of-plane directions).

Figure 6

Generalized Rhodes-Wohlfarth plot for the in-plane (blue) and out-of-plane (green) directions for ${\mathrm{LaCrGe}}_3$ along with other itinerant ferromagnets that avoid FM-PM QCP through tricritical wings under pressure. The values of parameters are estimated from Ref. [38] for ${\mathrm{ZrZn}}_2$ and MnSi and Ref. [40] for ${\mathrm{UGe}}_2$, URhGe, and URhAl. The red line represents the generalized Rhodes-Wohlfarth relation in the 3D system: $p_{\mathrm{eff}}/p_{\mathrm{s}}=1.4{(T_{\mathrm{C}}/T_0)}^{-2/3}$ [38].