The Brazil mine lays bare that, when it comes to the minerals vital for tomorrow’s economy and battlefields, the West is way behind and has few good options to catch up.

China dominates the mining and processing of rare earths, a collection of 17 elements that are essential to the auto, semiconductor, aerospace and defense industries. While abundant in the Earth’s crust, they are difficult to extract and separate, and the United States and other Western nations have largely left the work to China.

For some critical “heavy” rare earths — named because they have higher atomic numbers on the periodic table — China is essentially the only country that can separate and process them.

Rare earths have become so coveted because they help make the powerful magnets needed for new cars, missiles and drones. While “light” rare earths make up far more of those magnets, heavy rare earths are also needed to keep the magnets from weakening or being destroyed at high temperatures.

Heavy rare earths have overwhelmingly come from mines in China and Myanmar, which has sold its output to its powerful neighbor, because those countries have natural clay deposits rich in the elements.

But recently governments and industry have become excited that another country — Brazil — also has an abundance of such clay deposits.

“I’ve looked at 600 to 700 projects around the world, and in my view, Brazil has by far the best” access to heavy rare earths, said Constantine Karayannopoulos, a rare earths pioneer who co-founded one of the industry’s largest companies, Neo Performance Materials, based in Canada. “Brazil could be the game changer.”

In 2010, China halted exports of rare earths to Japan over a territorial dispute, raising alarms that the world depended on China for such critical minerals. That same year, Denham Capital, a Boston private equity firm, invested in a nascent project called Serra Verde to mine those minerals in Brazil.

Eight years later, the project was still trying to get off the ground and Serra Verde was searching for buyers to commit. There was essentially just one potential customer. Virtually no one outside of China could extract the heavy rare earths from the elemental sludge that Serra Verde aimed to sell.

“You can dig it up,” Mr. Karayannopoulos said. “But nowhere in the West is there existing capacity to take that feed and produce separated dysprosium and terbium.”

After 14 years — and an additional $150 million from American and British investors — the Serra Verde mine opened last year in Minaçu, Brazil, a town of 30,000 in central Brazil built around a decades-old asbestos mine. Everything the mine extracted was already contracted to go to China.

Mr. Moraitis, C.E.O. of Serra Verde, which is legally based in Switzerland, would not provide details of the contract but said the vast majority of his company’s product was committed to China until at least 2027. It hopes to then have enough production to begin taking new buyers.

Other producers of rare earths are in a similar situation.

MP Materials, a Las Vegas-based company partly funded by the Pentagon, mines and separates mostly light rare earths in Mountain Pass, Calif. Yet in a securities filing last year, it said it sold 80 percent of its product to China.

An MP Materials spokesman said that the company has been reducing its sales to China as it can separate more itself. It sells the separated rare earths to buyers in Japan and South Korea, as well as to the U.S. National Defense Stockpile. MP Materials cannot yet separate heavy rare earths but it is building another Pentagon-funded plant in California that can.

That joins other efforts across the West to separate heavy rare earths, including in France and Estonia. Those plants will likely take a few years to build, Mr. Moraitis said, but when they are ready, finding heavy rare earths is still likely to be difficult.